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Inkjet printing

Inkjet printing is a type of computer printing that recreates a digital image by propelling droplets of ink onto paper and plastic substrates. Inkjet printers were the most commonly used type of printer in 2008, and range from small inexpensive consumer models to expensive professional machines. By 2019, laser printers outsold inkjet printers by nearly a 2:1 ratio, 9.6% vs 5.1% of all computer peripherals.

The concept of inkjet printing originated in the 20th century, and the technology was first extensively developed in the early 1950s. While working at Canon in Japan, Ichiro Endo suggested the idea for a "bubble jet" printer, while around the same time Jon Vaught at Hewlett-Packard (HP) was developing a similar idea. In the late 1970s, inkjet printers that could reproduce digital images generated by computers were developed, mainly by Epson, HP and Canon. In the worldwide consumer market, four manufacturers account for the majority of inkjet printer sales: Canon, HP, Epson and Brother.

In 1982, Robert Howard came up with the idea to produce a small color printing system that used piezos to spit drops of ink. He formed the company, R.H. (Robert Howard) Research (named Howtek, Inc. in Feb 1984), and developed the revolutionary technology that led to the Pixelmaster color printer with solid ink using Thermojet technology. This technology consists of a tubular single nozzle acoustical wave drop generator invented originally by Steven Zoltan in 1972 with a glass nozzle and improved by the Howtek inkjet engineer in 1984 with a Tefzel molded nozzle to remove unwanted fluid frequencies.

The emerging ink jet material deposition market also uses inkjet technologies, typically printheads using piezoelectric crystals, to deposit materials directly on substrates.

The technology has been extended and the 'ink' can now also comprise solder paste in PCB assembly, or living cells, for creating biosensors and for tissue engineering.

Images produced on inkjet printers are sometimes sold under trade names such as Digigraph, Iris prints, giclée, and Cromalin. Inkjet-printed fine art reproductions are commonly sold under such trade names to imply a higher-quality product and avoid association with everyday printing.

Methods
Fluid surface tension naturally pulls a stream into droplets. Optimal drop sizes of 0.004 in require an inkjet nozzle size of about 0.003 in. Fluids with surface tension may be water based, wax or oil based and even melted metal alloys. Most drops can be electrically charged. There are two main technologies in use in contemporary inkjet printers: continuous (CIJ) and drop-on-demand (DOD). Continuous inkjet means the flow is pressurized and in a continuous stream. Drop-on-demand means the fluid is expelled from the jet nozzle one drop at a time. This can be done with a mechanical means with a push or some electrical method. A large electrical charge can pull drops out of a nozzle, sound waves can push fluid from a nozzle or a chamber volume expansion can expel a drop. Continuous streaming was investigated first many years ago. Drop-on-demand was only discovered in the 1920s.

Continuous inkjet

The continuous inkjet (CIJ) method is used commercially for marking and coding of products and packages. In 1867, Lord Kelvin patented the syphon recorder, which recorded telegraph signals as a continuous trace on paper using an ink jet nozzle deflected by a magnetic coil. The first commercial devices (medical strip chart recorders) were introduced in 1951 by Siemens. using the patent US2566443 invented by Rune Elmqvist dated September 4, 1951.

In CIJ technology, a high-pressure pump directs liquid ink from a reservoir through a gunbody and a microscopic nozzle (usually .003 inch diameter), creating a continuous stream of ink droplets via the Plateau-Rayleigh instability. A piezoelectric crystal may be used to create an acoustic wave as it vibrates within the gunbody and causes the stream of liquid to break into droplets at regular intervals: 64,000 to 165,000 irregular-sized ink droplets per second may be achieved. The ink droplets are subjected to an electrostatic field created by a charging electrode or by a magnetic flux field as they form; the field varies according to the degree of drop deflection desired. This results in a controlled deflection by electrostatic charge on each droplet. Charged droplets may be separated by one or more uncharged "guard droplets" to minimize electrostatic repulsion between neighboring droplets.

The droplets pass through another electrostatic or magnetic field and are directed (deflected) by electrostatic deflection plates or flux field to print on the receptor material (substrate), or allowed to continue on deflected to a collection gutter for re-use. The more highly charged droplets are deflected to a greater degree. Only a small fraction of the droplets is used to print, the majority being recycled.

CIJ is one of the oldest (1951) ink jet technologies in use and is fairly mature. Drop-on-demand was not invented until later. The major advantages of CIJ are the very high velocity (≈20 m/s) of the ink droplets, which allows for a relatively long distance between print head and substrate, and the very high drop ejection frequency, allowing for very high speed printing. Another advantage is freedom from nozzle clogging as the jet is always in use, therefore allowing volatile solvents such as ketones and alcohols to be employed, giving the ink the ability to "bite" into the substrate and dry quickly. The ink system requires active solvent regulation to counter solvent evaporation during the time of flight (time between nozzle ejection and gutter recycling), and from the venting process whereby air that is drawn into the gutter along with the unused drops is vented from the reservoir. Viscosity is monitored and a solvent (or solvent blend) is added to counteract solvent loss.

In the later 1950s, heated wax inks became popular with CIJ technologies. In 1971, Johannes F. Gottwald patent US3596285A, Liquid Metal Recorder used molten metal ink with a magnetic flux field to fabricate formed symbols for signage. This may have been the first 3D metal object printed using magnetic core memory as data to produce each symbol.

Drop-on-demand

There are many ways to produce a drop-on-demand (DOD) inkjet. Common methods include thermal DOD and piezoelectric DOD to speed up the frequency of drops. DOD may use a single nozzle or thousands of nozzles. One DOD process uses software that directs the heads to apply between zero and eight droplets of ink per dot, only where needed. Inkjet fluid materials have expanded to include pastes, epoxies, hot-melt inks, biological fluids, etc. DOD is very popular and has an interesting history. Mechanical DOD came first, followed by electrical methods including piezoelectric devices and then thermal or heat expansion methods.

 * Thermal DOD printing: Most consumer inkjet printers, including those from Canon (FINE Cartridge system, see photo), Hewlett-Packard, and Lexmark, use the thermal inkjet process. The idea of using thermal excitation to move tiny drops of ink was developed independently by two groups at roughly the same time: John Vaught and a team at Hewlett-Packard's Corvallis Division, and Canon engineer Ichiro Endo. Initially, in 1977, Endo's team was trying to use the piezoelectric effect to move ink out of the nozzle but noticed that ink shot out of a syringe when it was accidentally heated with a soldering iron. Vaught's work started in late 1978 with a project to develop fast, low-cost printing. The team at HP found that thin-film resistors could produce enough heat to fire an ink droplet. Two years later the HP and Canon teams found out about each other's work.
 * Thermal inkjet: In the thermal inkjet process, the print cartridges consist of a series of tiny chambers, each containing a heater, all of which are constructed by photolithography. To eject a droplet from each chamber, a pulse of current is passed through the heating element causing a rapid vaporization of the ink in the chamber and forming a bubble, which causes a large pressure increase, propelling a droplet of ink onto the paper (hence Canon's trade name of Bubble Jet). Early thermal heads ran at just 600–700 dpi but improvements by HP increased the firing range of 8–12 kHz per chamber and as high as 18 kHz with 5-picoliter drop volume by the year 2000. Thermal printheads do not have the power of piezo DOD or continuous inkjet, so the gap between the face of the head  and paper is critical. The ink's surface tension, as well as the condensation and resultant contraction of the vapor bubble, pulls a further charge of ink into the chamber through a narrow channel attached to an ink reservoir. The inks involved are usually water-based and use either pigments or dyes as the colorant. The inks must have a volatile component to form the vapor bubble; otherwise droplet ejection cannot occur. As no special materials are required, the print head is generally cheaper to produce than in other inkjet technologies.
 * Piezoelectric DOD printing: Piezos are electrically polarized ceramic devices, just as a magnet is polarized. Most commercial and industrial inkjet printers and some consumer printers (those produced by Epson (see photo) and Brother Industries) use a piezoelectric material in an ink-filled chamber behind each nozzle instead of a heating element. When a voltage is applied, the piezoelectric material changes shape, generating a pressure pulse in the fluid, which pushes a droplet of ink from the nozzle. Single nozzle tubular inkjets actually are fluid resonator chambers and the drops are expelled by sound waves in the ink chamber. The 1972 patent called them squeeze tube inkjets but later it was discovered to be acoustical inkjets. Piezoelectric (also called piezo) inkjet allows a wider variety of inks than thermal inkjet as there is no requirement for a volatile component, and no issue with kogation (buildup of ink residue), but the print heads are more expensive to manufacture due to the use of piezoelectric material (usually PZT, lead zirconium titanate). However, the ink cartridges can be separate from the head itself and individually be replaced as needed. Piezo, then has the potential for lower running costs. Piezo heads are said to achieve firing rates that are faster than thermal heads at comparable drop volumes.
 * Piezo inkjet: Piezo inkjet technology is often used on production lines to mark products. For instance, the "use-before" date is often applied to products with this technique; in this application the head is stationary and the product moves past. This application requires a relatively large gap between the print head and the substrate, but also yields a high speed, a long service life, and low operating cost.
 * Thermoplastic/3D printing: In the 1970s, the first DOD inks were water-based and higher-temperature use was not recommended. In the late 1970s, wax- and oil-based inks were used in the Silonics in 1975, Siemens PT-80i in 1977 and Epson and Exxon in 1980s DOD inkjets. In 1984, a small company, Howtek, Inc., found that solid ink materials (thermoplastics) could be jetted at 125 C by maintaining the piezo poling charge while printing. In 1986, Howtek launched the Pixelmaster solid ink-jetting printer, which opened the door to printing three-dimensional plastic inks and led to a 1992 3D patent, US5136515A. This patent was licensed by the first three major 3D printer companies (Sanders Prototype, Inc, Stratasys and 3D Systems).
 * Braillemaster: In the late 1980s, Howtek introduced the Braillemaster, a printer that used four layers of solid ink per character to create documents in Braille that could be read by people who were blind.
 * Howtek: Solidscape, Inc., currently uses the Howtek-style thermoplastic materials and Howtek-style single nozzle inkjets (see illustration) very successfully. Ballistic Particle Manufacturing also used the Howtek style materials and inkjets. These inkjets can produce up to 16,000 drops per second and shoot drops at 9 feet per second. Originally designed to only print on standard letter-sized paper sheets they now can print 3D models requiring hundreds of layers.
 * Thermojet: The thermoplastic inks in piezoelectric inkjets (called Thermojet technology by Howtek) are sometimes confused with the thermal (heat expansion) bubble-jet technology but they are completely different. Bubble jet inks are not solid at room temp and are not heated. Thermojet inks require 125 °C to reduce fluid viscosity in jetting range. Howtek was the first to introduce an inkjet color printer using thermoplastic inks in 1984 at Comdex, Las Vegas.

