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Linear congruential generator

A linear congruential generator (LCG) is an algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear equation. The method represents one of the oldest and best-known pseudorandom number generator algorithms. The theory behind them is relatively easy to understand, and they are easily implemented and fast, especially on computer hardware which can provide modular arithmetic by storage-bit truncation.

The generator is defined by the recurrence relation:

 * $$X_{n+1} = \left( a X_n + c \right)\bmod m$$

where $$X$$ is the sequence of pseudo-random values, and

 * $$ m,\, 0<m $$ — the "modulus"
 * $$ a,\,0 < a < m$$ — the "multiplier"
 * $$ c,\,0 \le c < m$$ — the "increment"
 * $$ X_0,\,0 \le X_0 < m$$ — the "seed" or "start value"

are integer constants that specify the generator. If c = 0, the generator is often called a multiplicative congruential generator (MCG), or Lehmer RNG. If c ≠ 0, the method is called a mixed congruential generator.

When c ≠ 0, a mathematician would call the recurrence an affine transformation, not a linear one, but the misnomer is well-established in computer science.

History
The Lehmer generator was published in 1951 and the Linear congruential generator was published in 1958 by W. E. Thomson and A. Rotenberg.

Period length
A benefit of LCGs is that an appropriate choice of parameters results in a period which is both known and long. Although not the only criterion, too short a period is a fatal flaw in a pseudorandom number generator.

While LCGs are capable of producing pseudorandom numbers which can pass formal tests for randomness, the quality of the output is extremely sensitive to the choice of the parameters m and a. For example, a = 1 and c = 1 produces a simple modulo-m counter, which has a long period, but is obviously non-random. Other values of c coprime to m produce a Weyl sequence, which is better distributed but still obviously non-random.

Historically, poor choices for a have led to ineffective implementations of LCGs. A particularly illustrative example of this is RANDU, which was widely used in the early 1970s and led to many results which are currently being questioned because of the use of this poor LCG.

There are three common families of parameter choice:

m prime, c = 0
This is the original Lehmer RNG construction. The period is m−1 if the multiplier a is chosen to be a primitive element of the integers modulo m. The initial state must be chosen between 1 and m−1.

One disadvantage of a prime modulus is that the modular reduction requires a double-width product and an explicit reduction step. Often a prime just less than a power of 2 is used (the Mersenne primes 231−1 and 261−1 are popular), so that the reduction modulo m = 2e − d can be computed as (ax mod 2e) + d $\floor{ax/2^{e}}$. This must be followed by a conditional subtraction of m if the result is too large, but the number of subtractions is limited to ad/m, which can be easily limited to one if d is small.

If a double-width product is unavailable, and the multiplier is chosen carefully, Schrage's method may be used. To do this, factor m = qa+r, i.e. q = $\floor{m/a}$ and r = m mod a. Then compute ax mod m = a(x mod q) − r$\floor{x/q}$. Since x mod q < q ≤ m/a, the first term is strictly less than am/a = m. If a is chosen so that r ≤ q (and thus r/q ≤ 1), then the second term is also less than m: r$\floor{x/q}$ ≤ rx/q = x(r/q) ≤ x < m. Thus, both products can be computed with a single-width product, and the difference between them lies in the range [1−m, m−1], so can be reduced to [0, m−1] with a single conditional add.

A second disadvantage is that it is awkward to convert the value 1 ≤ x < m to uniform random bits. If a prime just less than a power of 2 is used, sometimes the missing values are simply ignored.

m a power of 2, c = 0
Choosing m to be a power of two, most often m = 232 or m = 264, produces a particularly efficient LCG, because this allows the modulus operation to be computed by simply truncating the binary representation. In fact, the most significant bits are usually not computed at all. There are, however, disadvantages.

This form has maximal period m/4, achieved if a ≡ ±3 (mod 8) and the initial state X0 is odd. Even in this best case, the low three bits of X alternate between two values and thus only contribute one bit to the state. X is always odd (the lowest-order bit never changes), and only one of the next two bits ever changes. If a ≡ +3, X alternates ±1↔±3, while if a ≡ −3, X alternates ±1↔∓3 (all modulo 8).

It can be shown that this form is equivalent to a generator with modulus m/4 and c ≠ 0.

A more serious issue with the use of a power-of-two modulus is that the low bits have a shorter period than the high bits. Its simplicity of implementation comes from the fact that bits are never affected by higher-order bits, so the low b bits of such a generator form a modulo-2b LCG by themselves, repeating with a period of 2b−2. Only the most significant bit of X achieves the full period.

m a power of 2, c ≠ 0
When c ≠ 0, correctly chosen parameters allow a period equal to m, for all seed values. This will occur if and only if:
 * 1) $$m$$ and $$c$$ are coprime,
 * 2) $$a - 1$$ is divisible by all prime factors of $$m$$,
 * 3) $$a - 1$$ is divisible by 4 if $$m$$ is divisible by 4.

These three requirements are referred to as the Hull–Dobell Theorem.

This form may be used with any m, but only works well for m with many repeated prime factors, such as a power of 2; using a computer's word size is the most common choice. If m were a square-free integer, this would only allow a ≡ 1 (mod m), which makes a very poor PRNG; a selection of possible full-period multipliers is only available when m has repeated prime factors.

Although the Hull–Dobell theorem provides maximum period, it is not sufficient to guarantee a good generator. For example, it is desirable for a − 1 to not be any more divisible by prime factors of m than necessary. If m is a power of 2, then a − 1 should be divisible by 4 but not divisible by 8, i.e. a ≡ 5 (mod 8).

Indeed, most multipliers produce a sequence which fails one test for non-randomness or another, and finding a multiplier which is satisfactory to all applicable criteria is quite challenging. The spectral test is one of the most important tests.

Note that a power-of-2 modulus shares the problem as described above for c = 0: the low k bits form a generator with modulus 2k and thus repeat with a period of 2k; only the most significant bit achieves the full period. If a pseudorandom number less than r is desired, $\floor{rX/m}$ is a much higher-quality result than X mod r. Unfortunately, most programming languages make the latter much easier to write, so it is very commonly used.

The generator is not sensitive to the choice of c, as long as it is relatively prime to the modulus (e.g. if m is a power of 2, then c must be odd), so the value c=1 is commonly chosen.

The sequence produced by other choices of c can be written as a simple function of the sequence when c=1. Specifically, if Y is the prototypical sequence defined by Y0 = 0 and Yn+1 = aYn + 1 mod m, then a general sequence Xn+1 = aXn + c mod m can be written as an affine function of Y:
 * $$X_n = (X_0(a-1)+c)Y_n + X_0 = (X_1 - X_0)Y_n + X_0 \pmod m.$$

More generally, any two sequences X and Z with the same multiplier and modulus are related by
 * $${ X_n - X_0 \over X_1 - X_0 } = Y_n = {a^n - 1 \over a - 1} = { Z_n - Z_0 \over Z_1 - Z_0 } \pmod m.$$

In the common case where m is a power of 2 and a ≡ 5 (mod 8) (a desirable property for other reasons), it is always possible to find an initial value X0 so that the denominator X1 − X0 ≡ ±1 (mod m), producing an even simpler relationship. With this choice of X0, Xn = X0 ± Yn will remain true for all n. The sign is determined by c ≡ ±1 (mod 4), and the constant X0 is determined by 1 ∓ c ≡ (1 − a)X0 (mod m).

As a simple example, consider the generators Xn+1 = 157Xn + 3 mod 256 and Yn+1 = 157Yn + 1 mod 256; i.e. m = 256, a = 157, and c = 3. Because 3 ≡ −1 (mod 4), we are searching for a solution to 1 + 3 ≡ (1 − 157)X0 (mod 256). This is satisfied by X0 ≡ 41 (mod 64), so if we start with that, then Xn ≡ X0 − Yn (mod 256) for all n.

For example, using X0 = 233 = 3×64 + 41:
 * X = 233, 232, 75, 2, 61, 108, ...
 * Y = 0, 1, 158, 231, 172, 125, ...
 * X + Y mod 256 = 233, 233, 233, 233, 233, 233, ...

Parameters in common use
The following table lists the parameters of LCGs in common use, including built-in rand functions in runtime libraries of various compilers. This table is to show popularity, not examples to emulate; many of these parameters are poor. Tables of good parameters are available.

As shown above, LCGs do not always use all of the bits in the values they produce. In general, they return the most significant bits. For example, the Java implementation operates with 48-bit values at each iteration but returns only their 32 most significant bits. This is because the higher-order bits have longer periods than the lower-order bits (see below). LCGs that use this truncation technique produce statistically better values than those that do not. This is especially noticeable in scripts that use the mod operation to reduce range; modifying the random number mod 2 will lead to alternating 0 and 1 without truncation.

