Do Payment Systems Matter: A New Look

In this paper, we consider two alternative pure payments systems—the trade of goods for goods, or barter, and trade using intrinsically valueless fiat money. Here, the term payment system refers to the method of executing mutually beneficial trades, and ‘pure’ means that each method of exchange is considered exclusively. Each payment system is examined in an economy with location-specific commodities, and households consist of vendor-shopper pairs. The household’s decision problem includes a distance-related transaction cost; that is, the cost of trading with anyone from another location increases as the distance from the home location increases. We then ask, is the equilibrium set of consumption goods—and the quantity of each type—invariant to whether the vendor or the shopper pays the transaction cost? The answer is that in economies with monetary settlements, invariance fails. JEL Classifications: D12, D47, E42


Introduction 1.Introduce the Problem
In this paper, we consider two alternative payments systems-the trade of goods for goods, or barter, and trade using intrinsically valueless fiat money.Here, the term payment system is applied narrowly and refers to the method of executing mutually beneficial trades.By ignoring credit, we can avoid dealing with settlement issues.In addition, we consider either barter or fiat money separately.Our aim is to shed light on differences that arise when the economic decision unit exhibits a kind of heterogeneity.More specifically, we consider an economy with location-specific commodities, and households that consist of

Hypothesis
Our approach will emphasize the role that coordination plays within each household.Because the household consists of two parties with different prescribed activities, we study two cases differing only in what each household member takes as given.We then examine the equilibrium outcomes in a barter economy and in a monetary economy.If there is a coordination failure, which corresponds to our kind of specialization, then failure will occur in the monetary economy, but not in the barter economy.

Literature Overview
Researchers have long studied the nature of trade.The principle motive is straightforward enough; people specialize production in the item in which they possess a comparative advantage.The basis for trade in a world with comparative advantage does not require means of payment.Relative prices are determined by some trading protocol.If trading protocol includes money, the benefits of comparative advantage can be realized compared with trading protocols that are strictly bilateral.
There is no direct empirical literature that tests our hypothesis.Our results do offer a view that the payment system is a relevant state variable that can affect the breadth of trade.In our view, the large literature that seeks to account for the empirical relationship between the benefits associated with trade liberalization and trade outcomes provides results consistent with our hypothesis.Specifically, recent papers by Santos-Paulino and Thornquist (2015) seek to examine the impact that trade liberalization has on economic outcomes for low-income countries.Before that, Winters, McCulloch and McKay (2004)  and Goldberg and Pavnick (2007) provided survey of the expansive literature on the evidence that is consistent with the absence of widespread economic benefits associated with trade liberalization. 4Our 3 Product specialization is also embedded in the random matching models.See Kiyotaki and Wright (1993) and Lagos and Wright (2005). 4In these papers, the primary focus is on the effects of trade liberalization on inequality.Insofar as poorer households acquire a smaller set of consumer goods-that is, the necessities-then our results have something to say about the potential role that the coordination failure has on changes in income inequality in a country.Put another way, the hypothesis is that trade liberalization would, cetaris paribus, result in more trade and hence a greater variety of goods in a country.Yet, if the evidence is consistent with trade liberalization being associated with greater income inequality, then the coordination failure between production specialization and trade range associated with the monetary payment system could account for the observations.~ 4 ~ results suggest that the coordination problems associated with monetary payments systems can account for the absence of such widespread economic benefits.We start with the premise that production specialization exists, but is not sufficient to generate widespread trade opportunities because consumption and production specialization can suffer coordination problems because producers may want to specialize in acquiring money while consumers may want a wider variety of goods.In our case, consider a set of countries in which each possesses a specific kind of comparative advantage in production leading to production specialization.Because of trade frictions (transaction costs), not every country will trade with every other country.Our main result can be interpreted as follows: the pattern of trade depends on the means of payment.In a barter economy, the pattern of trade is invariant to a protocol in which one country bears the transaction cost.In contrast, in a monetary setting, the pattern of trade depends on which country bears the transaction costs.Hence, a coordination failure presents because importers will purchase a different range of goods when they take the transaction cost as given compared with exporters who will purchase a broader variety of goods when they take the transaction cost as given.The implication for studying trade patterns is clear: the benefits of trade liberalization depend on the payment system.Indeed, we show that there is coordination failure associated with a payment system built on monetary settlement and the resulting trade pattern can be greatly diminished in terms of variety of imports received and exported goods.
Formally, our results say that coordination problems can be conditional on the type of payment system.Note that we are not talking about coordination problems in the sense of multiple equilibria that reflect underlying strategic complementarities.In our setup, we focus on one equilibrium for each type of problem.For our purposes, a coordination problem exists when the two representations of the household maximization problem−that is the shopper version and the vendor version−do not generate identical equilibrium.With barter exchange, no such coordination problem exists yet with monetary exchange vendors and shoppers do not choose the same equilibrium.In the shopper's version, household utility is maximized by specializing in purchasing and taking what the other shoppers do as given.In the vendor's version, household utility is maximized by specializing in acquiring money, taking what all other vendors do as given.The point is that monetary exchange creates the opportunity for specialization.A coordination problem exists to the extent that the two equilibria deliver two different utility levels.In our view, our findings can easily account for hierarchial structures in economic units comprised of individuals with different skills.More specifically, governance is designed to choose the actions that maximize welfare for the economic unit from a broader perspective than would be brought by any individual.This governance issue is particularly important in economies marked by monetary settlement.So, even with the same objective function, monetary exchange is associated with specialization.It is in this sense that the payment system matters.
The remainder of the paper is organized as follows.Section 3: environment describes the general structure of the economic environment in terms of household preferences, locations, endowments and transaction cost functions.In section 4: barter, we consider the case of barter as the payment system and describe equilibrium outcomes for two economies-one in which the vendor pays the transaction cost of any exchange and one in which the shopper pays the cost.Similarly, section 5: money derives the equilibrium outcomes for the monetary economy, comparing outcomes under ‛vendor pays' and ‛shopper pays' rules.We offer a brief summary in Section 6: conclusion.An appendix contains proofs of some claims made in the text.