Ink formulations
The earliest reference to a continuous inkjet ink (CIJ) in the 1971 patent US3596285A states " The preferred ink is characterized by viscosity and surface tension characteristics such that the liquid will be maintained over span under the force with which it is moving in bridge or stream. Implicit in such requirement is that the pressure applied to the ink in formation of said stream is sufficient to form a jet and to impart enough energy to carry the jet as a continuous liquid mass notwithstanding the defective forces which are or may be applied. Furthermore, the color of the ink and the color of the carrier should be such that good optical contrast is formed there between the following printing. The preferred ink is a "hot-melt ink". That is to say it will assume a solid phase at the temperature of the carrier and liquid phase at some higher temperature. The range of commercially available ink compositions which could meet the requirement of the invention are not known at the present time. However, satisfactory printing according to the invention has been achieved with a conductive metal alloy as ink. It is extremely hard at room temperature and adheres well to the surface of the carrier.

The basic problem with inkjet inks is the conflicting requirements for a coloring agent that will stay on the surface versus rapid bleed through the carrier fluid.

Desktop inkjet printers, as used in offices and homes, tend to use aqueous ink based on a mixture of water, glycol and dyes or pigments. These inks are inexpensive to manufacture but difficult to control on the surface of media, often requiring specially coated media. HP inks contain sulfonated polyazo black dye (commonly used for dyeing leather), nitrates and other compounds. Aqueous inks are mainly used in printers with thermal inkjet heads, as these heads require water to perform the ink-expelling function.

While aqueous inks often provide the broadest color gamut and most vivid color, most are not waterproof without specialized coating or lamination after printing. Most dye-based inks, while usually the least expensive, are subject to rapid fading when exposed to light or ozone. Pigment-based aqueous inks are typically more costly but provide much better long-term durability and ultraviolet resistance. Inks marketed as "archival quality" are usually pigment-based.

Some professional wide format printers use aqueous inks, but the majority in professional use today employ a much wider range of inks, most of which require piezo inkjet heads and extensive maintenance.

 * Solvent inks: The main ingredient of these inks are volatile organic compounds (VOCs), organic chemical compounds that have high vapor pressures. Color is achieved with pigments rather than dyes for excellent fade-resistance. The chief advantage of solvent inks is that they are comparatively inexpensive and enable printing on flexible, uncoated vinyl substrates, which are used to produce vehicle graphics, billboards, banners and adhesive decals. Disadvantages include the vapor produced by the solvent and the need to dispose of used solvent. Unlike most aqueous inks, prints made using solvent-based inks are generally waterproof and ultraviolet-resistant (for outdoor use) without special over-coatings. The high print speed of many solvent printers demands special drying equipment, usually a combination of heaters and blowers. The substrate is usually heated immediately before and after the print heads apply ink. Solvent inks are divided into two sub-categories: hard solvent ink offers the greatest durability without specialized over-coatings but requires specialized ventilation of the printing area to avoid exposure to hazardous fumes, while mild or "eco" solvent inks, while still not as safe as aqueous inks, are intended for use in enclosed spaces without specialized ventilation of the printing area. Mild solvent inks have rapidly gained popularity in recent years as their color quality and durability have increased while ink cost has dropped significantly.
 * UV-curable inks: These inks consist mainly of acrylic monomers with an initiator package. After printing, the ink is cured by exposure to strong UV light. Ink is exposed to UV radiation where a chemical reaction takes place where the photo-initiators cause the ink components to cross-link into a solid. Typically a shuttered mercury-vapor lamp or UV LED is used for the curing process. Curing processes with high power for short periods of times (microseconds) allow curing inks on thermally sensitive substrates. UV inks do not evaporate, but rather cure or set as a result from this chemical reaction. No material is evaporated or removed, which means about 100% of the delivered volume is used to provide coloration. This reaction happens very quickly, which leads to instant drying that results in a completely cured graphic in a matter of seconds. This also allows for a very fast print process. As a result of this instant chemical reaction no solvents penetrate the substrate once it comes off the printer, which allows for high quality prints. The advantage of UV-curable inks is that they "dry" as soon as they are cured, they can be applied to a wide range of uncoated substrates, and they produce a very robust image. Disadvantages are that they are expensive, require expensive curing modules in the printer, and the cured ink has a significant volume and so gives a slight relief on the surface. Though improvements are being made in the technology, UV-curable inks, because of their volume, are somewhat susceptible to cracking if applied to a flexible substrate. As such, they are often used in large "flatbed" printers, which print directly to rigid substrates such as plastic, wood or aluminium where flexibility is not a concern.
 * Dye sublimation inks: These inks contain special sublimation dyes and are used to print directly or indirectly on to fabrics which consist of a high percentage of polyester fibers. A heating step causes the dyes to sublimate into the fibers and create an image with strong color and good durability.
 * Solid ink:These inks consist mainly of waxy compounds which are heated past their melting point to enable printing, and which harden upon hitting the cooled substrate. Hot-melt inks are typically used for masking processes and are found in graphic printing. The earliest hot-melt ink was patented in 1971 by Johannes F Gottwald, US3596285A, Liquid Metal Recorder was intended for printing. The patent states "As used herein the term "printing" is not intended in a limited sense but includes writing or other symbol or pattern formulation with an ink. The term ink as used is intended to include not only dye or pigment-containing materials, but any flowable substance or composition suited for application to surface for forming symbols, characters or patterns of intelligence by marking. The materials employed in such process can be salvaged for reuse. Another object of the invention is to increase the size of characters.....in terms of material requirements for such large and continuous displays".

Printing heads

There are two main design philosophies in inkjet head design: fixed-head and disposable head. Each has its own strengths and weaknesses.

Fixed head
The fixed-head philosophy provides an inbuilt print head (often referred to as a gaiter-head) that is designed to last for the life of the printer. The idea is that because the head need not be replaced every time the ink runs out, consumable costs can be made lower and the head itself can be more precise than a cheap disposable one, typically requiring no calibration. On the other hand, if a fixed head is damaged, obtaining a replacement head can become expensive, if removing and replacing the head is even possible. If the printer's head cannot be removed, the printer itself will then need to be replaced.

Fixed head designs are available in consumer products, but are more likely to be found on industrial high-end printers and large format printers. In the consumer space, fixed-head printers are manufactured primarily by Epson and Canon; however, many more recent Hewlett-Packard models use a fixed head, such as the Officejet Pro 8620 and HP's Pagewide series.

Disposable head

The disposable head philosophy uses a print head which is supplied as a part of a replaceable ink cartridge. Every time a cartridge is exhausted, the entire cartridge and print head are replaced with a new one. This adds to the cost of consumables and makes it more difficult to manufacture a high-precision head at a reasonable cost, but also means that a damaged or clogged print head is only a minor problem: the user can simply buy a new cartridge. Hewlett-Packard has traditionally favored the disposable print head, as did Canon in its early models. This type of construction can also be seen as an effort by printer manufacturers to stem third party ink cartridge assembly replacements, as these would-be suppliers do not have the ability to manufacture specialized print heads.

An intermediate method does exist: a disposable ink tank connected to a disposable head, which is replaced infrequently (perhaps every tenth ink tank or so). Most high-volume Hewlett-Packard inkjet printers use this setup, with the disposable print heads used on lower volume models. A similar approach is used by Kodak, where the printhead intended for permanent use is nevertheless inexpensive and can be replaced by the user. Canon now uses (in most models) replaceable print heads which are designed to last the life of the printer, but can be replaced by the user should they become clogged.

Additive manufacturing 3D printheads have very long operating "print times" and failures will occur from internal clogs, orifice damage from bumping obstacles on the print table, calibration failures from overstressed piezoelectric bond life failures and other unexpected causes. Replacement printheads are on spare parts lists for most long use-life 3D printers.

Cleaning mechanisms

The primary cause of inkjet printing problems is ink drying on the printhead's nozzles, causing the pigments and dyes to dry out and form a solid block of hardened mass that plugs the microscopic ink passageways. Most printers attempt to prevent this drying from occurring by covering the printhead nozzles with a rubber cap when the printer is not in use. Abrupt power losses, or unplugging the printer before it has capped the printhead, can cause the printhead to be left in an uncapped state. Even when the head is capped, this seal is not perfect, and over a period of several weeks the moisture (or other solvent) can still seep out, causing the ink to dry and harden. Once ink begins to collect and harden, the drop volume can be affected, drop trajectory can change, or the nozzle can completely fail to jet ink.

To combat this drying, nearly all inkjet printers include a mechanism to reapply moisture to the printhead. Typically there is no separate supply of pure ink-free solvent available to do this job, and so instead the ink itself is used to remoisten the printhead. The printer attempts to fire all nozzles at once, and as the ink sprays out, some of it wicks across the printhead to the dry channels and partially softens the hardened ink. After spraying, a rubber wiper blade is swept across the printhead to spread the moisture evenly across the printhead, and all jets are again fired to dislodge any ink clumps blocking the channels.