Contrarily, some libraries use an implicit power-of-two modulus but never output or otherwise use the most significant bit, in order to limit the output to positive two's complement integers. The output is as if the modulus were one bit less than the internal word size, and such generators are described as such in the table above.

Advantages and disadvantages
LCGs are fast and require minimal memory (one modulo-m number, often 32 or 64 bits) to retain state. This makes them valuable for simulating multiple independent streams. LCGs are not intended, and must not be used, for cryptographic applications; use a cryptographically secure pseudorandom number generator for such applications.

Although LCGs have a few specific weaknesses, many of their flaws come from having too small a state. The fact that people have been lulled for so many years into using them with such small moduli can be seen as a testament to the strength of the technique. A LCG with large enough state can pass even stringent statistical tests; a modulo-264 LCG which returns the high 32 bits passes TestU01's SmallCrush suite, and a 96-bit LCG passes the most stringent BigCrush suite.

For a specific example, an ideal random number generator with 32 bits of output is expected (by the Birthday theorem) to begin duplicating earlier outputs after $√m ≈ 2^{16}$ results. Any PRNG whose output is its full, untruncated state will not produce duplicates until its full period elapses, an easily detectable statistical flaw. For related reasons, any PRNG should have a period longer than the square of the number of outputs required. Given modern computer speeds, this means a period of 264 for all but the least demanding applications, and longer for demanding simulations.

One flaw specific to LCGs is that, if used to choose points in an n-dimensional space, the points will lie on, at most, $\sqrt{n!⋅m$hyperplanes (Marsaglia's theorem, developed by George Marsaglia). This is due to serial correlation between successive values of the sequence Xn. Carelessly chosen multipliers will usually have far fewer, widely spaced planes, which can lead to problems. The spectral test, which is a simple test of an LCG's quality, measures this spacing and allows a good multiplier to be chosen.

The plane spacing depends both on the modulus and the multiplier. A large enough modulus can reduce this distance below the resolution of double precision numbers. The choice of the multiplier becomes less important when the modulus is large. It is still necessary to calculate the spectral index and make sure that the multiplier is not a bad one, but purely probabilistically it becomes extremely unlikely to encounter a bad multiplier when the modulus is larger than about 264.

Another flaw specific to LCGs is the short period of the low-order bits when m is chosen to be a power of 2. This can be mitigated by using a modulus larger than the required output, and using the most significant bits of the state.

Nevertheless, for some applications LCGs may be a good option. For instance, in an embedded system, the amount of memory available is often severely limited. Similarly, in an environment such as a video game console taking a small number of high-order bits of an LCG may well suffice. (The low-order bits of LCGs when m is a power of 2 should never be relied on for any degree of randomness whatsoever.) The low order bits go through very short cycles. In particular, any full-cycle LCG, when m is a power of 2, will produce alternately odd and even results.

LCGs should be evaluated very carefully for suitability in non-cryptographic applications where high-quality randomness is critical. For Monte Carlo simulations, an LCG must use a modulus greater and preferably much greater than the cube of the number of random samples which are required. This means, for example, that a (good) 32-bit LCG can be used to obtain about a thousand random numbers; a 64-bit LCG is good for about 221 random samples (a little over two million), etc. For this reason, in practice LCGs are not suitable for large-scale Monte Carlo simulations.

Python code
The following is an implementation of an LCG in Python, in the form of a generator:

Free Pascal
Free Pascal uses a Mersenne Twister as its default pseudo random number generator whereas Delphi uses a LCG. Here is a Delphi compatible example in Free Pascal based on the information in the table above. Given the same RandSeed value it generates the same sequence of random numbers as Delphi.

Like all pseudorandom number generators, a LCG needs to store state and alter it each time it generates a new number. Multiple threads may access this state simultaneously causing a race condition. Implementations should use different state each with unique initialization for different threads to avoid equal sequences of random numbers on simultaneously executing threads.

LCG derivatives
There are several generators which are linear congruential generators in a different form, and thus the techniques used to analyze LCGs can be applied to them.

One method of producing a longer period is to sum the outputs of several LCGs of different periods having a large least common multiple; the Wichmann–Hill generator is an example of this form. (We would prefer them to be completely coprime, but a prime modulus implies an even period, so there must be a common factor of 2, at least.) This can be shown to be equivalent to a single LCG with a modulus equal to the product of the component LCG moduli.

Marsaglia's add-with-carry and subtract-with-borrow PRNGs with a word size of b=2w and lags r and s (r > s) are equivalent to LCGs with a modulus of br ± bs ± 1.

Multiply-with-carry PRNGs with a multiplier of a are equivalent to LCGs with a large prime modulus of abr−1 and a power-of-2 multiplier b.

A permuted congruential generator begins with a power-of-2-modulus LCG and applies an output transformation to eliminate the short period problem in the low-order bits.

Comparison with other PRNGs
The other widely used primitive for obtaining long-period pseudorandom sequences is the linear-feedback shift register construction, which is based on arithmetic in GF(2)[x], the polynomial ring over GF(2). Rather than integer addition and multiplication, the basic operations are exclusive-or and carry-less multiplication, which is usually implemented as a sequence of logical shifts. These have the advantage that all of their bits are full-period; they do not suffer from the weakness in the low-order bits that plagues arithmetic modulo 2k.

Examples of this family include xorshift generators and the Mersenne twister. The latter provides a very long period (219937−1) and variate uniformity, but it fails some statistical tests. Lagged Fibonacci generators also fall into this category; although they use arithmetic addition, their period is ensured by an LFSR among the least-significant bits.

It is easy to detect the structure of a linear-feedback shift register with appropriate tests such as the linear complexity test implemented in the TestU01 suite; a boolean circulant matrix initialized from consecutive bits of an LFSR will never have rank greater than the degree of the polynomial. Adding a non-linear output mixing function (as in the xoshiro256** and permuted congruential generator constructions) can greatly improve the performance on statistical tests.

Another structure for a PRNG is a very simple recurrence function combined with a powerful output mixing function. This includes counter mode block ciphers and non-cryptographic generators such as SplitMix64.

A structure similar to LCGs, but not equivalent, is the multiple-recursive generator: Xn = (a1Xn−1 + a2Xn−2 + ··· + akXn−k) mod m for k ≥ 2. With a prime modulus, this can generate periods up to mk−1, so is a useful extension of the LCG structure to larger periods.

A powerful technique for generating high-quality pseudorandom numbers is to combine two or more PRNGs of different structure; the sum of an LFSR and an LCG (as in the KISS or xorwow constructions) can do very well at some cost in speed.

title: Linear congruential generator


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Opportunity cost

In microeconomic theory, the opportunity cost of a choice is the value of the best alternative forgone where, given limited resources, a choice needs to be made between several mutually exclusive alternatives. Assuming the best choice is made, it is the "cost" incurred by not enjoying the benefit that would have been had by taking the second best available choice. The New Oxford American Dictionary defines it as "the loss of potential gain from other alternatives when one alternative is chosen". As a representation of the relationship between scarcity and choice, the objective of opportunity cost is to ensure efficient use of scarce resources. It incorporates all associated costs of a decision, both explicit and implicit. Thus, opportunity costs are not restricted to monetary or financial costs: the real cost of output forgone, lost time, pleasure, or any other benefit that provides utility should also be considered an opportunity cost.

Explicit costs
Explicit costs are the direct costs of an action (business operating costs or expenses), executed through either a cash transaction or a physical transfer of resources. In other words, explicit opportunity costs are the out-of-pocket costs of a firm, that are easily identifiable. This means explicit costs will always have a dollar value and involve a transfer of money, e.g. paying employees. With this said, these particular costs can easily be identified under the expenses of a firm's income statement and balance sheet to represent all the cash outflows of a firm.

Examples are as follows:

 * Land and infrastructure costs
 * Operation and maintenance costs—wages, rent, overhead, materials

Scenarios are as follows:

 * If a person leaves work for an hour and spends $200 on office supplies, then the explicit costs for the individual equates to the total expenses for the office supplies of $200.
 * If a printer of a company malfunctions, then the explicit costs for the company equates to the total amount to be paid to the repair technician.

