Weike Feng

Jean-Michel Friedt

Giovanni Nico

Gilles Martin

Motoyuki Sato

Motoyuki Sato Passive

Passive bistatic SAR imaging and interferometry by satellite digital TV signal

Keywords: Passive bistatic radar (PBR), Satellite digital TV signal, Synthetic aperture radar (SAR), SAR interferometry

I. INTRODUCTION

Recently, passive bistatic radar that uses existing broadcasting signals, communication signals, and navigation signals has drawn a lot of interests [START_REF] Griffiths | An introduction to passive radar[END_REF][START_REF] Gromek | Experimental results of passive SAR imaging using DVB-T illuminators of opportunity[END_REF]. Compared to other illuminators of opportunity, such as WiFi and terrestrial TV signal, PBR using satellite digital TV signal has several advantages, including: 1) one TV channel can provide a frequency bandwidth larger than 30 MHz; if multiple TV channels are combined, a bandwidth larger than 150 MHz and thus a sub-meter range resolution can be obtained; 2) since its working frequency is at Ku band, a high-resolution change detection capability via interferometry technique can be achieved, like that in ground-based SAR [START_REF] Nico | Measurement of pier deformation patterns by ground-based SAR interferometry: Application to a bollard pull trial[END_REF][START_REF] Feng | GB-SAR interferometry based on dimension-reduced compressive sensing and multiple measurement vectors model[END_REF]; 3) a larger illumination area and a clearer reference signal increase the usability and performance of the PBR system. For example, digital TV broadcasting with Broadcasting Satellite (BS) on the geostationary orbit of 110 degrees East longitude (BS 110°E) can provide services for the whole area of Japan.

However, there are also some difficulties when using the satellite TV signal for PBR applications, including: 1) the power density of the satellite TV signal on the Earth surface is normally much lower than some other signals used for PBR applications, such as FM and DAB, resulting in a lower signal to noise ratio (SNR) and a shorter detection range; 2) if some commercial-off-the-shelf (COTS) components are used to reduce the system cost, some modifications must be conducted to synchronize both frequency and phase between the reference channel and the surveillance channels for long-time coherent measurement; 3) the waveform of the digital TV signal is not designed for radar applications, its signal structure, including spectrum properties, pilot signals, and guard intervals, will introduce undesired artifacts in the range direction when the classical cross-correlation processing method is used; 4) when multiple frequency bands were combined to increase the range resolution, frequency gaps among different TV channels cause high-level artifacts in the range direction [START_REF] Feng | Passive radar imaging by filling gaps between ISDB digital TV channels[END_REF].

To solve these problems, we proposed a hardware design method and several processing algorithms in this paper. Firstly, we describe an LNB synchronization method to increase the integration time for SNR improvement. Secondly, we use the inverse filter technique to reduce the influence of the TV signal structure. Thirdly, we apply the super spatially variant apodization (Super-SVA) method to fill the frequency gaps among multiple TV channels to suppress the artifacts. Finally, based on a PBR prototype system using COTS components, SAR imaging and displacement estimation experiments are carried out to validate the proposed methods. The spectrum of the used satellite TV signal is shown in Fig. 1, where the local oscillator frequency of LNB is about 10.601 GHz. BS and communication satellite (CS) signals are broadcast by different satellites that are on the geostationary orbit of 110 degrees East longitude (110°E). Each TV channel has a frequency bandwidth of 34.5 MHz. If twelve channels of BS or CS are combined, a 475.5 MHz frequency bandwidth can be achieved, resulting in a maximal bistatic range resolution of 0.32 m. We note that, in this study, only CS signal is used for simplicity. BS signal transmitted via both left-hand and right-hand circular polarizations will be used for multi-polarization applications in the near future.