Some printers use a supplemental air-suction pump, using the rubber capping station to suck ink through a severely clogged cartridge. The suction pump mechanism is frequently driven by the page feed stepper motor: it is connected to the end of the shaft. The pump only engages when the shaft turns backwards, hence the rollers reversing while head cleaning. Due to the built-in head design, the suction pump is also needed to prime the ink channels inside a new printer, and to reprime the channels between ink tank changes.

Professional solvent- and UV-curable ink wide-format inkjet printers generally include a "manual clean" mode that allows the operator to manually clean the print heads and capping mechanism and to replace the wiper blades and other parts used in the automated cleaning processes. The volume of ink used in these printers often leads to "overspray" and therefore buildup of dried ink in many places that automated processes are not capable of cleaning. The ink consumed in the cleaning process needs to be collected to prevent ink from leaking in the printer. The collection area is called the spittoon, and in Hewlett-Packard printers this is an open plastic tray underneath the cleaning/wiping station. In Epson printers, there is typically a large absorption pad in a pan underneath the paper feed platen. For printers that are several years old, it is common for the dried ink in the spittoon to form a pile that can stack up and touch the printheads, jamming the printer. Some larger professional printers using solvent inks may employ a replaceable plastic receptacle to contain waste ink and solvent, which must be emptied or replaced when full.

There is a second type of ink drying that most printers are unable to prevent. For ink to spray from the cartridge, air must enter to displace the removed ink. The air enters via an extremely long, thin labyrinth tube, up to 10 cm long, wrapping back and forth across the ink tank. The channel is long and narrow to reduce moisture evaporation through the vent tube, but some evaporation still occurs and eventually the ink cartridge dries up from the inside out. To combat this problem, which is especially acute with professional fast-drying solvent inks, many wide-format printer cartridge designs contain the ink in an airtight, collapsible bag that requires no vent. The bag merely shrinks until the cartridge is empty.

The frequent cleaning conducted by some printers can consume quite a bit of ink and has a great impact on cost-per-page determinations.

Clogged nozzles can be detected by printing a standard test pattern on the page. Some software workaround methods are known for rerouting printing information from a clogged nozzle to a working nozzle.

Ink delivery developments
Ink cartridges have been the traditional method for delivering ink to the printhead. Continuous ink system (CISS) inkjet printers connect the printhead either to high-capacity ink tanks or packs, or replenish the built-in cartridges via external tanks connected via tubes, typically a retrofit configuration. Supertank printers–a subset of CISS printers–have high-capacity integrated ink tanks or ink packs, and are manually refilled via ink bottles. When supertank ink systems are paired with disposable printhead technology, replaceable cartridges are used to replace the exhausted print heads.

Advantages
Compared to earlier consumer-oriented color printers, inkjet printers have a number of advantages. They are quieter in operation than impact dot matrix or daisywheel printers. They can print finer, smoother details through higher resolution. Consumer inkjet printers with photographic print quality are widely available.

In comparison to technologies like thermal wax, dye sublimation, and laser printing, inkjets have the advantage of practically no warm up time, and often lower cost per page. However, low-cost laser printers can have lower per-page costs, at least for black-and-white printing, and possibly for color.

For some inkjet printers, monochrome ink sets are available either from the printer manufacturer or from third-party suppliers. These allow the inkjet printer to compete with the silver-based photographic papers traditionally used in black-and-white photography, and provide the same range of tones: neutral, "warm" or "cold". When switching between full-color and monochrome ink sets, it is necessary to flush out the old ink from the print head with a cleaning cartridge. Special software or at least a modified device driver are usually required, to deal with the different color mapping.

Some types of industrial inkjet printers are now capable of printing at very high speeds, in wide formats, or for a variety of industrial applications ranging from signage, textiles, optical media, ceramics and 3-D printing into biomedical applications and conductive circuitry. Leading companies and innovators in hardware include HP, Epson, Canon, Konica Minolta, FujiFilm, EFi, Durst, Brother, Roland, Mimaki, Mutoh and many others worldwide.

Disadvantages
Many "intelligent" ink cartridges contain a microchip that communicates the estimated ink level to the printer; this may cause the printer to display an error message, or incorrectly inform the user that the ink cartridge is empty. In some cases, these messages can be ignored, but some inkjet printers will refuse to print with a cartridge that declares itself empty, to prevent consumers from refilling cartridges. For example, Epson embeds a chip which prevents printing when the chip claims the cartridge is empty, although a researcher who over-rode the system found that in one case he could print up to 38% more good quality pages, even though the chip stated that the cartridge was empty. Third-party ink suppliers sell ink cartridges at significant discounts (at least 10–30% off OEM cartridge prices, sometimes up to 95%, typically averaging around 50%), and also bulk ink and cartridge self-refill kits at even lower prices. Many vendors' "intelligent" ink cartridges have been reverse-engineered. It is now possible to buy inexpensive devices to reliably reset such cartridges to report themselves as full, so that they may be refilled many times.

The very narrow inkjet nozzles are prone to clogging. The ink consumed in cleaning them—either during cleaning invoked by the user, or in many cases, performed automatically by the printer on a routine schedule—can account for a significant proportion of the ink used in the machine. Inkjet printing head nozzles can be cleaned using specialized solvents, or by soaking in warm distilled water for short periods of time (for water-soluble inks.)

The high cost of OEM ink cartridges and the intentional obstacles to refilling them have been addressed by the growth of third-party ink suppliers. Many printer manufacturers discourage customers from using third-party inks, stating that they can damage the print heads due to not being the same formulation as the OEM inks, cause leaks, and produce inferior-quality output (e.g., of incorrect color gamut). Consumer Reports has noted that some third-party cartridges may contain less ink than OEM cartridges, and thus yield no cost savings, while Wilhelm Imaging Research claims that with third-party inks the lifetime of prints may be considerably reduced. However, an April 2007 review showed that, in a double-blind test, reviewers generally preferred the output produced using third-party ink over OEM ink. In general, OEM inks have undergone significant system reliability testing with the cartridge and print-head materials, whereas R&D efforts on third-party ink material compatibility are likely to be significantly less. Some inkjet manufacturers have tried to prevent cartridges being refilled using various schemes including fitting chips to the cartridges that log how much the cartridge has printed and prevent the operation of a refilled cartridge.

The warranty on a printer may not apply if the printer is damaged by the use of non-approved supplies. In the US the Magnuson–Moss Warranty Act is a federal law which states that warrantors cannot require that only brand name parts and supplies be used with their products, as some printer manufacturers imply. However, this would not apply if non-approved items cause damage.

Durability
Inkjet documents can have poor to excellent archival durability, depending on the quality of the inks and paper used. If low-quality paper is used, it can yellow and degrade due to residual acid in the untreated pulp; in the worst case, old prints can literally crumble into small particles when handled. High-quality inkjet prints on acid-free paper can last as long as typewritten or handwritten documents on the same paper.

Because the ink used in many low-cost consumer inkjets is water-soluble, care must be taken with inkjet-printed documents to avoid even the smallest drop of moisture, which can cause severe "blurring" or "running". In extreme cases, even sweaty fingertips during hot humid weather could cause low-quality inks to smear. Similarly, water-based highlighter markers can blur inkjet-printed documents and discolor the highlighter's tip. The lifetime of inkjet prints produced using aqueous inks is generally shorter (although UV-resistant inks are available) than those produced with solvent-based inkjets; however, so-called "archival inks" have been produced for use in aqueous-based machines which offer extended life.

In addition to smearing, gradual fading of many inks can be a problem over time. Print lifetime is highly dependent on the quality and formulation of the ink. The earliest inkjet printers, intended for home and small office applications, used dye-based inks. Even the best dye-based inks are not as durable as pigment-based inks, which are now available for many inkjet printers. Many inkjet printers now utilize pigment based inks which are highly water resistant: at least the black ink is often pigment-based. Resin or silicone protected photopaper is widely available at low cost, introducing complete water and mechanical rub resistance for dye and pigment inks. The photopaper itself must be designed for pigment or for dye inks, as pigment particles are too large to be able to penetrate through dye-only photopaper protection layer.

The highest-quality inkjet prints are often called "giclée" prints, to distinguish them from less-durable and lower-cost prints. However, the use of the term is no guarantee of quality, and the inks and paper used must be carefully investigated before an archivist can rely on their long-term durability.

To increase the durability of inkjet printer prints, more attention is needed for the inkjet ink cartridge. One way to treat ink cartridges on an inkjet printer is to maintain the temperature of the printer itself. Excessive variation in space temperature is very bad for printer ink cartridges. The user should prevent the printer becoming too hot or too chilly as the cartridges can dry up. For lasting printer efficiency, the user should ensure the area has a regular and steady temperature level.

Operating cost tradeoffs
Inkjets use solvent-based inks which have much shorter expiration dates compared to laser toner, which has an indefinite shelf life. Inkjet printers tend to clog if not used regularly, whereas laser printers are much more tolerant of intermittent use. Inkjet printers require periodical head cleaning, which consumes a considerable amount of ink, and will drive printing costs higher especially if the printer is unused for long periods.

If an inkjet head becomes clogged, third-party ink solvents/head cleaners and replacement heads are available in some cases. The cost of such items may be less expensive compared to a transfer unit for a laser printer, but the laser printer unit has a much longer lifetime between required maintenance. Many inkjet printer models now have permanently installed heads, which cannot be economically replaced if they become irreversibly clogged, resulting in scrapping of the entire printer. On the other hand, inkjet printer designs which use a disposable printhead usually cost significantly more per page than printers using permanent heads. By contrast, laser printers do not have printheads to clog or replace frequently, and usually can produce many more pages between maintenance intervals.

Inkjet printers have traditionally produced better quality output than color laser printers when printing photographic material. Both technologies have improved dramatically over time, although the highest-quality giclée prints favored by artists use what is essentially a high-quality specialized type of inkjet printer.