Implicit costs
Implicit costs (also referred to as implied, imputed or notional costs) are the opportunity costs of utilising resources owned by the firm that could be used for other purposes. These costs are often hidden to the naked eye and are not made known. Unlike explicit costs, implicit opportunity costs correspond to intangibles. Hence, they cannot be clearly identified, defined or reported. This means that they are costs that have already occurred within a project, without exchanging cash. This could include a small business owner not taking any salary in the beginning of their tenure as a way for the business to be more profitable. As implicit costs are the result of assets, they are also not recorded for the use of accounting purposes because they do not represent any monetary losses or gains. In terms of factors of production, implicit opportunity costs allow for depreciation of goods, materials and equipment that ensure the operations of a company.

Examples of implicit costs regarding production are mainly resources contributed by a business owner which includes:

 * Human labour
 * Infrastructure
 * Time

Scenarios are as follows:

 * If a person leaves work for an hour to spend $200 on office supplies, and has an hourly rate of $25, then the implicit costs for the individual equates to the $25 that he/she could have earned instead.
 * If a printer of a company malfunctions, the implicit cost equates to the total production time that could have been utilized if the machine did not break down.

Sunk costs
Sunk costs (also referred to as historical costs) are costs that have been incurred already and cannot be recovered. As sunk costs have already been incurred, they remain unchanged and should not influence present or future actions or decisions regarding benefits and costs. Decision makers who recognise the insignificance of sunk costs then understand that the "consequences of choices cannot influence choice itself".

From the traceability source of costs, sunk costs can be direct costs or indirect costs. If the sunk cost can be summarized as a single component, it is a direct cost; if it is caused by several products or departments, it is an indirect cost.

Analyzing from the composition of costs, sunk costs can be either fixed costs or variable costs. When a company abandons a certain component or stops processing a certain product, the sunk cost usually includes fixed costs such as rent for equipment and wages, but it also includes variable costs due to changes in time or materials. Usually, fixed costs are more likely to constitute sunk costs.

Generally speaking, the stronger the liquidity, versatility, and compatibility of the asset, the less its sunk cost will be.

A scenario is given below:

A company used $5,000 for marketing and advertising on its music streaming service to increase exposure to the target market and potential consumers. In the end, the campaign proved unsuccessful. The sunk cost for the company equates to the $5,000 that was spent on the market and advertising means. This expense is to be ignored by the company in its future decisions and highlights that no additional investment should be made.

Despite the fact that sunk costs should be ignored when making future decisions, people sometimes make the mistake of thinking sunk cost matters. This is sunk cost fallacy.

Example: Steven bought a game for $100, but when he started to play it, he found it was boring rather than interesting. But Steven thinks he paid $100 for the game, so he has to play it through.

Sunk cost: $100 and the cost of the time spent playing the game. Analysis: Steven spent $100 hoping to complete the whole game experience, and the game is an entertainment activity, but there is no pleasure during the game, which is already low efficiency, but Steven also chose to waste time. So it is adding more cost.

Marginal cost
The concept of marginal cost in economics is the incremental cost of each new product produced for the entire product line. For example, if you build a plane, it costs a lot of money, but when you build the 100th plane, the cost will be much lower. When building a new aircraft, the materials used may be more useful, so make as many aircraft as possible from as few materials as possible to increase the margin of profit. Marginal cost is abbreviated MC or MPC.

Marginal cost: The increase in cost caused by an additional unit of production is called marginal cost. By definition, marginal cost (MC) is equal to the change in total cost (△TC) divided by the corresponding change in output (△Q): MC(Q) = △TC(Q)/△Q or, taking the limit as △Q goes to zero,

MC(Q) = lim(△Q→0) △TC(Q)/△Q = dTC/dQ.

In theory marginal costs represent the increase in total costs (which include both constant and variable costs) as output increases by 1 unit.

Adjustment cost
The phrase "adjustment costs" gained significance in macroeconomic studies, referring to the expenses a company bears when altering its production levels in response to fluctuations in demand and/or input costs. These costs may encompass those related to acquiring, setting up, and mastering new capital equipment, as well as costs tied hiring, dismissing, and training employees to modify production. We use "adjustment costs" to describe shifts in the firm's product nature rather than merely changes in output volume. We expand the notion of adjustment costs in this manner because, to reposition itself in the market relative to rivals, a company usually needs to alter crucial features of its goods or services to enhance competition based on differentiation or cost. In line with the conventional concept, the adjustment costs experienced during repositioning may involve expenses linked to the reassignment of capital and/or labor resources. However, they might also include costs from other areas, such as changes in organizational abilities, assets, and expertise.

Economic profit versus accounting profit
The main objective of accounting profits is to give an account of a company's fiscal performance, typically reported on in quarters and annually. As such, accounting principles focus on tangible and measurable factors associated with operating a business such as wages and rent, and thus, do not "infer anything about relative economic profitability". Opportunity costs are not considered in accounting profits as they have no purpose in this regard.

The purpose of calculating economic profits (and thus, opportunity costs) is to aid in better business decision-making through the inclusion of opportunity costs. In this way, a business can evaluate whether its decision and the allocation of its resources is cost-effective or not and whether resources should be reallocated.

Economic profit does not indicate whether or not a business decision will make money. It signifies if it is prudent to undertake a specific decision against the opportunity of undertaking a different decision. As shown in the simplified example in the image, choosing to start a business would provide $10,000 in terms of accounting profits. However, the decision to start a business would provide −$30,000 in terms of economic profits, indicating that the decision to start a business may not be prudent as the opportunity costs outweigh the profit from starting a business. In this case, where the revenue is not enough to cover the opportunity costs, the chosen option may not be the best course of action. When economic profit is zero, all the explicit and implicit costs (opportunity costs) are covered by the total revenue and there is no incentive for reallocation of the resources. This condition is known as normal profit.

Several performance measures of economic profit have been derived to further improve business decision-making such as risk-adjusted return on capital (RAROC) and economic value added (EVA), which directly include a quantified opportunity cost to aid businesses in risk management and optimal allocation of resources. Opportunity cost, as such, is an economic concept in economic theory which is used to maximise value through better decision-making.

In accounting, collecting, processing, and reporting information on activities and events that occur within an organization is referred to as the accounting cycle. To encourage decision-makers to efficiently allocate the resources they have (or those who have trusted them), this information is being shared with them. As a result, the role of accounting has evolved in tandem with the rise of economic activity and the increasing complexity of economic structure. Accounting is not only the gathering and calculation of data that impacts a choice, but it also delves deeply into the decision-making activities of businesses through the measurement and computation of such data. In accounting, it is common practice to refer to the opportunity cost of a decision (option) as a cost. The discounted cash flow method has surpassed all others as the primary method of making investment decisions, and opportunity cost has surpassed all others as an essential metric of cash outflow in making investment decisions. For various reasons, the opportunity cost is critical in this form of estimation.

First and foremost, the discounted rate applied in DCF analysis is influenced by an opportunity cost, which impacts project selection and the choice of a discounting rate. Using the firm's original assets in the investment means there is no need for the enterprise to utilize funds to purchase the assets, so there is no cash outflow. However, the cost of the assets must be included in the cash outflow at the current market price. Even though the asset does not result in a cash outflow, it can be sold or leased in the market to generate income and be employed in the project's cash flow. The money earned in the market represents the opportunity cost of the asset utilized in the business venture. As a result, opportunity costs must be incorporated into project planning to avoid erroneous project evaluations. Only those costs directly relevant to the project will be considered in making the investment choice, and all other costs will be excluded from consideration. Modern accounting also incorporates the concept of opportunity cost into the determination of capital costs and capital structure of businesses, which must compute the cost of capital invested by the owner as a function of the ratio of human capital. In addition, opportunity costs are employed to determine to price for asset transfers between industries.

Comparative advantage versus absolute advantage
When a nation, organisation or individual can produce a product or service at a relatively lower opportunity cost compared to its competitors, it is said to have a comparative advantage. In other words, a country has comparative advantage if it gives up less of a resource to make the same number of products as the other country that has to give up more.

Using the simple example in the image, to make 100 tonnes of tea, Country A has to give up the production of 20 tonnes of wool which means for every 1 tonne of tea produced, 0.2 tonnes of wool has to be forgone. Meanwhile, to make 30 tonnes of tea, Country B needs to sacrifice the production of 100 tonnes of wool, so for each tonne of tea, 3.3 tonnes of wool is forgone. In this case, Country A has a comparative advantage over Country B for the production of tea because it has a lower opportunity cost. On the other hand, to make 1 tonne of wool, Country A has to give up 5 tonnes of tea, while Country B would need to give up 0.3 tonnes of tea, so Country B has a comparative advantage over the production of wool.

Absolute advantage on the other hand refers to how efficiently a party can use its resources to produce goods and services compared to others, regardless of its opportunity costs. For example, if Country A can produce 1 tonne of wool using less manpower compared to Country B, then it is more efficient and has an absolute advantage over wool production, even if it does not have a comparative advantage because it has a higher opportunity cost (5 tonnes of tea).