II. DESIGNED SYSTEM OVERVIEW

A. Adopted ISDB-S signal

B. Designed radar system

The designed radar system is shown in Fig. 2. It has three parallel receiving channels, one reference channel and two surveillance channels. For reference channel, a 45-cm parabolic antenna is used, while only the feed-horns of parabolic antennas are used for the surveillance channels to achieve a wider beamwidth. Three LNBs with a local frequency of 10.601 GHz are synchronized by an oscillator controller. To further amplify the received signal, three COTS BS/CS boosters were used, whose working frequency is from 10 to 2600 MHz and gain is from 26 to 34 dB adjustable. Surveillance antennas are mounted on a positioner to generate a synthetic aperture with a fixed step in the horizontal direction. The signal flow will be sampled by a digital storage oscilloscope with a sampling frequency of 10 GHz. Finally, the acquired raw data are transferred to a local PC for off-line signal processing, consisting in frequency gaps filling, SAR imaging, and interferometric processing.

C. LNB synchronization

Since COTS LNBs have different local oscillators, their phase differences will reduce the coherence of the three receiving channels. When the data are sampled in a short time, the phase difference is approximately caused by their local frequencies only. Thus, a simple phase difference estimation method can be used [START_REF] Feng | Passive radar imaging by filling gaps between ISDB digital TV channels[END_REF], consisting in: 1) Divide the signal into U short-length (T) subsets, within which the phase difference is assumed to be constant, i.e., f1t and f2t, where t=[0, T, ... , (U-1)T], f1 and f2 are the frequency differences between the surveillance LNBs and the reference LNB; 2) Do crosscorrelation between the co-located reference and surveillance antennas to obtain the phase of peaks in each subset, which gives e -j2πf 1 t and e -j2πf 2 t ; 3) Finally, do Fourier transform of the peak phases, providing us with f1 and f2.

However, since SAR imaging and interferometric processes are desired and a longer integration time can increase the SNR and increase the detection distance, coarse phase correction is not enough. Thus, an advanced LNB synchronization approach is further proposed, whose setup is shown in Fig. 3. Based on the unpublished NXP application note "X-tal driver for using multiple TFF10xx to the same X-tal as reference" describing the mechanism for locking multiple TFF10xx PLLs on the same reference as desired, a dedicated Pierce oscillator was built around a 25 MHz resonator and a 74HC04 inverter. The output of the Pierce oscillator feeds another 74HC04 used to generate three sets of in-phase and phase-opposition (180-degree phase shift) signals feeding the PLL inputs. Care must be taken on the one hand to tune the output voltage amplitude to acceptable levels (500 mVpp) using a voltage divider bridge, and on the other hand to include a DC-blocking capacitor (5.6 nF) between the oscillator output and the PLL to avoid DC-current leakage from the PLL, which would prevent PLL locking. Under the proper conditions, frequency/phase coherence was observed to be stable over tens of minutes, as needed for SAR measurement.

III. INVERSE FILTER AND FREQUENCY GAP FILLING

A. Cross-correlation and inverse filter

Normally, a cross-correlation method is used to estimate the delay of the target, given by 0

( ) ( ) ( ) int T a a sur ref s t s t dt       (1)
which can be implemented by Fast Fourier Transform, giving

( ) [ ( ) ( ) ] H H a a sur ref      s f s f s f (2)
where sref(t) is reference signal, ssur(t) is surveillance signal, a = 1 or 2 denotes the first or the second surveillance channel, (• ) * denotes the complex conjugate, χ(τ) is the range-compression result, τ is the expected time delay of the target, Tint is the integration time, Φ is the Fourier transform matrix, denotes element-wise multiplication, sref(f) and ssur(f) are the frequency domain signals of the reference and surveillance channels.

However, since the waveform of satellite TV signal is not designed for radar applications, the cross-correlation processing will introduce high-level artifacts in the estimation. A simple but effective method to solve this problem is to use an inverse filter to avoid the influence of the signal structure of the TV signal, which can be expressed as

2 ( ) [ ( ) ( ) / | ( ) | ] H H a a a sur ref ref      ' s f s f s f s f (3)