Business model

A common business model for inkjet printers involves selling the actual printer at or below production cost, while dramatically marking up the price of the (proprietary) ink cartridges (a profit model called the "razor and blades model"). Most current inkjet printers attempt to enforce this product tying by anticompetitive measures such as microchips in the cartridges to hinder the use of third-party or refilled ink cartridges. The microchips monitor usage and report the ink remaining to the printer. Some manufacturers also impose "expiration dates". When the chip reports that the cartridge is empty (or out of date) the printer stops printing. Even if the cartridge is refilled, the microchip will indicate to the printer that the cartridge is depleted. For many models (especially from Canon), the 'empty' status can be overridden by entering a 'service code' (or sometimes simply by pressing the 'start' button again). For some printers, special circuit "flashers" are available that reset the quantity of remaining ink to the maximum.

Some manufacturers, most notably Epson and Hewlett-Packard, have been accused of indicating that a cartridge is depleted while a substantial amount of ink remains. A 2007 study found that most printers waste a significant quantity of ink when they declare a cartridge to be empty. Single-ink cartridges were found to have on average 20% of their ink remaining, though actual figures range from 9% to 64% of the cartridge's total ink capacity, depending on the brand and model of printer. This problem is further compounded with the use of one-piece multi-ink cartridges, which are declared empty as soon as one color runs low. Of great annoyance to many users are those printers that will refuse to print documents requiring only black ink, just because one or more of the color ink cartridges is depleted.

In recent years, many consumers have begun to challenge the business practices of printer manufacturers, such as charging up to US$8,000 per gallon (US$2,100 per liter) for printer ink. Alternatives for consumers are cheaper copies of cartridges, produced by third parties, and the refilling of cartridges, using refill kits. Due to the large differences in price caused by OEM markups, there are many companies selling third-party ink cartridges. Most printer manufacturers discourage refilling disposable cartridges or using aftermarket copy cartridges, and say that use of incorrect inks may cause poor image quality due to differences in viscosity, which can affect the amount of ink ejected in a drop, and color consistency, and can damage the printhead. Nonetheless, the use of alternative cartridges and inks has been gaining in popularity, threatening the business model of printer manufacturers. Printer companies such as HP, Lexmark, and Epson have used patents and the DMCA to launch lawsuits against third-party vendors. An anti-trust class-action lawsuit was launched in the US against HP and office supply chain Staples, alleging that HP paid Staples $100 million to keep inexpensive third-party ink cartridges off the shelves.

In Lexmark Int'l v. Static Control Components, the United States Court of Appeals for the Sixth Circuit ruled that circumvention of this technique does not violate the Digital Millennium Copyright Act. The European Commission also ruled this practice anticompetitive: it will disappear in newer models sold in the European Union. While the DMCA case dealt with copyright protection, companies also rely on patent protection to prevent copying and refilling of cartridges. For example, if a company devises all of the ways in which their microchips can be manipulated and cartridges can be refilled and patents these methods, they can prevent anyone else from refilling their cartridges. Patents protecting the structure of their cartridges prevent the sale of cheaper copies of the cartridges. For some printer models (notably those from Canon) the manufacturer's own microchip can be removed and fitted to a compatible cartridge thereby avoiding the need to replicate the microchip (and risk prosecution). Other manufacturers embed their microchips deep within the cartridge in an effort to prevent this approach.

In 2007, Eastman Kodak entered the inkjet market with its own line of All-In-One printers based on a marketing model that differed from the prevailing practice of selling the printer at a loss while making large profits on replacement ink cartridges. Kodak claimed that consumers could save up to 50 percent on printing by using its lower-cost cartridges filled with the company's proprietary pigmented colorants while avoiding the potential problems associated with off-brand inks. This strategy proved unsuccessful and Kodak exited the consumer inkjet printer business in 2012.

A more recent development is the supertank printer, which uses an integrated continuous ink system. Supertank printers are defined by their large, permanently-installed ink tanks which are filled from ink bottles. The printer itself is typically sold at a substantial premium, but ink bottles are inexpensive and contain enough ink to print thousands of pages. Supertank printers generally ship with full bottles of ink in the box, allowing up to two years of printing before the tanks needs to be refilled. Epson pioneered this technology by launching the EcoTank range, first in Indonesia in 2010, with a North American launch in 2015. The supertank concept proved commercially successful, and Canon and HP launched their own lines of supertank printers, under the names MegaTank (Canon) and Smart Tank (HP).

Region-coding of printers and ink cartridges
Many manufacturers give their printers and cartridges region codes, comparable to those of DVDs, so customers cannot import them from a cheaper region. The region code can be changed a few times by the customer or the customer-service department of the manufacturer, but then, the printer is region-locked like a RPC-2 DVD drive. One method to bypass printer-region-coding is to store empty cartridges from the old region and refill them with ink from the new region, but, as mentioned above, many modern ink cartridges have chips and sensors to prevent refilling, which makes the process more difficult. On the Internet, there are refill instructions for different printer models available. Another method is have ink cartridges from the old region shipped to the new region.

Some manufacturers of region-coded printers also offer region-free printers specially designed for travelers.

Professional models
In addition to the widely used small inkjet printers for home and office, there are professional inkjet printers, some for "page-width" format printing and many for wide format printing. Page-width format means that the print width ranges from about 8.5 - 37 in. "Wide format" means print width ranging from 24" up to 15' (about 60 cm to 5m). The most common application of page-width printers is in printing high-volume business communications that do not need high-quality layout and color. Particularly with the addition of variable data technologies, the page-width printers are important in billing, tagging, and individualized catalogs and newspapers. The application of most wide format printers is in printing advertising graphics; a lower-volume application is printing of design documents by architects or engineers. But nowadays, there are inkjet printers for digital textile printing up to 64" wide with good high definition image of 1440×720 dpi.

Another specialty application for inkjets is producing prepress color proofs for printing jobs created digitally. Such printers are designed to give accurate color rendition of how the final image will look (a "proof") when the job is finally produced on a large volume press such as a four-color offset lithography press. An example is an Iris printer, whose output is what the French term giclée was coined for.

The largest-volume supplier is Hewlett-Packard, which supplies over 90 percent of the market for printers for printing technical drawings. The major products in their Designjet series are the Designjet 500/800, the Designjet T Printer series (including the T1100 and T610), the Designjet 1050 and the Designjet 4000/4500. They also have the HP Designjet 5500, a six-color printer that is used especially for printing graphics as well as the new Designjet Z6100 which sits at the top of the HP Designjet range and features an eight color pigment ink system.

Epson, Kodak, and Canon also manufacture wide-format printers, sold in much smaller numbers than standard printers. Epson has a group of three Japanese companies around it that predominantly use Epson piezo printheads and inks: Mimaki, Roland, and Mutoh.

Scitex Digital Printing developed high-speed, variable-data, inkjet printers for production printing, but sold its profitable assets associated with the technology to Kodak in 2005 who now market the printers as Kodak Versamark VJ1000, VT3000, and VX5000 printing systems. These roll-fed printers can print at up to 305m per minute.

Professional high-volume inkjet printers are made by a range of companies. These printers can range in price from US$35,000 to $2 million. Carriage widths on these units can range from 54" to 192" (about 1.4 to 5 m), and ink technologies have tended toward solvent, eco-solvent, and UV-curing with a more recent focus toward water-based (aqueous) ink sets. Major applications where these printers are used are for outdoor settings for billboards, truck sides and truck curtains, building graphics and banners, while indoor displays include point-of-sales displays, backlit displays, exhibition graphics, and museum graphics.

The major suppliers for professional high-volume, wide- and grand-format printers include: EFI, LexJet, Grapo, Inca, Durst, Océ, NUR (now part of Hewlett-Packard), Lüscher, VUTEk, Scitex Vision (now part of Hewlett-Packard), Mutoh, Mimaki, Roland DG, Seiko I Infotech, IQDEMY, Leggett and Platt, Agfa, Raster Printers, DGI and MacDermid ColorSpan (now part of Hewlett-Packard), swissqprint, SPGPrints (formerly Stork Prints), MS Printing Systems and Digital Media Warehouse.

SOHO multifunction inkjet photo printers
SOHO multifunction inkjet printers for photo printing use up to 6 different inks:
 * Canon: cyan, yellow, magenta, black, pigment black, gray. 1 pl thermal.
 * Epson: cyan, yellow, magenta, light cyan, light magenta, black. 1.5 pl piezo variable. Also with A3 paper printing, or FAX and duplex ADF.

Professional inkjet photo printers
Inkjet printers for professional photo printing use up to twelve different inks:

 * Canon: photo magenta, photo cyan, yellow, magenta, cyan, red, photo black, matte black, grey, plus either blue, photo gray, and one chroma optimiser for black density and uniform glossiness, or light gray, dark gray and one chroma optimiser, or green, blue, and photo gray. 4 pl thermal.
 * Epson (10 colors from 12): vivid magenta, yellow, cyan, orange, green, vivid light magenta, light cyan, light black, matte black or photo black, plus an irreversible choice of either light light gray or violet (V not for photo). 3.5 pl piezo variable.
 * HP: magenta, yellow, red, green, blue, light magenta, light cyan, gray, light gray, matte black, photo black, and one gloss enhancer. 4 pl thermal.

They can print an image of 36 megapixels on A3 borderless photo paper with 444 ppi.

Compact photo printers
A compact photo printer is a stand-alone inkjet printer designed to produce 4×6 or 2×3 inch prints from digital cameras. It works without the use of a computer. It is also known as a portable photo printer or a snapshot printer. Compact photo printers came on the market shortly after the popularity of home photo printing took off in the early 2000s. They were designed as an alternative to developing photos or printing them on a standard inkjet photo printer.

The majority of compact photo printers can only print 4 x pictures. Given this limitation, they are not meant to replace standard inkjets. Many manufacturers advertise the cost per page of photos printed on their machines; this theoretically convinces people that they can print their own pictures just as cheaply as retail stores or through online printing services. Most compact photo printers share a similar design. They are small units, usually with large LCDs in order to allow people to browse and edit their photos, as can be done on a computer. The editing options are usually somewhat advanced, allowing the user to crop photos, remove red eye, adjust color settings as well as other functions. Compact photo printers typically feature a large number of connection options, including USB and most memory card formats.