Absolute advantage refers to how efficiently resources are used whereas comparative advantage refers to how little is sacrificed in terms of opportunity cost. When a country produces what it has the comparative advantage of, even if it does not have an absolute advantage, and trades for those products it does not have a comparative advantage over, it maximises its output since the opportunity cost of its production is lower than its competitors. By focusing on specialising this way, it also maximises its level of consumption.

Opportunity cost at governmental level
Similar to the way people make decisions, governments frequently have to take opportunity cost into account when passing legislation. The potential cost at the government level is fairly evident when we look at, for instance, government spending on war. Assume that entering a war would cost the government $840 billion. They are thereby prevented from using $840 billion to fund healthcare, education, or tax cuts or to diminish by that sum any budget deficit. In regard to this situation, the explicit costs are the wages and materials needed to fund soldiers and required equipment whilst an implicit cost would be the time that otherwise employed personnel will be engaged in war.

Another example of opportunity cost at government level is the effects of the Covid-19 pandemic. Governmental responses to the COVID-19 epidemic have resulted in considerable economic and social consequences, both implicit and apparent. Explicit costs are the expenses that the government incurred directly as a result of the pandemic which included $4.5 billion dollars on medical bills, vaccine distribution of over $17 billion dollars, and economic stimulus plans that cost $189 billion dollars. These costs, which are often simpler to measure, resulted in greater public debt, decreased tax income, and increased expenditure by the government. The opportunity costs associated with the epidemic, including lost productivity, slower economic growth, and weakened social cohesiveness, are known as implicit costs. Even while these costs might be more challenging to estimate, they are nevertheless crucial to comprehending the entire scope of the pandemic's effects. For instance, the implementation of lockdowns and other limitations to stop the spread of the virus resulted in a $158 billion dollar loss due to decreased economic activity, job losses, and a rise in mental health issues.

The impact of the Covid-19 pandemic that broke out in recent years on economic operations is unavoidable, the economic risks are not symmetrical, and the impact of Covid-19 is distributed differently in the global economy. Some industries have benefited from the pandemic, while others have almost gone bankrupt. One of the sectors most impacted by the COVID-19 pandemic is the public and private health system. Opportunity cost is the concept of ensuring efficient use of scarce resources, a concept that is central to health economics. The massive increase in the need for intensive care has largely limited and exacerbated the department's ability to address routine health problems. The sector must consider opportunity costs in decisions related to the allocation of scarce resources, premised on improving the health of the population.

However, the opportunity cost of implementing policies to the sector has limited impact in the health sector. Patients with severe symptoms of COVID-19 require close monitoring in the ICU and in therapeutic ventilator support, which is key to treating the disease. In this case, scarce resources include bed days, ventilation time, and therapeutic equipment. Temporary excess demand for hospital beds from patients exceeds the number of bed days provided by the health system. The increased demand for days in bed is due to the fact that infected hospitalized patients stay in bed longer, shifting the demand curve to the right (see curve D2 in Graph1.11). The number of bed days provided by the health system may be temporarily reduced as there may be a shortage of beds due to the widespread spread of the virus. If this situation becomes unmanageable, supply decreases and the supply curve shifts to the left (curve S2 in Graph1.11). A perfect competition model can be used to express the concept of opportunity cost in the health sector. In perfect competition, market equilibrium is understood as the point where supply and demand are exactly the same (points P and Q in Graph1.11). The balance is Pareto optimal equals marginal opportunity cost. Medical allocation may result in some people being better off and others worse off. At this point, it is assumed that the market has produced the maximum outcome associated with the Pareto partial order. As a result, the opportunity cost increases when other patients cannot be admitted to the ICU due to a shortage of beds.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Opportunity cost


text:
Talk:Nutella

Differences between Nutella from each of the factories?
Everyone who likes Nutella knows that you can taste the difference between each factory. Can someone who has tried all of them describe the differences? — Preceding unsigned comment added by 2A00:EE2:600:900:30A3:D4BA:AC12:9EC7 (talk) 15:48, 3 July 2015 (UTC)

"not recommended for people with allergy to nuts"
Why is this needed? The fact that the product is called Nutella kind of makes it obvious that it contains nuts? -Grim- 17:06, 30 November 2007 (UTC)
 * Nutella is made with hazelnuts, but it may not be obvious that people with severe allergies to peanuts might also react to it, whether due to possible traces of peanuts, or maybe antigenic similarities between hazelnuts and peanuts. Either way, best to be safe, since some people can have life-threatening allergic reactions. Many companies will also put warnings on products to protect themselves against lawsuits, even in obvious cases. For example, I'm pretty sure that jars of peanut butter say "ALLERGY INFORMATION:CONTAINS PEANUTS". -- Kyok o  17:14, 30 November 2007 (UTC)

 * "jars of peanut butter say "ALLERGY INFORMATION:CONTAINS PEANUTS""... Are you serious?-Grim- (talk) 14:35, 28 February 2008 (UTC)

 * I think you overestimate people a little. ALTON   .ıl  21:49, 15 April 2008 (UTC)

 * Not sure if the BBC reference is right. I searched the article and found nothing on Nutella. If its just about nuts and allergy, isnt it kind of well known? kGomadam   —Preceding unsigned comment added by 99.148.195.122 (talk) 05:17, 16 January 2009 (UTC)

 * It's not just the companies who are taking labeling initiatives, Kyok  o  In the US, the Food and Drug Admistration *requires* the manufacturer of any food that may have *even the slightest chance* of coming in contact with an item on the FDA Severe Food Allergies List (what's the real name of the list called?) must have that suspect allergic ingredient stated on the label, whether it's used in the food product or not.   This gives you odd warnings like "This Product Contains Nuts of Nut Products" notices on peanut butter or obvious cautions like "This Product Contains Soy" on bags of bean curd or bottles of soy sauce.  Also, per USFDA regs, foods that don't contain such allergic products, but are processed and handled by the same machinery (a warehouse conveyer or lift, for example) have a very slight change of containing an allergic compound and must also be labeled appropriately. (i.e. "processed on equipment that also processes nuts and dairy")  For food items where a certain ingredient name is not readily identifiable by Average Moe Consumer, FDA regs require to list the technical source of the ingredient - if a food has milk protein " processed casein" as one of it's ingredients, then the label must read "Contains Dairy"  Likewise "hydrolyzed vegetable protein" (usually derived from soybeans, as they're quite high in protein,) earns the item "Contains Soy" comment.  Again with Gluten, Shellfish or other important allergens.  As  Kyok  o  said above a couple of years ago, it's a disclaimer against lawsuits, but more than that it's about labeling safety in processed foods.

 * The US went at this in earnest beginning with the FDA's Food Allergen Labeling and Consumer Protection Act of 2004 and various works in progress. For the curious, The US FDA keeps a basic FALCPA page with more information on the subject matter in regards to US regs on Yet Another US FDA Page.  IMHO, some mildly interesting information, if not a bit disturbing  -- just when *did* humans start becoming more food alergic?  Is it just an American thing?  Seems I've read quite a few stories out of the UKoGBNI and Her antipodal commonwealths over the past years, they I may not have been listening correctly.  ;-)
 * Fernblatt (talk) 06:15, 21 March 2009 (UTC)

 * Re "The fact that the product is called Nutella kind of makes it obvious that it contains nuts?"
 * You mean, like Grape-Nuts cereal, Chock full o’Nuts coffee, and Beech-Nut baby food? ☺ --Macrakis (talk) 23:24, 27 February 2011 (UTC)

Type-o
Can't seem to log in on my phone, but the title of the book cited is ' Chocolate: The Saga ...' — Preceding unsigned comment added by 184.96.233.244 (talk) 17:14, 18 February 2012 (UTC)

Advertising complaints
TRANS FATS IN NUTELLA? Since it's much like peanut butter, the question is inevitable--at least for people who want to know what they're eating! I have contacted the company in Italy several times with this simple question, and they have steadfastly avoided giving me a clear yes-or-no answer to the question: 'does their product contain trans fats (i.e. partially hydrogenated veg. oil)?' Instead, they informed me that the vegetable fat in Nutella is 'very healthy' nut oil. From this, I conclude that the product must indeed contain industrial trans fats, only they don't want to admit it (for if Nutella didn't contain these, there should be no problem for them to state the fact--and it would be an advertising plus for them to be able to say so). The USA website gives no information, and there is no e-mail address. The info there about the peanut oil seems intended to convince people that the oil used is no issue. And why is there no recipe given for Nutella sold in Denmark? Perhaps because it is not available there, since trans fats are practically banned in that country? (Please don't remove this comment--it is intended to contribute to the discussion which has already been started here--thanks.) —Preceding unsigned comment added by 83.21.141.224 (talk) 12:22, August 28, 2007 (UTC)