B. Frequency gap filling

To improve the range resolution, multiple TV channels can be combined to obtain a wider bandwidth. However, different TV channels are separated by frequency gaps to guarantee a high-quality signal transmission, introducing artifacts into the range compression result. Several spectral gaps filling methods can be used, such as auto-regressive (AR) based method, Super-SVA based method, and sparsity and low-rank property based methods [START_REF] Feng | Passive radar imaging by filling gaps between ISDB digital TV channels[END_REF]. In this paper, Super-SVA method is used for its simplicity and effectiveness. Based on the SVA algorithm, the range compression result of the n-th (n = 1, 2,...,12) TV channel is given by ,, [ ( )

( )] SVA H a n n a n   ' s f W f (4)
where () Wf is a nonlinear "cosine on pedestal" weighting function that can be expressed as

( ) 1 2 cos(2 / ), 0 0.5 W m m M       
(5) Then, the frequency gaps can be filled by Super-SVA via the following steps:

1) Perform Fourier transform of , The imaging geometry of the designed radar system is shown in Fig. 4, where the reference antenna is located at (0, 0) and the surveillance antenna is scanned along a rail from ( / 2, )

The designed passive radar system can acquire a time series of 2D SAR images of the scene with a temporal baseline of few minutes as the used geostationary satellite is continuously illuminating the area of interest. This allows many interesting interferometric SAR applications. For each pair of SAR images, an interferometric phase image can be generated by , where λ is the wavelength, which is 24 mm for the CS signal. Besides, we note that, since two surveillance antennas can be used, the developed system can also generate a high resolution Digital Elevation Model (DEM) of the imaging scene by properly setting a spatial baseline between the two surveillance antennas.

-( , ) ( , a )( r )
DEM generation experiments are on-going and will be further researched.

V. EXPERIMENT RESULTS

In this section, some experimental results will be shown to validate the designed radar system and the proposed processing methodologies. At the beginning, a time delay estimation experiment using the satellite TV signal was conducted, as shown in Fig. 5, where two parabolic antennas with synchronized LNBs were faced toward the CS 110°E satellite. Twelve TV channels were combined and inverse filter is used for range compression. The estimation results are shown in Fig. 6, where two different integration times are assessed. As we can see, by increasing the integration time from 1 μs to 100 μs, the SNR can be increased about 10 dB, which proves that the LNBs are well synchronized. Otherwise, the SNR will not be increased but decreased because the two receiving channels are not coherent [START_REF] Feng | Passive radar imaging by filling gaps between ISDB digital TV channels[END_REF]. However, as indicated by the black circle in Fig. 6, high-level periodical artifacts will be generated by the frequency gaps. By applying Super-SVA based frequency gap filling method, these artifacts can be well suppressed, as shown in Fig. 7, where the integration time is 100 μs. Furthermore, in order to check the coherence of two channels, 250 measurements were conducted with a period of 5 minutes, and the peak phase of the result was extracted, as shown in Fig. 8. It is observed that, the peak phase difference has a mean value of -0.16 degree and a standard deviation of 2.50 degree for 250 measurements. Based on the aforementioned methodologies, passive bistatic SAR imaging experiments were carried out, as shown in Fig. 9, where the surveillance antenna is sled along a rail to detect a metallic plate. The moving step was 5 mm and the total sledding length was 1.2 m. The range compression results for each surveillance antenna position and the SAR image obtained by the BP algorithm are shown in Fig. 10. As we can see, the metallic plate can be well detected and focused. At last, the displacement of the metallic plate, which was moved on a rail from 1 mm to 15 mm with a 1-mm step, was estimated. The acquisition time of each SAR image was about 45 seconds. The estimation results are shown in Fig. 11. It can be seen that the displacement of the metallic plate can be accurately estimated. The root mean square error (RMSE) of the estimation is about 0.27 mm.