Compact photo printers are currently manufactured by most of the leading printer manufacturers such as Epson, Canon, HP, Lexmark and Kodak. While they have increased in popularity in recent years, they still make up a relatively small share of the inkjet printer market. LG's Pocket Photo uses Zink thermal paper which has chemistries embedded on each inkless photo paper and the image will appear with the heat.

Other uses
U.S. Patent 6,319,530 describes a "Method of photocopying an image onto an edible web for decorating iced baked goods". In other words, this invention enables one to inkjet print a food-grade color photograph on a birthday cake's surface. Many bakeries now carry these types of decorations, which are printable using edible inks and dedicated inkjet printers. Edible ink printing can be done using normal home use inkjet printers like Canon Bubble Jet printers with edible ink cartridges installed, and using rice paper or frosting sheets.

Inkjet printers and similar technologies are used in the production of many microscopic items. See Microelectromechanical systems.

Inkjet printers are used to form conductive traces for circuits, and color filters in LCD and plasma displays.

Inkjet printers, especially models produced by Dimatix (now part of Fujifilm), Xennia Technology and Pixdro, are in fairly common use in many labs around the world for developing alternative deposition methods that reduce consumption of expensive, rare, or problematic materials. These printers have been used in the printing of polymer, macromolecular, quantum dot, metallic nanoparticles, and carbon nanotubes. The applications of such printing methods include organic thin-film transistors, organic light emitting diodes, organic solar cells, and sensors.

Inkjet technology is used in the emerging field of bioprinting. They are also used for the production of OLED displays.

title: Inkjet printing


text:
Talk:Mathematical economics

Tautology
Reading the source on Popper, his complaints were that a complete mathematical (or philosophical) system could not make novel predictive statements without making assumptions so broad and forceful that the result could come from the assumptions itself. While this sounds the same as a rhetorical tautology (in the sense that we often see this when people make a defining statement and proceed to argue the truth value of the proposition from the defining statement), Popper clearly meant is as a philosophical constraint on theories.

My feelings for the why the link is proper stem from the History section on logical tautologies and the clear connection alluded by the (seven decades of economic methodology) sourcing. I may be wrong.

Protonk (talk) 21:12, 19 June 2008 (UTC)

 * What you want is quite clearly a tautology in the informal sense of the word. Tautology (logic) gives a precise definition in the context of formal logic. Most tautologies, when translated into a formal language such as first-order logic, become only what the article calls "validities", but not tautologies. I don't like this technical (ab)use of the word "tautology" at all, but it seems to be general practice. The following are tautologies:
 * He committed the crime or he didn't commit the crime.
 * Someone in this room committed the crime or nobody in this room committed the crime.
 * The following is unfortunately not a tautology:
 * Everybody in this room either committed the crime or did not commit the crime.
 * I am quite sure that Popper didn't want to make this distinction. If you feel that you must link to a formal(!) logic article, then it would have to be the (non-existent) one for validity. But I am quite sure that what Popper means is tautology in an informal sense. This is discussed, in passing, in tautology (rhetoric).
 * The best solution would be to add a discussion of the informal meaning to tautology (logic), but I am not going to do this because I only have a PhD in mathematical logic, while this is philosophical formal logic. --Hans Adler (talk) 21:34, 19 June 2008 (UTC)

Sorry for the delay. I don't have a phd in mathematical logic or otherwise formal logic (I actually don't have a phd in anything), but I'll try and make an argument nonetheless. Quotations are from Boland, L. A. (2006) Seven Decades of Economic Methodology. pp. 219-223 In: I. C. Jarvie, K. Milford, D.W. Miller Eds Karl Popper:A Centenary Assessment. London:Ashgate Publishing p. 219 unless otherwise noted. the full text of the article is available here. Instead, the 1940s and 50s were the battle ground for the movement to make economics a mathematical science. A main criticism of mathematical economics was that mathematics could only provide tautologies – which were claimed to be statements or theorems that are true by virtue of their logical form rather than their empirical content. More correctly, a tautology is a statement which does not depend on the definition of its non-logical words but only on its logical words such as ‘and’, ‘or’, ‘is’ and ‘not’. Thus, a tautology is a statement which is true simply because one cannot conceive of a counter-example. For example, the statement ‘I am here or I am not here” is true regardless of who ‘I’ am or where ‘here’ is." "At the time of Hutchison’s [Here Hutchinson is an exponent of Popper's views] launch of testability-directed methodology, Paul Samuelson was beginning to write his Ph.D. thesis that promoted the mathematical basis for all economic theory. And Samuelson directly confronted the critics by saying that his version of mathematical economics could not be dismissed as a bunch of tautologies because he would require economic theorems to be testable and thereby conceivably false. For Samuelson, a testable theorem is ‘operationally meaningful’ by which he merely meant that it must be ‘refutable in principle’. To be refutable in principle, a theorem could not be a tautology. QED"

It is 100% possible that the confusion has arisen from my interpretation of this passage (and others), my communication of that interpretation on the page or my further confusion in attempting to explain it to you. If that is the case, I'm sorry. But as I see it this doesn't result in the proper link being to the current article on rhetorical tautologies. I notice that you are removing inappropriate internal links to logic articles. That is an important and valuable cleanup task. But I don't feel you are correct in this instance. At the very least (as you suggest above), a link to tautology_(rhetoric) is inappropriate. the tone and subject of the article don't match the intent of the source or the internal link (in my mind). A new article in logic (should I be correct about the link to rhetorical but incorrect about the link to logical tautology) might be appropriate, but such an article would be wholly out of my scope of competence. So, as I said, if the disagreement here is to the insufficient depth of knowledge I displayed about logic or the subject at hand, please accept my apologies. But as I see it, the link to tautology_(logic) is the proper reading of the source material. Protonk (talk) 16:54, 23 June 2008 (UTC)

 * Your quotation contains a perfectly reasonable definition of tautology. Until recently I never had a reason to concern myself with this notion, and naturally I thought that this was the definition in formal logic. Unfortunately I was wrong. In my opinion the confusion comes from the fact that formal logic uses a counterintuitive definition for the term. Our article tautology (logic) discusses only this counterintuitive term. It may be that some people, including Popper, work with a more liberal definition of the term. Such people may or may not know that the definition in formal logic is different. The important point for me is that so long as the article tautology (logic) discusses only one (unfortunate) meaning and this article uses the other (straightforward) meaning, such a wiki link contributes to the confusion. It's not about some esoteric distinction; it's a very straightforward problem, as if we were linking the word number from an article such as this one in a hypothetical world in which mathematicians use the word "number" only for positive integers and do not discuss anything else in that article.
 * Yes, the problem should be fixed on the logic side, but as I said I am not qualified for this, either. I thought that we could fix this by not linking. You don't seem to be happy with this, but I don't know what to do. I can't write the obvious other meaning into the article without any sources, and I already checked my books: They all use the weird meaning. --Hans Adler (talk) 18:36, 23 June 2008 (UTC)
 * thanks for the reply. I am happy with not linking, though not as happy as I would be were there an article to link to.  I think in order to not impute an incorrect meaning into this article (linking to rhetoric) and not generate unnecessary confusion linking to the logic article, we can find a second best solution by temporarily removing the link.  Thanks for your help. Protonk (talk) 18:48, 23 June 2008 (UTC)

Copyedit
Hi Protonk, I'm not your GAN reviewer, but I can help you get past the "well-written" criterion. Economics isn't my field, but I'm a fan of game theory and other applications of the field. Feel free to disagree; please put any responses directly under the bullet point that you're responding to. I don't generally cover images or endsections when I copyedit. I'm doing a little more than I usually do for a WP:GAN article because I could easily see this article heading to FAC in the future.

Lead section:
 * I removed the Mathematical problem link; I didn't think that page added anything to this article.
 * What makes "What use is Economic Theory?" a reliable source? Since most of economics these days has a heavy math component, it should be possible to find peer-reviewed papers to say what you want to say.
 * There were two links to Model (economics); I removed the first link.
 * I think it's likely your GAN reviewer will want a longer lead section. See WP:LEAD.

Mathematical_economics:
 * Flavors of English other than British should only use single-quotes when necessary inside of double-quotes; I'll make the changes. (And I will generally make the case to use double-quotes in British English articles, too.)
 * It's fine to use a quote to convey the consensus of the field, or the precise or witty language of the leaders of the field. I didn't think the Sheila Dow quote fit that description, so I reworded it.
 * I inserted commas before conjunctions joining two independent clauses.
 * I inverted the order of "engineering problems" because of potential ambiguity, but please change it if I guessed wrong.
 * I went with "Operations research, a newly formed discipline which influenced and was influenced by mathematical economics".  To say that it arose from economics is contradicted by the sources over at that article (and by my one operations research professor at college); it initially was concerned more with logistics and engineering.
 * I added the word "paradigm", and having done that, I felt that "and an attempt to turn economics into a normal science" was probably redundant. Let me know if there's some deeper concept from Kuhn's work that you want to work into the text.