 * Why would you assume that there are trans-fats in Nutella? The purpose of using partially hydrogenated oils in food production is to make oils that are normally liquid at room tempurature (~20°C, 68°F)(i.e, those with predominantly unsaturated fats) become solid or semi-solid at room tempurature (highly saturated fats). Nutella (at least in the USA), uses palm oil, which is semi-solid at room tempurature (high in saturated fat) and does not need to be hydrogenated in order to remain semi-solid. The ingredient list clearly states "modified palm oil", and in this case, the modification consists of a process to REMOVE some of the unsaturated fatty acids from the palm oil, giving it a higher concentration of saturated fat. Hydrogenation, on the other hand, is a process that chemically CONVERTS existing unsaturated fatty acid molecules into saturated fatty acid molecules, creating artificial trans-fats as a byproduct. Food labeling laws are quite strict in the US, and if partially hydrogenated oils are used, they MUST be listed in the ingredients as "partially hydrogenated", not simply as "palm oil" or "modified palm oil", or "vegetable oil". Since the label does not indicate the presence of hydrogenated oils and modified palm oil itself contains contains no naturally occurring trans-fats (since it is not an animal product), we can reasonably conclude that Nutella DOES NOT CONTAIN TRANS-FATS. -Diego Gravez 00:13, 6 September 2007 (UTC)

 * > Why would you assume that there are trans-fats in Nutella?
 * There definitely used to be, at least in the US. I looked at the list of ingredients a couple of years ago, and was perplexed by the claim of "0 g trans fats" given the presence of hydrogenated oils in the list of ingredients. I wrote to them and they confirmed my suspicion that the "0 g" was merely the result of rounding down, which is apparently allowed under what passes for US law. (I believe that there has been a change in the ingredients in the US within the past year, so this may no longer be the case.) However, at least in the US, industry is constantly trying to wiggle out of its responsibility to society by (re)writing the law to allow deceptive labeling, and has made attempts to allow hydrogenated oils to be called by different names. Most people don't have the time to keep up with never-ending stream of deceptions allowed under US law. Maybe the Ferrero company is above this. I don't know. But, in answer to your question of "why would you assume ...", the reason why is that many industries in the US cannot be trusted to tell the truth. Thomas.Hedden (talk) 01:58, 15 January 2009 (UTC)

I want to clarify my removal of the advertisement complaints section. Simply put, it's unnecessary. There's only one verifiable complaint -just one!- not many. There must be significant dissent with Nutella's advertising claims, otherwise it isn't worth mentioning on Wikipedia. One person's viewpoint skews the reader's perception. Sure, it was a silly commercial, and the biggest point was never even made by the plaintiff; that is, the children's teacher was not billed or certified as a dietitian and has zero authority on the subject. She also may have no idea what she's even talking about.

Also, the part about sugar was incorrect. Sugar by itself is a high GI-food, but I doubt these kids were packed off to school with lunchboxes full of pure crystalline sucrose. Other food will lower the glycemic index of the carbohydrates (like sucrose, which is what most people think of when "sugar" is mentioned) in their meals. The US Dietary Guidelines might have mentioned something about the sugar rush if it mattered in meal planning. Check bullet #5, it just talks about moderation.

I seconded. Dancheng 13:15, 2 September 2006 (UTC)

 * I'm removing the POV notice as this doesn't constitute a POV dispute.... BCorr | Брайен 19:51, 4 September 2006 (UTC)

Ferrero
Ferrara makes it. as far as i know it's from italy so why to mention that the french places sell it?????????? No actually it is Ferrero SpA, which is in Alba in Piedmont. Ferrara is a city in another region of Italy. Zisa
 * Actually, the company is Ferrero in Germany (or perhaps Switzerland).

 * Why mention it? Have you tried a Nutella croissant or a Nutella crepe? The Italians might have invented the stuff, but when it comes to serving it, the French have definitely taken Nutella to a new level! —Preceding unsigned comment added by 79.6.57.196 (talk) 13:51, 1 October 2007 (UTC)

 * The company's name is indeed Ferrero, and yes, it is based in Italy. One can easily tell that by all the work on Nutella's official Italian site and Nutella's community site hosted on the same place, something you won't find on the foreign versions (like the US one itself). In fact, I'm thinking of adding those two links to the article.

 * About the French comment, Nutella is a very famous product all over Europe. The crêpes comment was probably added because people in France discovered that it goes well with Nutella, thus becoming a popular snack. I guess that's all. Mackeriv 04:26, 14 Apr 2004 (UTC)

There may be more than one formula of Nutella. The ingredient list in the article matches the one on the official U.S. site (http://www.nutellausa.com/nutrition.htm). I have seen containers of Nutella from Italy, however, and they do not appear to list any partially hydrogenated oils in the ingredients (the only oil appears to be listed as "oli vegetali," or vegetable oil). I can't say for sure, but I expect that Nutella from Europe, or at least Italy, does not contain any trans fats. Can anyone confirm this? I found a discussion (thread starts at post 11) on just this topic, but no definitive answer. Optimizer 22:28, 14 Mar 2005 (UTC)

 * The ingredients posted are in fact from a US jar. I strongly suspect that the actual ingredients in Nutella are the same everywhere it is made.  I think the difference you see may come from differing requirements in how ingredients are listed.  Partially hydrogenated peanut oil is a type of vegetable oil, so both could be referring to the same physical substance.  While this is all speculation, we could get closer to the answer by finding out if any products in Italy specifically mention hydrogenated oil in their ingredients.  -SCEhardt 05:04, 15 Mar 2005 (UTC)

 * Based on subjective tests, the formulation of Nutella does in fact differ by the country in which it is produced. The Nutella sold in Germany is, for example, vastly superior to that made in the US plant, while being only a slight improvement over that produced in Austria. This is no doubt why Europeans eat the stuff by the ton, while it has yet to make much of an impression on American consumers. If you have ever had a Coke in Europe, you'll know that companies inexplicably change formulations of products based on 'local tastes,' which I expect involves finding the cheapest possible production methods and ingredients in each country.

About the pronunciation of "Gnutella" - I was under the impression that software names derived from the GNU project were pronounced with a hard 'G' (to distinguish it from the animal I suppose) like G'nome (unlike the garden gnome), etc. --Millard73 05:24, 28 September 2005 (UTC)

Nupedia
Was this term also the precursor of the coinage of Nupedia which later became Wikipedia? (unsigned comment from anon)

Nudossi?
Can anyone confirm the claim that the East German equivalent was called Nudossi? Considering Ossi is a West German semiderogatory term for an East German, it seems more likely that this is a joke. --Angr ( tɔk ) 12:39, 12 January 2006 (UTC)
 * It looks legit to me unless it is an incredibly prevalent joke. See: - SCEhard  T  14:13, 12 January 2006 (UTC)

 * It is true! However, this product exists since the late 1960's. The term Ossi was almost unknown at this time, particularly in East Germany. The use of Ossi and Wessi emerged in the 1990's.
 * see also: http://vadossi.de/nudossi/index2.html Mintaru 06:11, 19 February 2006 (UTC)

!Yum!
I eat nutella everyday in the morning it tastes very nice it is chocolatey. Why does it sometimes go very runny in the bottle? Do people in other countries eat nutella? I never knew this site had such a broad range of topics it even has stuff on nutella! yum! —Preceding unsigned comment added by 203.26.16.67 (talk)
 * Yes, it is sold in the States and it goes runny becuase it relates to science, becuase it expands with the heat.  K ilo-Lima|(talk)
 * When I'm having 'fat' days, I like to drink Nutella. Women's psychology... it makes me feel fatter... but we enjoy feeling miserable, I think. 58.166.243.40 11:50, 25 June 2006 (UTC)
 * Is there a food group that includes strange brown sauces such as Nutella, Vegemite, and Marmite? - Amorwikipedia 20:05, 26 December 2006 (UTC)
 * This article is not NPOV. If it does not assert unequivocally that Nutella is the most delicious food on Earth, then it is biased against Nutella. Octavabasso (talk) 16:33, 11 October 2009 (UTC)
 * Perhaps the extremely high sugar content of this product should be made clearer in the article? It's mostly sugar, which may account for why people like it.  Most chocolate bars have less sugar.  One might also argue that it's an awful food product to give to kids (because of all the sugar) but you'd need to cite a reference. 14.200.208.126 (talk) 04:56, 9 February 2011 (UTC)

Pronunciation
In english, I have always heard the 'u' pronounced as a schwa. What's the source for the pronunciations given? Stevage 14:35, 29 March 2007 (UTC)
 * I've always heard it pronounced as noo-tell-uh
 * Clearly it varies from place to place. In southern England I think I’ve always heard the first syllable pronounced to rhyme with ‘nut’. Err, as ‘nut’ is pronounced in southern England. How is it pronounced in adverts—again in different parts of the world? That would be semi-authoritative. —Ian Spackman 07:02, 11 July 2007 (UTC)

I think this needs to be specified. I've NEVER heard anyone say it with a schwa in the first syllable. At least in America, it's "noo-TELL-uh". Can we change this something reflecting the US/UK difference in pronunciation?