VI. CONCLUSION

In this study, we developed a passive bistatic radar system using geostationary satellite TV signal with commercial-offthe-shelf hardware. LNB synchronization was used to increase the coherence for the long-time measurement and thus increase the SNR and the detection range. High range resolution was obtained by combing multiple TV channels. The artifacts caused by frequency gaps among different TV channels were reduced by means of a super-SVA based method. High azimuth resolution was achieved by moving the surveillance antenna on a rail to generate a synthetic aperture. Focused SAR images of targets were obtained by the back projection algorithm with reasonable approximations. Displacement of the target in the scene was estimated by the differential interferometric process. Compared to current GB-SAR system used for displacement estimation, the developed system is cheaper as it is does not need a transmitting unit. Multiple-direction displacement estimations can be obtained with multiple receivers using different bistatic geometries. Further work will be devoted to the generation of a DEM of the study area using an additional surveillance antenna. Multi-polarization capacity provided by the BS TV signal is also worthy to be studied. The potential applications of the developed system includes the continuous monitoring of landslides, buildings and dams.

Fig. 1 .

 1 Fig. 1. The spectrum of the satellite TV signal in Japan.

Fig. 2 .

 2 Fig.2. The designed PBR system using satellite TV signal.

Fig. 3 .

 3 Fig. 3. LNB synchronization setup.

Fig. 4 .

 4 Fig. 4. SAR imaging geometry.

1 R

 1 with L as the synthetic aperture length. The elevation angle of the satellite is35.3 sat  in Sendai (Japan) area. For the o-th (o=1, 2,..., O) surveillance antenna position, the range compression can be conducted by applying Fourier transform to the gap filled signal, giving ,, () SAR image of the target can be obtained by applying the back projection (BP) algorithm, giving amplitude of the point at (x, y),  is the path difference between the TV satellite to the target and to the reference antenna, the target to the o-th antenna position of the a-th surveillance antenna, and , by the linear interpolation process. Since the satellite is far from the experiment position, i.e., |yT| is much bigger than x and y, 1 R  can be approximately calculated by

Fig. 5 .

 5 Fig. 5. Time delay estimation experiment setup.

Fig. 7 .

 7 Fig. 7. Delay estimation result obtained by filling frequency gaps.

Fig. 9 .

 9 Fig. 9. SAR imaging of a stationary metalli plate.

Fig. 10 .

 10 Fig. 10. Top: Range compression results. Bottom: SAR image.

Fig. 11 .

 11 Fig. 11. Displacement estimation result.

ACKNOWLEDGEMENTS

This work was supported by JSPS Grant-in-Aid for Scientific Research (A) 26249058. The passive radar investigation is partly supported by the French Centre National de la Recherche Scientifique (CNRS) PEPS grant.


Daniel Levy

Simulating a Multiproduct Barter Exchange Economy

We describe a multiproduct barter trading experiment in which students exchange real goods in an open market based on their own personal preference. The experiment is designed for simulating a pure exchange market in order to demonstrate the role of money and its functions in real economies by showing the limitations and inefficiencies of the traditional barter economy. In addition, the simulation is very effective in highlighting some of the key features that an object that serves as money needs to possess in order to function as an efficient medium of exchange, unit of account, and store of value.

I. INTRODUCTION

As a research tool, experimental economics is a very useful device for studying many issues in economics, including choice theory, industrial organization, public finance, financial markets, etc. However, by its nature, most of the classroom applications are concentrated in simulating microeconomic markets for specific goods or assets. For example, various versions of "double-oral auction" type experiments popularized by Smith [1962; 1965] and his students are designed to demonstrate supply-demand interactions in generating competitive equilibria, and to show the effects of various market organizations and regulations on competitive equilibrium outcomes. Similarly, various asset market experiments usually demonstrate different aspects of asset market organizations and operations, such as asset valuation, informational efficiency, individual rationality, etc.

In this paper we describe a multiproduct barter trading simulation experiment which we have successfully used since 1988 at the University of Minnesota, University of California/Irvine, Pepperdine University, University of Chicago, and Union College. The experiment can be used in introductory and intermediate macroeconomic classes as well as in more advanced classes such as money and banking. Despite the prevalence of various forms of barter in today's economies, most students are not aware of barter trade as a mechanism for exchange. 1 Experimenting with barter exchange provides a useful starting point for a classroom discussion of money and its role in the economy. Our implementation of the experiment is specifically designed for demonstrating limitations and inefficiencies of the traditional barter economy and for emphasizing the role of money as a medium of exchange, unit of account, and store of value. 2 In addition, this experiment helps in demonstrating some of the key features that an object that serves as money should possess in order to function effectively and efficiently.