Mathematical_economics:
 * I took out "According to the Editors, each is a non-specialist journal" because it seemed to be implied by "diverse" in the next sentence, but feel free to revert. This is a judgment call, but if it were my article, I would give more than just saying "non-specialist" or "diverse"; I would list the subject areas accepted or solicited by the journals.
 * This is a little beyond "copyediting", but the part of this article I would like to see expanded for GAN, and that would probably have to be expanded for FAC, is the sentence "Mathematical economics provides methods to model behavior in diverse, real world situations, including international climate agreements, reactions to changes in divorce laws, and pricing in the futures markets for commodities." This seems to me to need a section to itself, justifying and illustrating that proposition.
 * "mathematically competent professionals are needed in industry and government for dealing with the subject" seems ambiguous to me. Do you mean that you probably can't get a job without the mathematical background, or that these people are or were in high demand at some time (specify the time)?
 * "Graduate programs in economics and finance programs in graduate schools of management require strong undergraduate preparation in mathematics": the reference, a presentation by Sheila Dow, doesn't establish this (probably). A few links to entrance requirements on university websites that are known for strong economics programs would work for me; even better would be some reliable source that summarizes this information.
 * "empirical interpretation" is not a common phrase (12k Google hits). Is that the way your sources describe it, or did they say "interpretation of empirical data"?
 * I think the "Warwick Department of Economics" probably won't qualify as a reliable source, and the sentence will have to go. If it does qualify, then you want to change the word "recent" to "in 2008".  But a departmental study could be used to answer questions about what that university is looking for in applicants.

Mathematical_economics

 * Looks good.

Mathematical_economics and the section after:

 * One of the style guidelines specifically mentioned at WP:Good article criteria is WP:Embedded list; check it out. Raw lists (including in See also) can be very useful in B-class articles by letting everyone know which other articles to look at; material often flows between articles.  When you get up to the GA level of maturity, you're supposed to be largely finished with this process of shifting information in and out of this article, and most wikilinks should be either discarded or worked into the proper section, accompanied by context.  When you really do want a list, it's better if the list looks more like the lists in WP:Embedded list, or sometimes lists work best when they're converted into tabular form.

Okay that's it. Best of luck with your review, and I'll be happy to answer questions. I enjoyed learning more about the subject. - Dan Dank55 (talk)(mistakes) 02:43, 16 August 2008 (UTC)

 * thanks for the questions and updates. I just got back from being out of town, so I'll try to answer these questions more fully later tonight or tomorrow.  Thank you for your help and attention to detail. :) Protonk (talk) 02:29, 16 August 2008 (UTC)

Some reponses to questions above:

 * "what use is economic theory" is used in here for two reasons. One, I can't find (or don't know of) too many histories of economic theory (or encyclopedias of economic theory) aside from the new palgrave (and the Handbook of Economics, which each volume is 3 weeks away on interlibrary loan), so introspective discussions of 'mathematical economics' as a concept are hard to come by.  Two, Hal Varian is a reliable source on economics, no matter the venue.  I shouldn't probably find out what conference he gave that talk at and cite it properly.

 * Regarding your rewording of ''normal science' to paradigm. That is probably ok for now because I didn't have too much content to go on with the normal science bit.  I'll re-insert it with some content when I can find a source talking about the transition of economics from some Baconian style inquiry to a narrow, normal science.

 * "Mathematical economics provides methods to model behavior in diverse, real world situations, including international climate agreements, reactions to changes in divorce laws, and pricing in the futures markets for commodities"--That sentence was meant (at the time) as a kind of end to a section with some examples for flair. I'll take a look at the article itself and see if I can't make a small section from that.  The papers (and website) linked are pretty interesting.

 * the warwick paper. that is probably not an impeccable source, but again the author is pretty reliable.  I have to see the 'followon' paper in Econometrica (here), maybe that is helpful (although it seems like that is more of a cautionary tale to university hiring committees.

 * You are right about operations research. Not sure why I worded the sentence that way.

 * "Graduate programs in economics and finance programs in graduate schools of management require strong undergraduate preparation in mathematics" I will look for a source on this, because it is certainly true. I feel slimy enough linking one course catalog in this article, I probably won't link another.  Wow.  I guess Sheila C. Dow wrote a book on methodology: Economic Methodology:An Inquiry (link).  Maybe I should check that out of the library. :)

 * "mathematically competent professionals are needed in industry and government for dealing with the subject" -Reworded.

Thanks for the help so far. I'll see what I can check out of the library. Protonk (talk) 02:54, 16 August 2008 (UTC)

More
Very nice work. I'm not good with advice on images, but it seems to me that a couple more images that should be easy to find might help nail the WP:GAN. You might illustrate your sentence "Much of classical economics can be presented in simple geometric terms or elementary mathematical notation" with a simple supply-demand curve, contrasted with some more intricate 3-D plot. If that seems too dry, most of the articles on notable economists have pictures you could borrow. - Dan Dank55 (talk)(mistakes) 02:24, 18 August 2008 (UTC)

 * Thanks for the continuing help. I'll try to gin something up in inkscape, but I can't think of a good visual for modern mathematical economic concepts.  Take the Edgeworth box portrayed in the article.  The concept there works fine with more than two actors, but the box becomes vectors in Rn space.  Maybe the black-scholes smile? Protonk (talk) 03:51, 18 August 2008 (UTC)

 * Or the "Heat equation, to which the Black–Scholes PDE can be transformed." Wikipedia economics articles have very few images, I see, but math articles have tons of 2-D and 3-D representations. - Dan Dank55 (talk)(mistakes) 04:15, 18 August 2008 (UTC)

 * That's a really good idea. I just picked up a book on partial differential equations and the heat equation is the first thing discussed. Protonk (talk) 04:20, 18 August 2008 (UTC)

- Dan Dank55 (talk)(mistakes) 13:10, 18 August 2008 (UTC)
 * The addition of Adam Smith was appropriate, I thought. Reviewers at GAN and especially FAC tend to like historical contexts, especially historical contexts they understand; throwing in a portrait of Adam Smith and one of the 19th-century guys will help your case, I think.
 * I don't understand what the sentence that includes "as the highest level of mathematical technique" means.
 * What you've done covers my concerns (and a lot more), except for the list of economists. It's actually easier to review for FAC than for GAN because GAN is more flexible, but it's hard to guess how flexible.  At FAC, you'd probably want to turn that list into a table, perhaps with the birth and death dates in the second column and a one (or at most two) sentence description of their importance in the third column.  Btw, even the See also section would probably be too long for FAC (although it's probably fine for GAN).  At FAC, the reviewers (if they're diligent and consistent) would look at the links and think about whether any of them could be moved up into the text, perhaps as a See also link directly below the relevant heading or subheading, or perhaps just as a link, with text that explains the relationship of the link to this article.
 * In summary, a very nice article. Your GAN reviewer might have a few requests but I don't see any big problems at GAN here.

List of economists
I see what you mean about that. I'm going to try and flesh out the early 20th century history bit first and then I'll try to come up with a short blurb for each economist on the list (and prune as necessary). Protonk (talk) 14:32, 18 August 2008 (UTC)

Structure
On the advice of Jay Henry, I've checked out a few mathematical economics textbooks to get a feel for the basic structure of a course on the matter.

This is from: I:Prolegomena 1. Cournot, Walras and Edgeworth II:The founding Years (1900-1949) 2. Pareto and General equlibrium 3. Classical General equilibrium 4. Wald and existence proofs 5. Early game theory 6. Early multi-sectoral growth 7. Dynamic modeling 8. Iring Fischer and Interest theory 9. Widening General Equilibrium Theory 10. Applied general equilibirum III: Extensions, Fitness and formalism (1950 on) 11. Walras cum Leontief 12. From classical to modern analysis 13. Linear programming and extensions 14. Consumer's analysis 15. Firm's analysis 16. General competitive equlibrium 17. Stability and more 18. Regular economics ... it continues for a while

I think this is a little helpful, insofar as it points to some good ways to break the article history, applications and examples down. Nicola's breakdown is by no means the only one but I picked his book specifically because it made an attempt at grounding the chapters in history. Perhaps a new layout could be: * 1 History o 1.1 Marginalists and the roots of neoclassical economics o 1.2 General equilibrium and the interwar years o 1.3 Emergence of modern mathematical economics o 1.3.1 Econometrics * 2 Application o 2.1 Early Models of competition o 2.1.1 Perfect competition o 2.1.2 Monopoly o 2.1.3 Duopoly o 2.2 Models of equilibrium o 2.2.1 Walrassian equilibrium o 2.2.2 IS/LM o 2.3 Models of choice o 2.3.1 Game theory and oligopoly o 2.3.2 Public choice o 2.4 The theory of the firm * 3 Relationship to the discipline as a whole o 3.1 Mathematical economics as methodology o 3.2 Mathematical finance o 3.2 Views from inside and outside the professon (maybe, if I can find stuff) * 4 Criticism of mathematical economics * 5 Mathematical economists o 5.1 19th century o 5.2 20th century * 6 See also * 7 Notes * 8 External links

Thoughts?

 * Looking good. In my opinion, a nice structure might start by following the one included in the Historical Introduction of the Elsevier's Handbook of mathematical economics (written by Arrow and Intriligator, Vol. 1, p. 1):

* 1 History o 1.1 The calculus-based marginalist period (1838-1947) o 1.2 The set-theoretic/linear models period (1948-1960) o 1.3 The current period of integration (1961-1984)

 * OK, maybe section 1.3 should not be named "current" since the quoted handbook was published in 1984! Nonetheless, whatever the title of that section be, I suggest to include at least these topics there: The theory of diversifiable risk sharing (as in Karl Borch's and Christian Gollier's work); and Social choice theory (as in Sen's work).

 * In section 1.2, an "Arrow-Debreu Model" subsection would be useful, since it has had a tremendous impact on microeconomic methodology over the last decades.

 * I agree with the mathematical economists section. French economist Maurice Allais deserves a special spot, of course.