I agree. I have lived in several regions in the US and I have NEVER heard the product referred to as nut-ELL-uh (first syllable rhyming with "nut", whether nʌt, or nət), but always as noo-TELL-a, so referring to that as the standard "English" pronunciation is misleading. -Diego Gravez 21:30, 5 September 2007 (UTC)

 * I know I'm 4 years late here, but here it is being pronounced with a schwa: http://www.tellyads.com/show_movie.php?filename=TA4574 — Preceding unsigned comment added by 122.59.185.240 (talk) 09:46, 22 August 2011 (UTC)

Most Canadians switch between either pronunciation. Yay for multiculturalism.

Late to the game, but I (American, East Coast) pronounce it NUH-tell-ah Lovellama (talk) 01:53, 18 July 2010 (UTC)

Given that this is from origin an Italian product I can confirm that the Italians pronounce it as noo-TELLL-a. Cbetta (talk) 11:57, 29 May 2011 (UTC)

 * Okay, this is bordering on original research but this German TV advert for Nutella seems to suggest that User:Cbetta may be right. Most of the TV ads in German never pronounce the product name, but in this one there is a small child who does. I'd expect the manufacturer would get the pronunciation right in their own TV adverts... —Tom Morris (talk) 12:34, 29 May 2011 (UTC)

I'm of Italian origin. The American english pronunciation is closer to the real thing: Noo-tell-ah. Except the "oo" part for the "u" should be a short sound rather than the "oo" sound. A bit like some older English people pronounce the "u" in "bus". Modern english has changed the "u" to be more like an "ah" sound and that is not how to pronounce the "u" in Nutella. Also, in the article is states that Nutella is prononuced "Nut-tell-ah" in Italian (the language of origin of the name) but in Italian, you cannot add a letter where one does not exist. There is no double "t" in Nu-tel-la. 203.214.22.116 (talk) 22:23, 17 August 2017 (UTC) Typo correction203.214.22.116 (talk) 22:24, 17 August 2017 (UTC)

I know I may be a bit late to this discussion, but I do think a UK IPA pronunciation should be added. As a Brit, I've only ever heard nut-ELL-ah and only heard noo-TELL-ah on American TV shows or videos or in Europe. It is much more common in the UK to say it nut-ELL-ah therefore I think it should be added to the article. Heinzbakedbeanz (talk) 06:33, 27 September 2020 (UTC)

Ingredients - USA
Hello, vanillin is not considered an artificial flavour-its substitute bourbonal is. 01:46, 12 April 2007 (UTC)

wrong, "Artificial vanilla flavoring is a solution of pure vanillin, usually of synthetic origin" —Preceding unsigned comment added by 173.34.95.41 (talk) 06:36, 5 October 2009 (UTC)

Containers and glasses
What is a stereotypical container? --Gbleem 23:21, 1 June 2007 (UTC)

I agree with Gbleem that a bit of history on the containers and glasses is missing. As far as I can remember back the containers have been pretty much the same, but there has always also been other containers including the 1KG, 2KG, and sometimes 5LG and 10KG jars.

Next to that there has always been the option to get Nutella in little glasses that can be used as drinking glasses after they're emptied. These glasses also come in collectors editions with cartoons on them. I would love to find some more info on the history behind this, especially seeing as how the glasses haven't really changed in years. Cbetta (talk) 12:02, 29 May 2011 (UTC)

In Italy the jars can be find in many different sizes: 30 grams, 250 grams, 400 grams, 750 grams, 1, 2, 3, 5 and 10 kilos. — Preceding unsigned comment added by 93.41.197.169 (talk) 21:43, 2 June 2011 (UTC)

Competitors
In Australia "Sweet William"? Never heard of it. "Sweet william spread" only yields 4 results in Google. I'm deleting it. 203.171.193.113 07:24, 8 July 2007 (UTC)
 * That search is probably too restrictive. Here's a slightly better one, which yields about 20,000 hits, including each of the products offered by that company. Adding the word "spread" to the search reduces it to about 1,000 results. I'm not going to undo your edits, I'm only citing this so other editors can inspect the results. Mindmatrix 14:28, 8 July 2007 (UTC)
 * It’s nut-free, which seems to me to make it distinctly marginal. —Ian Spackman 07:15, 9 July 2007 (UTC)

Availability in USA
Nutella was available in the USA in the 70's. As a child I would buy it at local mainstream food stores. It did not cost much more than a jar of peanut butter so it was not too expensive and certainly not hard to find. But than, maybe this was only true in the New York metroplitan area where I grew up. The article as written is misleading on this point. —Preceding unsigned comment added by 69.125.146.118 (talk) 14:50, 30 October 2007 (UTC)

 * just bought a jar yesterday in amarillo walmart —Preceding unsigned comment added by 69.55.20.229 (talk) 19:41, 17 February 2010 (UTC)

Popular in Canada?
Nutella popular in Canada?? Where?? Sure, it might be available in grocery stores but the bottles are always dusty because nobody buys it. I would guess that it might be popular with European expats but apart from that, the average Canadian has probably never bought the stuff or even heard of Nutella. —Preceding unsigned comment added by 209.226.4.163 (talk) 15:10, 16 April 2008 (UTC)

Okay, I don't know which Canada you're living in, because where I live, it's quite popular.68.149.121.27 (talk) 03:19, 9 February 2009 (UTC)

Ditto, especially in Western Canada.

Listed ingredients table
Can someone fix the listed ingredients table so it appears under composition like it's supposed to instead of at the bottom of the page? I'd do it myself, but I'm at a loss when it comes to computer code. PeRiDoTs13 (talk) 20:10, 11 November 2008 (UTC)

Picture caption
The jar in the picture is from Germany, not from Spain as it said before. One can even see the German print ("mit dem Besten aus gut 1/3 Liter entrahmter Milch") on the label.--86.103.202.16 (talk) 17:45, 6 June 2009 (UTC)

Article was gutted
On 2009-10-19, this article was robust, if somewhat bloated.

On 2009-10-20, the article was completely gutted by an overzealous editor, SluggoOne. 75% of the article was wholesale removed at once. Good form.

I'm going to reinstate the ingredients list. If anything else of value was lost, I don't personally know about it, but someone else might. For me, it's nice to be able to benefit from the superior consumer protection and labeling laws in countries outside of North America. Please don't take that away from us. Especially in Canada, you can hide an entire food product under "spices" or "natural flavor". It's bad.

I'm bringing this up because SluggoOne never bothered to. That, to me, is important. I'm sorry, but I refuse to assume good faith here; that was forfeited when such a massive edit was undertaken without any discussion whatsoever. Too often have I seen articles secretly deteriorate because people remove information in ostensibly mundane edits. Please discuss large scale changes on the talk pages, rather than hiding them in nondescript edit summaries. Thanks.