In the experiment students exchange real goods (various food items) in an open, pure-exchange market, without any restrictions. Unlike many experiments that last weeks and sometimes even an entire term, this experiment is not time consuming, and can be easily conducted in one 90-minute session, including the follow-up discussion. Also, unlike the experiments in which participants' preferences are set exogenously by the instructors, here the students are acting based on their own personal preferences, and their trade objects are real goods, not plastic chips, or index cards. This makes the experiment very realistic and life-like. 3

II. DESCRIPTION OF THE EXPERIMENT

In principle the experiment can be conducted after a regular classroom lecture on "Money and its Role in the Economy". However, we find that students act more naturally, and also learn and enjoy more, when it is conducted before the lecture. During the lecture prior to the experiment day, we announce in class that we are preparing a surprise for the next meeting: we will serve a food during regular lecture meeting and instead of talking economics, they will eat a nice breakfast/lunch/dinner (depending on the class meeting time). If the class meeting time falls outside ordinary dining hours, then promising every student 3 or 5% of the final course grade just for coming hungry to the classroom is always sufficient for a successful simulation of the experiment in class. 4 Class size usually is not a problem. We have simulated barter economies in classes with as few as 7 students and as many as 35 students.

The experiment starts by giving each student (or alternatively each group of 3-5 students) an initial endowment of various food items. The example presented in Table I provides a list of some of the food items that can be distributed in a class of 25 students along with initial endowment allocations. We have used similar menus for various afternoon and evening classes. The initial endowments should be distributed so that complementary products will not end up in the hands of the same group of students or the same individual. This guarantees that some exchange will take place before the food is consumed. For example, if one student gets a two-liter bottle of soft drink, then some other student should get the plastic cups. The total amount of food distributed should be sufficient for feeding the entire class, otherwise the students leave the classroom unhappy.

The students are told that they can consume whatever they wish, and that there is enough food for everybody in the classroom. We also emphasize that their initial wealth allocation is such that at least some of them will have to exchange part of their supply for other items in order to consume it. They are allowed to make whatever exchange they desire following their individual or group preferences, the exchange price is negotiable, and should be determined by participating parties. Although we do not really talk about ideal menu content, most students usually attempt to achieve a balanced meal through barter trade, that is, a meal that contains a main dish and/or vegetable salad, a drink, and some desert.

There are no restrictions on exchange and any exchange is valid. The students are not allowed to buy or sell on credit. That is, they cannot get pizza today and tell their friends that they will pay for it tomorrow. Also, there is no storage technology, so the students must return any unused items to the instructor. This guarantees that the students will exchange at least some of their commodities, as they will not be able to just eat whatever they like and take home the leftover. Each student or group of students is given a simple form in which they are asked to record their endowment along with their final consumption bundle, every single transaction they make, which goods were involved in the exchange, what were the quantities, and what was the exchange rate. An example of such a form is provided in Table II. This information is later used in the follow-up discussion.

Physically, the students are asked to form a circle with their chairs (if the classroom setup permits), and clearly display whatever they wish to exchange. In order to initiate an exchange, they can either go from chair to chair with their supplies and offer exchange prices, or they can negotiate right from their seats. The entire simulation including the dining time, usually takes about 45-50 minutes. If time is a concern, the experiment can be shortened by reducing the number of groups. It can be further shortened by reducing the number of commodities used.

III. FOLLOW-UP DISCUSSION

Following the simulation, the class discussion usually focuses on their impressions from the experiment. The students are asked to freely describe their observations about what they saw, whether they have noticed anything unique, unusual, or different from ordinary market mechanisms, and what lessons, if any, they have learned from the experiment. While discussing the students comments, we usually try to lead the discussion towards specific issues on money, and its role in the economy in a more structured format.