The Environment
The physical environment we will describe can be interpreted as a group of households, each living at a specific stretch of beach on an atoll, which we idealize as a circle.
~ 5 ~ More formally, there is a large, finite number of infinitely-lived households living at distinct locations along a circle.Time is discrete and indexed by t = 0,1,2,....For our purposes, let there be N > 2 locations equally spaced on the circle; by implication, the circle has circumference N.For symmetry, we assume that each location is populated by a large number of identical households.Each household consists of a vendor and a shopper.The vendor stays at the home location, trading with visitors from other locations on the atoll.Meanwhile, the shopper visits locations along the atoll to purchase goods for the household.

5
Thus, N is also the number of household types.The households at each location are endowed with units of a nonstorable, location-specific good, so that there are also N types of commodities at each date.
Trade takes place as agents from each household move around the atoll to visit the locations of other households.Let index locations on the atoll; hence, i indexes both the locations from which the household hails and the goods.

6
We assume that consumers do not derive utility from consuming their home-location good.On the other hand, we assume that households at each location do derive utility from the goods at all other locations, and that households have identical preferences defined over the full range of goods (modulo the home good).There is thus no double coincidence of wants problem in our economy.
At the start of each period, the household's shopper travels to other locations on the circle to purchase goods, either with units of the home good or cash, depending upon the payment system under consideration.Meanwhile, the vendor remains at the home location to transact with the shoppers of households from other locations.locations which its shopper visits and with all shoppers visiting the household's location.With this interpretation in mind, we proceed to lay out the model in more precise detail.
The structure of preferences is identical across households, and the preferences of each household treat all goods symmetrically.The momentary utility function for each household type i N ∈ is represented by ( ) where 0 < α <1,