--99.240.223.41 (talk) 22:24, 19 November 2009 (UTC)

I agree, SluggoOne edited the article considerably, some useful information got lost in that edit. Still a good article. — Preceding unsigned comment added by 80.3.102.203 (talk) 15:03, 15 April 2012 (UTC)

Cocoa
Cocoa is a disambiguation page; likely all links to it from this article intend cocoa powder but there is a chance they intend chocolate liquor. I have tagged some of the links dn. --Una Smith (talk) 21:49, 8 January 2010 (UTC)

Vegetarian?
Does Nutella is vegetarian? —Preceding unsigned comment added by 66.185.62.208 (talk) 14:49, 23 February 2010 (UTC)

 * Nutella does it vegetarian, yes. --92.74.18.114 (talk) 19:42, 23 February 2010 (UTC)
 * source? 177.105.90.10 (talk) 18:02, 1 June 2024 (UTC)

Grapeseed oil, really?
According to the ingredients list, the Polish version would contain grapeseed oil. I highly doubt that (rather expensive stuff that) - rapeseed seems much more likely. —Preceding unsigned comment added by HStreek (talk • contribs) 07:57, 18 May 2010 (UTC)
 * I'm inclined to agree. We could do with a reliable source that lists the ingredients, but despite searching I cannot locate one. magnius (talk) 11:27, 18 May 2010 (UTC)
 * The article used to say "rapeseed". I managed to pinpoint the edit where this was changed into "grapeseed". The edit's author was an anonymous IP, and this is its only edit. So, even knowing nothing about Polish Nutella, I'd be inclined to revert to "rapeseed". Any thoughts? Goochelaar  (talk) 13:39, 18 May 2010 (UTC)
 * I support that, Grapeseed is unsourced anyway, and as Rapeseed was the original word it should be used. magnius (talk) 13:41, 18 May 2010 (UTC)

Ingredients list
I'm a little confused by the ingredients list and it's not explained - does the list reflect an actual difference of ingredients in different countries, or is it the same product everywhere, and the list is meant to demonstrate divergent international labelling requirements? For example, I know rapeseed oil and vegetable oil are clearly different (I notice the uncertainty of this fact), but palm oil can also be listed as vegetable oil (which it is). Similarly cocoa vs reduced fat cocoa (cocoa powder is by definition cocoa solids with most of the cocoa fat removed), or vanillin vs flavouring (vanillin is a flavouring), or whey vs lactose (lactose being the principle constituent of whey). Without explanation this listing is pretty unhelpful. Is it a different product in different countries, or not?90.194.145.141 (talk) 00:51, 6 February 2011 (UTC)

What is the point of the ingredients list table? The vast majority of the entries are identical from country to country; a few are minor variants (vanillin vs. flavouring); and some have slightly different quantities (different rules on how to measure?). In only one case are there apparently substantive differences: is the oil palm or rapeseed? Do we really believe that Polish and Romanian Nutella are actually that different, or is this just some sort of error? In any case, the whole table seems pointless. --Macrakis (talk) 13:33, 24 February 2011 (UTC)

What happened to the nutrition facts?
They used to be on here, and they are absolutely useful information, why were they deleted? It seems like it's a lot shorter than it used to be, I kinda understand the deletion of the international ingredients difference table, but what is the need for deleting so many large swaths of an already somewhat short page? ," said The Person Who Is Strange. ~Yup. It's all true.  Click here for more.  My page is outdated, but there are a lot of boxes. 04:48, 3 September 2011 (UTC)

 * The article currently reads:
 * About half of the calories in Nutella come from fat (11 g in a 37 g serving, or 99 kcal out of 200 kcal) and about 40% of the calories come from sugar (20 g, 80 kcal).
 * Do we really need to know much more detail about the nutritional value of Nutella? And in any case, since the recipe varies from country to country, the detailed nutritional analysis will as well. I think that's all trivia. --Macrakis (talk) 17:25, 3 September 2011 (UTC)

Ingredients are incomplete
According to the Nutella website (for America, anyway), Nutella contains soy oils. This is not reflected, and I'm not sure my edits are taking hold because of the autoconfirmation. http://www.nutellausa.com/ingredients.htm Cocomaan (talk) 14:06, 30 March 2012 (UTC)

World Nutella Day
According to http://www.nutelladay.com/ February 5th 2012 is the 6th World Nutella Day. Their press page http://www.nutelladay.com/press/ has several cites. Should this be added to the article? — Preceding unsigned comment added by 131.107.0.81 (talk) 18:17, 3 February 2012 (UTC)

French Nutella Tax
The French seem to have passed (or about to pass) a tax on Palm Oil. Nutella is 20% Palm Oil, hence why the tax is dubbed the Nutella-tax. Might be worth covering.

http://www.guardian.co.uk/world/2012/nov/12/france-nutella-amendment-international-row Cbetta (talk) 16:50, 20 November 2012 (UTC)

Ingredients lists as original source?
User:Cbetta asked me to have a look at this article. In the current edit history, there is some back and forth about whether quoting an ingredients list counts as WP:OR. I would suggest that it isn't for the following reason. An ingredients list is a self-published primary source. I don't see the fact that it's on the side of a jar to be that problematic. In fact, some ingredients lists and dietary information notices on foodstuffs is certainly going to be held legally by the governments of various nations to a higher standard than things like newspapers, which we do consider a reliable source.

This kind of thing probably ought to be something WikiProject Food and drink decide across food articles generally. —Tom Morris (talk) 21:13, 22 November 2012 (UTC)

 * The refe on this section, http://www.nutellausa.com/ingredients.htm, also list these. I removed vegetble oil(mainly palm..) as only palm oil is mentioned in the reference. Murry1975 (talk) 05:22, 26 November 2012 (UTC)

Sugar
There's been a flurry of edits back and forth on sugar after this post http://www.reddit.com/r/todayilearned/comments/13kevd/til_that_the_first_ingredient_in_nutella_is_sugar/. It used to state 50% sugar, was edited to 15%, back and forth a few times and ended up being removed. According to the nutrition facts on nutella's usa web page http://www.nutellausa.com/nutrition-facts.htm there's 21g sugar in a 37g serving. That's about 57% sugar. I don't feel comfortable editing the page myself. Just wanted to bring it up.

Bibiarndal (talk) 04:14, 23 November 2012 (UTC)

 * That only applies to the USA. Recipes vary regionally. Alohamesamis (talk) 14:35, 25 November 2012 (UTC)

 * So what? That can be easily mitigated by adding the qualifier "In the United States...". The information is not original research if it has a credible source. Ingredients for the Italian version of the product can be found here, which clearly states that sugar constitutes 56.7% of the product (the line "di cui: zuccheri" translates to "of which: sugar"), and hazelnuts represent 13%. The US product, from the source mentioned above, has sugar as 56.8% of the product. [User:Mindmatrix|Mind]]matrix 17:04, 26 November 2012 (UTC)
 * Zuccheri means sugars, not sugar. If someone were to read "sugar", they would assume that it refers to sucrose. Sugars has an altogether different connotation. Alohamesamis (talk) 20:43, 26 November 2012 (UTC)

 * Then the statement "Nutella consists of 56.7% sugars" is valid. We can include a parenthetical listing the sources of the sugar from the ingredient list (namely: sugar, hazelnuts, milk solids). [User:Mindmatrix|Mind]]matrix 22:30, 26 November 2012 (UTC)
 * I don't believe that the ingredients list provides a breakdown of where the sugars come from. I have nothing against listing the amount of sugars, once it is noted that the proportion listed refers to the amount in one particular country, rather than claiming to represent nutella worldwide. Alohamesamis (talk) 22:55, 26 November 2012 (UTC)
 * Regarding the claim it's for only one country - the nutritional label for the US has the same proportions for sugars, as does the one for Canada and Mexico (Nutella for these markets is produced in Canada, specifically Brantford, Ontario). We get the same results for Italy, UK and Ireland, France, Belgium, Spain, Sweden, the Netherlands, and other European nations (don't know about Germany, as Ferrero's site for Germany seems to be void of info). I don't have the energy to list them all. The product for South American and Oceania countries does appear to differ, but not much. For example, New Zealand and Australia are 54.4% sugars. The China site is marketing fluff. [User:Mindmatrix|Mind]]matrix 02:54, 27 November 2012 (UTC)
 * A german ingredient list has the ingredient with the highest quantity on top, though not necessarily specifying percentage. If it says "Zucker" (sugar) it means sucrose - fructose syrup or glucose syrup would be referred to separately. A german nutrition list however lists carbohydrates and to which degree they are made up of sugars, here "Zucker" means not only sucrose, but all types of sugar contained in the product, with no regard to whether they are added or a natural component of an ingredient. — Preceding unsigned comment added by 46.115.64.85 (talk) 23:01, 12 April 2013 (UTC)

Gobbledook
"Now that the paste is what is societally identified as Nutella"

What? Even given the silly use of "societal" for "social", which I suppose we have to just accept now, this makes no sense. --31.185.192.220 (talk) 13:42, 10 October 2013 (UTC)

Broken Reference
Reference #2 (Carridice, Adriel. "The History of Nutella (3)". NutellaUSA.com. Retrieved 2013-01-28) is broken. Anyone has an alternative? --199.203.92.42 (talk) 13:08, 21 December 2015 (UTC)

 * I've added archive links for all three uses of that site as refs. [User:Mindmatrix|Mind]]matrix 13:36, 22 December 2015 (UTC)

Food energy
The 'Food energy' line in the info box seems to be constrained to just state a number (of kcal) without indication of portion size. A Nutella label shows 80 kcal for a 15g serving. But I'm not sure how to fix this. Can anyone help? Onanoff (talk) 08:48, 17 March 2017 (UTC)

Gianduja not created by Ferrero.
Article says:

The traditional Piedmont recipe, Gianduja, was a mixture containing approximately 71.5% hazelnut paste and 19.5% chocolate. It was developed in Piedmont, Italy, due to a lack of cocoa beans after post-war rationing reduced availability of the raw material.