For example, in our introductory macro classes, we initially focus students' attention on the problems caused by the lack of a commonly acceptable medium of exchange, unit of account, and store of value. Afterwards we try to focus on the importance of the features that an object that serves as money should possess in order to function effectively and efficiently. These features include homogeneity, divisibility, storability, durability, and scarcity. 5 Finally, we often get to one or two additional issues, such as efficiency versus equity, money's contribution to social welfare by promoting specialization, etc. This follow up discussion usually lasts about 40 minutes. The discussion can be shortened by reducing the number of topics discussed or by avoiding in-depth discussion of some issues. For example, in advanced classes (like money and banking) the instructor may choose to focus on the functions of money. The following list is a sample of some of the issues and topics raised and discussed. The list is not exhaustive, and instructors may choose to discuss other aspects or implications of the experiment following their own interest.

Functions of Money

Money as a Medium of Exchange. After noting that in this classroom economy we had no real money, we ask the students to identify any one object or food item that played in the experiment a role similar to the role money plays in exchanges that take place in real economies. The problem of double coincidence of wants caused by the lack of a commonly accepted medium of exchange is one of the central problems of barter economy.

In the experiment we demonstrate this problem by allocating endowments so that some of the trades will benefit one group but not another, and so no transaction will take place between these groups. For example, according to the sample menu presented in Table I, Groups 3 and 7 probably will not trade directly because of the lack of double coincidence of wants.

Money as an Unit of account. After collecting the Transaction Record's form from the students, we ask them questions like: What is the value of a commodity in a barter economy? What was the market price of a slice of pizza? This leads to discussions on the multiplicity of prices in a barter economy. We also try to see whether the prices that were set in various transactions are consistent with each other. Obviously, they are rarely consistent. The discussions about price multiplicity and the lack of unit of account usually leads to discussions about value. Questions of the type: "how do you know that the price you paid is a good price?," or, "how would you define a good price in this economy?," or "what determines the exchange rate in this barter economy?," always lead to interesting discussions about individual preferences, demand-supply interaction, subjective marginal rates of substitution, etc. 6 Then we go back to the issue of lack of consistency of the prices and discuss the observed price inconsistency by relating it to the issue of individual preferences.

Money as a Store of Value. Because the experiment only lasts 40-50 minutes, highlighting this role of money in our experimental setup is not easy. We use (partially melted) ice cubes to demonstrate the importance of this function of money. As the trade progresses, the ice melts almost completely. Consequently, it starts to loose its usefulness, and students often refuse to accept it in exchange, or they only offer very low price for it. This shows the students that an object must offer a good store of value in order to function as money.

Features of Money

To highlight the main features that an object that serves as money should possess, we ask the students to identify one commodity that could serve as a commodity money? While in principle any commodity could serve as money, some commodities would make a "better" commodity money than others. For example, students always complain if their endowment includes something like Organic Nasoya Well Water Tofu, since usually nobody is willing to exchange anything for it in this experimental setup. 7 Introduction of the concept of commodity money makes the following discussion of features of money tangible to students that just participated in barter exchange.

Homogeneity. By distributing close, but not perfect substitutes as a part of initial endowments, we demonstrate the importance of homogeneity for an object in order to serve as a commonly acceptable medium of exchange. For example, a student would refuse to accept a Tuna-Salad sandwich and instead would demand Cheese or Ham sandwich. We obviously do not have such problems with modern money since modern money is homogeneous.

Divisibility. This is another important feature that modern money possesses. In the experiment we demonstrate this feature by distributing a food item which is not easily divisible, yet it is consumable: two liter bottled soft drinks. By limiting the number of plastic cups available in the market, we make some of the bottled soft drinks indivisible. 8 Indivisibility makes the soft drinks a very inefficient medium of exchange.

Durability and Storability. Because the experiment is conducted in a classroom, and it only lasts about 45-50 minutes, it was tricky to find a commodity which would be hard to store or which would not be durable enough to last such a short time. It turns out that ice cubes can serve this purpose as well. At the beginning of the trade, fresh ice cubes are usually accepted in exchange for other food items. However, as the ice starts to melt, it becomes useless, and so students refuse to accept it. Melted ice is almost impossible to store in the classroom setup since we distribute the ice cubes in plastic bags.