 * Finally, I just want to say that the whole econometrics/mathematical economics marriage seems ackward to me... sure, it has a historical meaning, but nowadays there are very few mathematical economists who are profficient at econometrics and viceversa.--Forich (talk) 06:15, 15 October 2008 (UTC)

Econometrics
A question has been raised about the distinction between mathematical economics and econometrics in this article. I originally did not distinguish between the two but started to due to some sources making the distinction. What comes immediately to mind is the Stigler article. He notes a distinction between Econometrica and other mathematical economics journals and relates some stories about Keynes and other journal editors refusing to publish material that would today be considered econometrics in the AER and QJE. I'll see which other sources cited here distinguish between econometrics and mathematical economics. Protonk (talk) 20:41, 20 August 2008 (UTC)

 * Thanks for bringing the matter up. In further support of the distinction, there is JEL: C6 (under JEL classification codes).  It lists some mathematical methods as applied to non-game-theory econ applications of "mathematical methods."   Math methods are distinguished from other subcategories under "econometric methods."  The JEL usages suggest at least the convenience of distingushing math econ and econometrics.   --Thomasmeeks (talk) 20:07, 21 August 2008 (UTC)
 * Oh, also Oskar R. Lange makes this split explicit in his review of economic modeling here. Protonk (talk) 20:59, 26 August 2008 (UTC)

 * It's been awhile, but let me extend congrats on well-deserved GA outcome. I did not press the point earlier, but there is a distinction in usage between 'mathematical economics' & 'econometrics'. The unwary reader might get the impression econometrics is a proper subset of math econ.  Textbooks on the respective subjects indicate otherwise.  Debreu's "mathemtatical economics" article in The New Palgrave does not even mention econometrics.  It's true that Econometrica has always published a lot of math econ articles (in addition to articles on econometrics). Still, usage of the 2 terms is distinct. It is also reflected in the JEL codes as indicated above and in hierarchical The New Palgrave: A Dictionary of Economics (1987) where the articles are their respective headings. That subsection is ine history section of the article.  There's really no need to go into the history of econometrics as such (unless it is merely  to mention their co-development.  --Thomasmeeks (talk) 21:40, 23 May 2009 (UTC)

Withdrawn GAN
I've withdrawn the GAN as I've discovered that the scope of the article doesn't come close to covering the scope of the subject. I'll expand it (as best I can) in the next week or so to look like the structure seen above. Any help is much appreciated. Also, anyone that can get Economic Methodology by Dow would be a help, as my interlibrary request for it got denied. Don't they KNOW I need to edit wikipedia?! Protonk (talk) 15:27, 21 August 2008 (UTC)
 * As an update, I've started a draft page, User talk:Protonk/Draft of mathematical economics for broad reworking of the history and applications sections. Changes are welcome there but it is prone to change rapidly. Protonk (talk) 20:11, 21 August 2008 (UTC)

General sources
Here are a few general sources that might be helpful in addition to those already in the article.

For a classic discussion: F.Y. Edgeworth (2008), "mathematical methods in political economy," The New Palgrave Dictionary of Economics, 2nd Edition, earlier (with "method" in the title) at (1987) The New Palgrave: A Dictionary of Economics, v. 3, pp. 404-05, and (1987) Palgrave's Dictionary of Political Economy''

For later treatment: Gerard Debreu (2008), "mathematical economics," (Abstract.) The New Palgrave Dictionary of Economics, 2nd Edition.

The JEL classification codes list some mathematical methods as applied to non-game-theory applications under  JEL: C6. Game theory has its own subbategories. --Thomasmeeks (talk) 20:13, 21 August 2008 (UTC)

Congrats on the GA
If you are interested in heading to A-class or FAC with this one, let me know, I'd love to help. - Dan Dank55 (send/receive) 20:42, 27 September 2008 (UTC)
 * I'm looking to send it to A class review. I'm temporarily burned out on the article right now, but there is a lot of room for improvement.  I did enjoy discovering that...I have a LOT to learn about economics, although writing this article is helping me in my Mathematical econ. class. :) Protonk (talk) 21:33, 27 September 2008 (UTC)
 * Waiting works for me, A-class works for me. I've got 0.7 stuff til Oct 20. - Dan Dank55 (send/receive) 21:54, 27 September 2008 (UTC)

 * For the record, there is currently no FA general-field article in Econ. The only current general-field WP:Good article-rated in Econ is here per http://en.wikipedia.org/wiki/Wikipedia:Good_articles/Social_sciences_and_society#Economics_and_business -- a stunning achievement -- with most of the non-minor Edits due to Protonk, which took  the article from here to here (that is, shortly after GA status).  Protonk continued making careful, not-infrequent Edits thereafter. P's last 1.5 sentences above evince an attitude that doubtless contributed to the success of the outcome. -- Thomasmeeks (talk) 22:26, 19 July 2010 (UTC)
 * Above are updated & added links, an added last phrase, and 2 sentences. --14:09, 22 December 2010 (UTC)(UTC)

 * In mathematical economics, GA status was awarded yesterday to the Shapley–Folkman lemma, which describes the head-aches of non-convex sets, largely motivated by economic applications. Editing (especially copy editing) would be welcome! Cheers,  Kiefer.Wolfowitz (talk) 09:52, 20 January 2011 (UTC)

Odd Paragraph
Is it just me, or does the following paragraph fail to relate to the topic:

Around the end of the 19th century, the effort to place mathematics on secure logical foundations reached its most ambitious heights with the publication of Principia Mathematica by Russell and Whitehead. In 1918, David Hilbert continued the call for a complete axiomatic system in mathematics.[9]. Although the ultimate goal of a complete, consistent and self-contained mathematical system was ultimately shown by Godel to be unachievable, economists continue to regard mathematical rigor as a desirable objective.

I think it should be removed 70.61.48.113 (talk) 19:42, 29 March 2009 (UTC)

Criticisms of mathematical economics
I'll make a few comments: Karl Marx and Mathematical Economics, Leon Smolinski, The Journal of Political Economy, Vol. 81, No. 5 (Sep. - Oct., 1973), pp. 1189-1204.
 * The (lead) discussion of Hayek's assertions is not helpful to the reader. It should be removed (as a cranky theory, imho) or expanded.
 * The discussion seems to reflect the obsessions of the 1950s (Popper and Friedman, etc.), but don't discuss contemporary discussions of mathematical economics.
 * One of the main criticisms of mathematical economics was by Marxism-Leninism. There was a nice article in Journal of Political Economy called "Karl Marx and Mathematical Economics", about the Communist campaigns against mathematics (more advanced than used in Das Kapital):

Any biography of Leonid Kantorovich discusses the problems of using mathematics, in the U.S.S.R. which was most intense during the time of Stalin; he has an autobiographical essay "My Journey in Science" which recounts him being denounced and compared to "the fascist Pareto" during the most repressive years. Thanks. Kiefer.Wolfowitz (talk) 21:21, 12 January 2010 (UTC)
 * Another problem of mathematical economics stems from the Humboldtian sibling rivalry between the natural sciences versus humanities & social-sciences. In some European countries, especially Sweden, social scientists have long received inferior mathematical education while in gymnasium.
 * There is a related problem, worth mentioning: In England, economics grew out of moral philosophy, and was conceived as a non-historical and a priori science. Edgeworth and Marshall were hostile towards (German) economic history, and took various actions against the development of statistical methods. (Mirowski's book of Edgeworth's writings discusses this.)

 * This is about 6 months late, but I'll attempt a reply. I don't think Hayek's criticism is cranky or iconoclastic in this regard.  I'll agree that the LEDE is too short and a longer lead might not put so much focus on the that particular criticism.  However, the core critique that human behavior is not well modeled by physics remains--especially after the financial crisis of 2007/8.
 * As for the historical school and "physics envy" points, I agree completely. I don't know if I'll make any substantial revisions to the article, but please feel free to update or fix it as necessary. Protonk (talk) 20:03, 13 July 2010 (UTC)

 * Uh Hayek is a nobel prize laureate. You can disagree with him but his ideas were obviously important at one time or another. Actually it is quite amusing how you talk so highly of Marx with his theories have been proven to be an abject failure. Hayek has been vindicated in many regards and well respected by esteemed economist such as Milton Friedman. —Preceding unsigned comment added by Sabaton10 (talk • contribs) 11:57, 15 September 2010 (UTC)

 * Editor Sabaton10, your comments puzzle me. Kantorovich was denounced as a mathematical fascist by Stalinists; these same criticisms are parroted by many anti-math leftist economists in "western" countries. My stating that these criticisms are common (like the common cold) does not imply their validity, unless you wrongly impute to me a belief (shudder!) that Stalin or The Monthly Review or URPE be infallible --- a false belief that I disavow. I suggest you read Smolinski, who describes the Stalinist campaign. Thanks, Kiefer.Wolfowitz (talk) 23:51, 15 September 2010 (UTC)
 * I added references that discuss the Communist/Stalinist campaigns against mathematical economics, previously noted: Kantorovich and Polyak. Kantorivich's abbreviation of prices as O.O.O. was particularly brave/humorous during Stalin's dictatorship. Kiefer.Wolfowitz (talk) 23:49, 11 December 2010 (UTC)

Use of honorifics/titles with names
I tentatively added "Sir" to both R.G.D. Allen and John Hicks's names in the list of MEs to be consistent with its use for Mirrlees. (Their WP articles show them as having been knighted, although Hicks's article doesn't give his specific honor/order. Their articles also refer to them as "Sir" in the lead sentence.)

I have no strong feelings one way or the other about whether to use of honorifics and titles for British (and possibly other) economists, e.g., Lord J.M. Keynes (1st Baron Tilton). Clearly, though, usage should be consistent throughout the article, especially in such a list. --Jackftwist (talk) 19:37, 13 July 2010 (UTC)
 * I'd prefer not to have a list of economists, especially since what constitutes a mathematical economist has changed so radically over the past 100 years. But I don't have the motivation to remove the lists made by other folks.  I also am ignorant of the particulars of our MOS for names, so I'll defer to your judgment on that subject. Protonk (talk) 19:59, 13 July 2010 (UTC)

 * Consistency in a list might begin by at least not adding an honorific not already in the title.   The New Palgrave does not use such in titles.  And it has strong British roots.  Usage within the article is different from its title. Naming conventions (royalty and nobility) says
 * 4. Titles of Knighthood such as Sir and Dame are not normally included in the article title: e.g. Arthur Conan Doyle, not "Sir Arthur Conan Doyle" (which is a redirect). However, Sir may be used in article titles as a disambiguator when a name is ambiguous and one of those who used it was knighted, e.g. Sir Arthur Dean. A person's full title (including both prefix and post-nominals) should be given in the article itself. (Remember that honorary knights – roughly, those not from the Commonwealth – are not called Sir, and that knights bachelor have no post-nominals.)
 * So, that guideline is to drop the "sir" in the article title.  --Thomasmeeks (talk) 21:04, 13 July 2010 (UTC)

Criticisms of mathematical economics — or of non-empirical economics?
The "criticism" of Hayek can stay (although one wonders whether engineers have to suffer through such criticism of the role of calculus in their practices).