With a citation from the Nutella USA website

But in reality, Guanduja https://en.m.wikipedia.org/wiki/Gianduja_(chocolate)

Was invented in Turin, Piedmont during French occupation (1796-1814)

Some parts of this article also seem to imply credit to Ferrero for the creation of Gianduja 2001:8003:2463:ED00:ADB9:112:D45E:9AAC (talk) 04:14, 21 December 2017 (UTC)

Advertising Nutella
I have seen your add on television and it’s not right as in schools in the uk you cannot give children Nutella due to some people being allergic but it clearly shows a teacher in a play ground spreading Nutella clearly your company have not done any inquiries into this situation Gilliantones (talk) 10:25, 23 January 2018 (UTC)

Nutella riots?
CNN: "It is not the first time that demand for Nutella has turned violent." nutella-discount-sparks-chaos Gråbergs Gråa Sång (talk) 10:54, 27 January 2018 (UTC)

Chocolate spread?
Is it a chocolate spread or not? Link to chocolate spread keeps being reverted. 71.198.89.109 (talk) 16:08, 13 April 2019 (UTC)

 * Yeah, at least it was always what they tell me, let's start:
 * 1- Well, any soft or pasty texture can be regarded as being a spread, although this is too generalized, still, it remains being a spread.
 * 2- According to Nutella story, it was initially block-shaped and it was sliced to spread on bread, later becoming a cream, as everyone knows nowadays, and if you go to the dictionary you will see that "cream" and "spread" are synonyms.
 * Also, every website or whatever, always refer to Nutella as a spread, in this case, hazelnut. 177.105.90.10 (talk) 18:18, 1 June 2024 (UTC)
 * I just can't put the source, because that's not "authoritative", according Wikipedia, what is unfair and needless 177.105.90.10 (talk) 18:30, 1 June 2024 (UTC)

Nutella and Gianduja
My documentation of hazelnuts and cocoa being used together in Piedmont was deleted because it "Seems out of the scope for the Nutella page". Presumably because it ALSO gives info on Gianduja. But the existing entry already mentions the latter and gives the (false) impression that it was invented after World War II.

Basically, the mixture of the two was originally known as gianduja. That already existed as a candy long before the reference given from the Nutella page. It is NOT out of scope for the Nutella page because Nutella itself is said to derive from gianduja.

Maybe my own entry needs to be rewritten. But just deleting it leaves people with the false impression that the product which became Nutella did not exist until after World War II. 23.113.53.110 (talk) 21:24, 13 April 2020 (UTC)
 * Separated "Pasta" from the link of just gianduja. Vaselineeeeeeee★★★ 22:33, 13 April 2020 (UTC)
 * I don't get what's going on here at all. The product in question was called Pasta Gianduja: "He created Pasta Gianduja: a small loaf of chocolate hazelnut paste meant to be sliced and served on bread. The same year he sold an initial batch of 600 pounds of Pasta Gianduja." https://www.thevintagenews.com/2018/01/06/napoleon-nutella/ Gianduja was already a candy at that point, and still is today; not the same thing as a paste made of the two ingredients. And why clarifying this point is considered irrelevant is beyond me. You will see numerous sites claiming that Nutella came about after the idea of cutting chocolate with hazelnuts appeared after WW2, when in fact it existed since just after Napoleon. Why ever would it be considered irrelevant that the mixture from which this paste was made, and the name applied to it, both pre-existed the dates given in the article?

23.113.53.110 (talk) —Preceding undated comment added 23:22, 13 April 2020 (UTC)
 * It doesn't need that long winded explanation. All it really needs is the link to Gianduja where it is explained. Altered: "...batch of Pasta Gianduja, derived from Gianduja." Vaselineeeeeeee★★★ 23:39, 13 April 2020 (UTC)

Nuttella is made out of melted chocolate or coca beansns????
Do we believe it's natural or is it made out of other chocolate we will never no except what they tell us 82.25.145.201 (talk) 21:25, 12 February 2022 (UTC)

Link to "chocolate spread" instead of "cocoa" and "spread"
The first line links to "cocoa" and "spread" but maybe it's more sensible to link to "chocolate spread" (https://en.m.wikipedia.org/wiki/Chocolate_spread) instead. Axelbrink (talk) 18:50, 15 June 2022 (UTC)

Moved gallery to Wikimedia Commons
Decided to move that removed gallery into the Wikimedia Commons page for Nutella under the header 3 "Nutella as an ingredient". I believe this would be a more suitable place to add large galleries of Nutella-related stuff.

Speaking of Wikimedia Commons, should we still do a Commons link to the category variant of "Nutella" or the article variant of "Nutella"? We are currently linking to Commons' category variant of "Nutella". Qwertyxp2000 (talk | contribs) 02:24, 19 September 2023 (UTC)

 * See WP:GALLERY. Veverve (talk) 06:37, 19 September 2023 (UTC)

title: Talk:Nutella


text:
Talk:Sicily

External links modified
Hello fellow Wikipedians,

I have just modified 4 external links on Sicily. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
 * Added archive https://web.archive.org/web/20140420062023/http://www.hindustantimes.com/india-news/newdelhi/gangs-of-tourists-invade-wasseypur/article1-925786.aspx to http://www.hindustantimes.com/India-news/NewDelhi/Gangs-of-tourists-invade-Wasseypur/Article1-925786.aspx
 * Added archive https://web.archive.org/web/20120912165936/http://www.worldheritagesite.org/sites/t1164.html to http://www.worldheritagesite.org/sites/t1164.html
 * Added archive https://web.archive.org/web/20101230060505/https://www.porsche.com/all/targaflorio/international.aspx to http://www.porsche.com/all/targaflorio/international.aspx
 * Added archive https://web.archive.org/web/20091030202145/http://faculty.ed.umuc.edu/~jmatthew/naples/symbols.htm to http://faculty.ed.umuc.edu/~jmatthew/naples/symbols.htm

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Cheers.— InternetArchiveBot  (Report bug) 00:23, 23 December 2017 (UTC)

Autonomous Status and Effective Degree thereof
I would like to question the following statement: "However, much of the autonomy still remains unapplied, especially financial autonomy, because the autonomy-activating laws have been deferred to be approved by the joint committee (50% Italian State, 50% Regione Siciliana), since 1946." First, a citation should be given to support these claims. Second, much of the information contained in the official Statute (translated from Italian) contradicts the facts presented in that statement. See, for instance, pages 7; 13-15; 21-22. The link to the document is: http://pti.regione.sicilia.it/portal/page/portal/PIR_PORTALE/PIR_Statutoregionale/Statute%20of%20the%20Sicilian%20Regional%20Government.pdf

Please amend the text. Thank you. — Preceding unsigned comment added by 92.1.69.146 (talk) 19:04, 10 February 2020 (UTC)
 * ✅ Indeed the statement was probably made-up and inserted with by someone with incomplete knowledge of Sicily. Mottezen (talk) 06:55, 24 January 2021 (UTC)

A Commons file used on this page or its Wikidata item has been nominated for speedy deletion
The following Wikimedia Commons file used on this page or its Wikidata item has been nominated for speedy deletion: You can see the reason for deletion at the file description page linked above. —Community Tech bot (talk) 11:31, 17 March 2020 (UTC)
 * Flag of Emilia-Romagna.svg

Removal of statements with not RS
I have again removed two referenced sentences that had been already removed by an anonymous user. The main problem is the quality of the sources: the first is a blog on a newspaper, the second the website of a municipality. As far as the second sentence is concerned, the article is about Sicily, not the Kingdom of the two Sicilies, and the island was certainly not "one of the most industrialized areas of Italy". I suggest using RS, such as Mack Smith's masterful work on Sicily, where the situation of the island is explained, which was certainly more complex than the one described by the two removed sentences. Alex2006 (talk) 10:55, 3 December 2021 (UTC)

"Expand Italian" template
I propose the removal of the "Expand Italian" template; number of bytes of the Italian language Wikipedia page: 181,351 (https://it.wikipedia.org/wiki/Sicilia), only 20,000 more (en.wiki: 162,659; https://en.wikipedia.org/wiki/Sicily). JacktheBrown (talk) 10:04, 7 April 2024 (UTC)

title: Talk:Sicily