Scarcity. We demonstrate this important feature of money by simply including a particular commodity in every group's endowment bundle. 9 It is not surprising that the students always refuse to exchange anything for that item. 10

Efficiency versus Equity

During the simulation some students, especially those with relatively poor initial endowments (like groups 4 or 5 in the example of Table I), often express frustration and complain about an unfair allocation of the initial endowments, without noticing that they are making normative statements. Sometimes, in order to give these students a feeling of fairness, or in order to demonstrate a need of some kind of income redistribution schemes in real economies, we intervene in the market in the middle of trade, and declare that the government has decided to follow a Robin Hood kind of policy by taxing the rich and giving to the poor. The policy is implemented by simply taking some food items from rich groups or individuals and giving them to the poor. The reaction of various groups or individuals to this type of policy quite often leads to interesting discussions about fairness, fair allocation mechanisms, the need for government intervention, income redistribution schemes, etc. [START_REF] Smith | An Experimental Study of Competitive Market Behavior[END_REF] This gives us an opportunity to discuss the ability of money to enhance the efficiency of the market mechanism against its inability to enhance equity along the lines presented by Okun [1978]. Since the students participating in this experiment naturally are concerned with equity, the act of taxing helps us to motivate this discussion.

Information and Identification Cost

The experiment could be further deepened by demonstrating the idea that it is the costliness of the information about the attributes of various goods that induces the use of money as a medium of exchange, as discussed in Alchian [1977], and Brunner and Meltzer [1971]. 12 Product identification can be made difficult and costly by using generic (not brand name) or homemade products as in the endowment of Group 1 in Table I.

Obviously, students have less information about the attributes of such products than brand name goods which they often consume, and consequently will be more reluctant to accept them in exchange.

Other Issues and Extensions

Other related issues that we often discuss include: money's contribution to social welfare by promoting specialization; historical episodes of bartering; possible emergence of a single commodity as "money" in barter economies, like cigarettes in the P.O.W. camp as discussed in Radford [1945]; used goods market; rental goods market, etc. 13 One shortcoming of the experiment for the purpose of demonstrating the limitations of a barter economy is the fact that the students eventually make enough exchanges to have a balanced meal, although some of the exchanges are complicated and often involve 3-4 groups of students and 5-8 commodities. This is so because in our setup everything is portable, and information flow is perfect. Therefore, our setup lacks two important difficulties of real barter economies. In addition, in our experiment no storage technology is available, and since we collect any leftovers, students may be exchanging things that perhaps they would prefer to keep. The information flow can be made imperfect by scattering the students in a large auditorium, a football field, or even in several classrooms.

The portability problem can be created by imposing restrictions on the market mechanism.

With some modifications, the experiment can also be used to complement classroom discussions on other economic concepts and issues such as monopoly, the fairness of market mechanisms and resulting allocations, supply and demand interaction, taxation and income distribution (as described in the Efficiency versus Equity section), market failures and the need for government intervention, the effects of various regulations on market activities, the role of marketing in improving transaction efficiencies, etc. Also, there may be a way to introduce production technology in this experiment, along the lines suggested by Karpoff [1984].

transaction takes the form of present and counter-present."

3. An interesting experiment suggested by Karpoff [1984] is somewhat similar to our experiment, but there are some differences. Unlike our experiment, Karpoff's experiment is designed as a microeconomic teaching device. Also, his experiment simulates a twogood barter economy, whereas we often use about 20 (and sometimes even more) different commodities. Finally, unlike our experiment, Karpoff's experiment is designed to last several weeks. The use of many commodities makes this simulation experiment more lifelike. However, as Karpoff [1984] suggests, use of many commodities also increases the complexity of such experiments.

4. This will have no effect on course grades' distribution, as usually all the students show up to this session. 5. This experiment is not well suited for demonstrating the importance of an additional feature that modern money possess, namely portability, as the experiment is conducted in a classroom.

6. We have frequently encountered cases in which some students respond with astonishment when they see the price their classmates paid for some commodities.