Most of the noted criticisms of mathematical economics are not criticisms of mathematical economics per se. They are rather criticisms of economics, as neglecting empirical theory construction and testing. Those criticisms should be moved off.

Could somebody find better criticisms of economics?
 * Keynes's decadent sophistry shows the worst aspects of his Brittish upper-class breeding and public-school education.
 * Heilbroner was a famous para-economist, but a half-coherent quote in an interview doesn't belong in an encyclopedia article.

For example, Martin Shubik wrote an entertaining criticism of microeconomics and the Oskar Morgenstern wrote a much sharper critique of actually existing economics in the 1970s. There was an American Economic Association blue-ribbon commission (c. 1993)that complained that grad programs rivaled McDonald's in their standardization, and rivaled metaphysical academies in their divorce from practice. Such criticisms would better serve the public than Keynes's snobbery and Heilbroner's dotage.

Sincerely, Kiefer.Wolfowitz (talk) 04:04, 12 December 2010 (UTC)

Agent-based computational economics
There is not citation saying that this is an important part of math econ. There is not citation of a competent good textbook in math econ with a chapter on agent based econ.

It's all very interesting, but computer experiments are as old as Schelling and Rapaport, and were old hat in the 1970s. At least Axelrod's updating of Rapapport had a theoretical point, correcting Mancur Olson et al on cooperation. (But see Smale for a math approach.)

Why not move the section to computational economics?

This is not the only article to feature agency/based econ, or what is sometimes called simulations by honest people, but this seems to be the least excusable. Kiefer .Wolfowitz 20:55, 19 January 2012 (UTC)

 * Let me label points below if reference to them is necessary.
 * 1T. May things have cooled since the above Edit. On the last 2 words the ("least excusable"), for the benefit of other readers, KW re-introduced computational economics (CE) to the Template:Economics sidebar. So, given the close relation of CE to agent-based computational economics (ACE), I’m a bit surprised that the above points would be raised in such manner. I have argued at Template talk:Economics sidebar that CE should be moved down there from the "Technical methods" section to help re-simplify that section. May KW's points indicate no stated opposition to such re-simplification (which would involve no backing off principle -- a lot has happened in the interim to warrant such resimplifacation).

 * 2T. Per Applied mathematics, few of the math econ textbooks there have game theory sections. That does not mean that game theory is not a noteworthy part of math econ.  Textbook references there on math methods of ACE include:
 * John Stachurski, 2009. Economic Dynamics: Theory and Computation, MIT Press. Description and preview.
 * Kenneth L. Judd, 1998. Numerical Methods in Economics, MIT Press. Description and chapter-preview links.
 * Of the latter, there is Avinash Dixit's testimonial:
 * "Judd's book is a masterpiece which will help transform the way economic theory is done. It harnesses the computer revolution in the service of economic theory by collecting together a whole array of numerical methods to simulate and quantify models that used to be purely algebraic and qualitative."
 * Dixit is author of among many other works the gem, Optimization in Economic Theory, 1990, 2nd ed., Oxford (description and contents preview), and so, well situated to comment on the matter. He is by no means dismissive of simulation used in ACE.  Reasons why other math econ texts don't have much on CE/ACE may that the latter builds on the former & is distinctive enough to warrant separate treatment, just as game theory textbooks or economics handbooks do.

 * 3T. Agent-based computational economics is a distinctive constituent and method of "computational economics" of which in math econ is important enough to warrant:
 * referencing in JEL classification codes within: JEL: C6 - Mathematical Methods;  Programming Models; Mathematical and Simulation Modeling, which includes:
 * JEL: C63 - Computational techniques; Simulation modeling
 * an article "agent-based models", similarly JEL classified, in The New Palgrave Dictionary of Economics (there is no such article for "computational economics").
 * the most recent of the 2-volume Handbook of Computational Economics: v. 2, 2006. Agent-Based Computational Economics, Elsevier (Description & and chapter-preview links).
 * other supportive references at Mathematical economics, including by recent Nobel laureates in econ and leaders in math econ.
 * As to the last, I don't believe that most persons who peruse the links there would be very cautious about dismissing ACE, including economists, even if they don't choose to add it to their own repertoires. --Thomasmeeks 13:41, 16 March 2012 (UTC) [Correction per strikeout in last sentence above. 10:38, 20 March 2012 (UTC)]

 * Name one theorem (with a proof) in this area. If it doesn't have a theorem, how is it mathematical economics?
 * It is an area of computational economics, often with strong ties to macroeconomics or industrial organization, I suppose. Kiefer .Wolfowitz 14:21, 16 March 2012 (UTC)

 * 4T. A question-begging demand, IMO, which Avinash Dixit (per his quotation at 2T above), presumably would be untroubled by, given his expertise in more conventional methods of optimization, which certainly includes theorems. The same Kenneth L. Judd whose whose CE-methods textbook Dixit recommends answers the above question in "Computationally Intensive Analyses in Economics," Handbook of Computational Economics, v. 2, ch. 17, pp. 881-893 (pre-pub PDF).

 * 5T. A search of The New Palgrave Dictionary of Economics Online for "computational economics" brings up  a link to "agent-based models" (a variant name of ACE) at the top of the hits list of 9 (http://www.dictionaryofeconomics.com/search_results?q=%22computational+economics%22&edition=current&button_search=GO) and per (3T) above, at  JEL classification codes under JEL: C6 - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling.  Of course ACE is a method of mathematical economics. And of course ACE is related to macroeconomics and industrial organization among others, as the linked fn. for Mathematical economics exemplify, beginning with Leigh Tesfatsion, 2006. "Agent-Based Computational Economics: A Constructive Approach to Economic Theory," ch. 16, Handbook of Computational Economics, v. 2, Agent-based Computational Economics,  pp. 831-880, Abstract and pre-pub PDF. For many other JEL Econ sub-areas that ACE has been applied to, see beginning of each remaining chapter therein (Description and chapter-preview links).

 * 6T. Per (1T) above, other readers may still be interested as to why KW put computational economics (CE) in the Econ sidebar under a heading link to JEL classification codes if he did not think it was mathematical and important. By the measures of (5T), ACE is not only important in CE but the most important aspect of CE considered as an economic methodology.  --Thomasmeeks (talk) 21:17, 18 March 2012 (UTC) --10:38, 20 March 2012 (UTC)

Dr. Krawczyk's comment on this article
Dr. Krawczyk has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

"I am not certain whether ‘mathematical economics’ should have a separate entry in Wikipedia. The way I see it, this article provides many links to mathematical economics’ topics, which exist independently in Wikipedia. Also, there exist independent articles in Wikipedia which cover what this article purports to cover, e.g., “Walrasian auction”, “Cournot competition”, Krush-Kuhn-Tucker conditions, and more.

Here are my more detailed comments:

First para … Calculus, difference and differential equations etc are not computational methods.
 * “Calculus, difference and differential […] and other computational methods”

Grammar?
 * “.. is its allowing formulation”

Grammar?
 * “optimization problems as to goal equilibrium …”

I would say “early 19th” to allow for Cournot’s works.
 * “Formal economic modeling began in the 19th century ..”

History … “… in (?) German universities…” At ?

You could mention that ‘statistics’ and ‘state’ have the same root.

…than the nth market
 * “… if there were n markets and n-1 markets cleared [..] that the nth market would clear…”

While Krush is mention in a link, he is missing from the article.
 * Nonlinear programming …

Finally, I would include in the list of the 20th century mathematical economists J. B. Rosen for his works on concave games and coupled constraint equilibrium (see e.g. http://www.jstor.org/stable/1911749?seq=1#page_scan_tab_contents) and K. L. Judd https://en.wikipedia.org/wiki/Kenneth_Judd for his works on taxation and multiple contribution to computational economics."

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

Dr. Krawczyk has published scholarly research which seems to be relevant to this Wikipedia article:

 * Reference 1: J.B. Krawczyk and K.L. Judd. A NOTE ON DETERMINING VIABLE ECONOMIC STATES IN A DYNAMIC MODEL OF TAXATION. Macroeconomic Dynamics, available on CJO2015. doi:10.1017/S1365100514000868.

 * Reference 2: Contreras, J., J. B. Krawczyk, and J. Zuccollo. "Economics of collective monitoring: a study of environmentally constrained electricity generators." Computational Management Science (2015): 1-21.

ExpertIdeasBot (talk) 11:11, 28 May 2016 (UTC)

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Como autorevisor caso tu interesses em traduzir e botar para EAB seria grato por isso. att 2804:14C:5BB1:8AF2:8DE1:61A8:EFA6:A1C2 (talk) 00:43, 25 November 2021 (UTC)

The purpose of Wikipedia
I have a background in math and not economics. The example in this article has cool math, but the function choices are made up, the constant choices are made up, and its conclusion is in complete disagreement with the empirical reality of corporate tax cuts and wage growth in the United States over the last 50 years. Does no one see a problem with this? Is the purpose of Wikipedia to provide truthful knowledge to the public, or to provide justification for crap policies to benefit corporations? Dudewaldo4 (talk) 11:51, 25 February 2022 (UTC)
 * what you're describing is a problem with how economics uses math and not (as far as I know, it's been many years since I touched this article) a problem with how Wikipedia describes how economics uses math. Protonk (talk) 20:05, 25 February 2022 (UTC)

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title: Talk:Mathematical economics