Reactions like, "What? You gave entire bottle of Coca Cola for a plastic cup? Are you nuts?" are very common. 7. According to the producers of the TV game, Jeopardy, the correct response to the statement "This is the most hated food in America," is "What is Tofu?" 8. We owe this idea to Hal Fried.

Table II .

 II Transactions' Record Form

	______________________________________________________________________________
	Name/s of the student/s: __________________ __________________ ___________________
	Endowment: ____________ Final Consumption: ____________ Leftover: ____________
	____________	____________	____________
	____________	____________	____________
	____________	____________	____________
	____________	____________	____________
	____________	____________	____________
	____________	____________	____________
	Transactions List:
	______________________________________________________________________________
	Type and Quantity	Type and Quantity	The Exchange Rate
	of the Good Sold	of the Good Bought
	______________________________________________________________________________
	1.
	______________________________________________________________________________
	2.
	______________________________________________________________________________
	3.
	______________________________________________________________________________
	4.
	______________________________________________________________________________
	5.
	______________________________________________________________________________
	6.
	______________________________________________________________________________
	7.
	______________________________________________________________________________
	8.
	______________________________________________________________________________

FOOTNOTES

* Assistant Professor, Union College, and Assistant Professor, Graduate School of Business, University of Chicago. All correspondence should be addressed to the first author. We thank an anonymous referee for useful comments and suggestions. We owe special thanks to the Teaching Tools section editor, Robert L. Moore for his guidance and many specific helpful comments, which greatly improved the manuscript. We also thank Hal Fried, Doug Klein, Eshi Motahar, Bruce Reynolds, Shelton Schmidt, and James Stodder for useful discussions and suggestions. The second author acknowledges financial support of the Bozell, Jacobs, Kenyon, and Eckhardt Endowment Fund at the Graduate School of Business, University of Chicago. All the errors are ours.

1. Modern versions of barter include countertrade, counterpurchase, compensation, import entitlement programs, offsets, clearing arrangements, switch trading, etc. Some of these forms of barter are an alternative form of financing for deals that would otherwise not have taken place. These forms of barter are growing phenomena in the world economy, and according to the USITC [1982] estimates, may account for 20-30% of world trade, and 5-10% of domestic U.S. commerce. Other estimates cited in Higgiston [1985] are in range 3-25% of the GNP. As Kaikati [1982] suggests, one cause of domestic barter expansion is the increase in popularity of barter clubs. Fisher [1985, 5] notes, "the principle of reciprocal exchange of goods, of giving and taking, appears to be deeply rooted in human nature. Commerce in the form of regular acts of exchange appears even in the lowest level of primitive peoples. Variations on the direct exchange of goods against goods include 'silent trade,' or dumb barter, with neither party holding any communications with the other, and the 'gift-exchange,' in which the 9. In the example of Table I, plastic spoon is such a commodity. Note that in this example lack of scarcity of spoons is not universal. That is, the amount of spoons available is not unlimited. In this setup spoons have no transaction value simply because nobody needs more than one spoon to eat a lunch. 10. In one occasion, the student that was endowed with napkins decided to ask in exchange for them what many students thought was ridiculously high price. One student got really mad, went to the restroom and brought paper towel to use as napkins. As soon as other students saw that, they did the same. The napkins' purchasing power instantaneously dropped to zero, since it was not scarce anymore.

As

11. We had an opportunity in one occasion to see a spontaneous tax evasion attempt in response to our implementation of income redistribution scheme: after declaring that we are taxing the rich and giving it to the poor, we took one half of ice-cream container from a "rich" student and gave it to the "poor. There was another lucky student in class that was endowed with ice-cream and as soon as he saw what we did, he spontaneously took the ice-cream container and hid it underneath his desk, and he was not joking! 12. We thank the referee for suggesting this idea.

13. In one of the recent experiments we witnessed an emergence of "used cups" market as well as "cups for rental" business. We have created a shortage of cups by distributing only five cups in a class of 14 students. This made 2-liter bottled soft drinks indivisible.

To overcome the problem, the students rented used cups in two occasions. Afterwards, some students actually bought used cups.