{ }
/ N i is the relative complement of {i} in N, and is the consumption `‛bundle' at date t.Each household seeks to maximize the discounted sum Identical preferences make the analysis substantially more tractable.For one thing, given the further assumptions we make below on transactions costs, we can conduct our analysis for a representative household-the household at location 0-without loss of generality.
Each household i is endowed with ( ) 0 t e i > units of commodity i at each date t.The endowment goods are perishable.We will assume that endowment levels are identical across households and across time; that is ( ) = for all i and t.
We have not yet developed a specific role for spatial separation.Here, its force derives from the transaction cost's dependence on distance.We will consider environments where this cost is borne by either the vendor or the shopper in a given transaction.In the 'shopper-pays' environment, a shopper who travels from the home location to a location k units away-for example, rom location 0 to location kpays a cost ( ) a k before trade can take place.In the 'vendor-pays' environment, the vendor at any location who wishes to trade with a shopper coming from a location k units away-that is, from location N k − to 0-must incur the cost ( ) a k before trade can take place.
A trading range is defined as the set of locations with which the household member will seek to trade, when the choice is theirs to make. 8In the shopper-pays case, the shopper will choose a range of locations for which he is willing to pay the transaction cost in order to trade with the vendors at those locations.
Similarly, the trading range in the vendor-pays case consists of those locations for which the vendor is willing to pay the transaction cost in order to trade with shoppers visiting from those locations.
As we develop the analysis, we will further distinguish the shopper-pays and vendor-pays cases in the context of the household's problem.For now, it is sufficient to note that the transaction cost represents resources used up and subtracted from the payer's endowment.Thus, for example, in the shopper-pays environment, if the shopper from a household at location 0 visits locations 1 through k, the household's endowment net of transactions costs is ( ) Note that this also the net endowment of the household at location 0 in the vendor-pays environment if the household trades with shoppers coming from locations N k − through 1 N − .
We make some assumptions on the transaction cost function ( ) . a in order to guarantee nontrivial equilibria.In particular, we assume that ( ) a k is increasing in k and that there is a k N ∈ such that 0 1 k N < < − with ( ) ( ) > In words, it's feasible for a shopper or vendor to transact with some locations, but too costly to transact with all locations.
We can show there are gains from trade under our assumptions on tastes and technology.Given our assumptions on the transaction cost function a, it's straightforward that there exist From the inequality (2) it follows that a feasible allocation exists in which each household's shopper visits the first k locations in the direction of travel from the home location, each household's vendor trades with visitors from the k locations lying in the counterclockwise direction, and each household consumes c units of every good from these 2k locations. 9The utility each household receives from this allocation is With this basic environment in place, we now investigate whether it matters if the shopper or the vendor pays the transaction costs across three pure payments systems.The assumption of which party bears the transaction cost would seem to be innocuous in terms of affecting equilibrium outcomes under a given payment system.In the next section, we present a case in which the equilibrium is in fact identical regardless of whether the shopper or the vendor pays the transactions fee.

Payment System I: Barter
In this section, we consider trading environments in which the vendor and shopper exchange units of their endowment goods-that is, barter economies.Given our assumption that households are price-takers, the equilibria we focus on are competitive equilibria.And, given symmetric transaction costs and preferences-and, moreover, preferences which treat all goods identically-it is natural to focus on competitive equilibria which are symmetric.By symmetric equilibria, we mean equilibria in which: 1.All households trade with households from k adjacent locations lying in both directions from the home location.
3. For any i and j, the relative price of the good at location i in terms of the good at location j depends only on the distance between i and j. 9 The transaction cost associated with these trades at the k different locations is ( ) for each household; the inequality (2) then states that the endowments net of those transaction costs are sufficient to consume c units of each good from 2k locations.

~ 8 ~
Moreover, as we discuss further below (and prove in Appendix B), a necessary feature of symmetric equilibria is that all relative prices are unity.That is, if we restrict attention to equilibria where households make identical choices and relative prices depend only on distance-which are natural assumptions given the environment-it follows that we may further restrict attention to equilibria where all relative prices are unity.Thus, we will focus on equilibria obeying properties 1, 2 and 3 ′ .For any i and j, the relative price of the good at location i in terms of the good at location j is 1.
Note that from 3 ′ , it will also follow that household consumption bundles are constant across locations-that is, ( ) ( ) for all i and j.
Because of the symmetry of preferences and transaction costs, we can discuss the problem from the perspective of a representative household located at 0 i = , without loss of generality.To elaborate the barter economy in concrete terms, we first consider the case where the vendor pays the transaction cost associated with any exchange.Later, we show how the expressions characterizing equilibria change (or not) when shoppers bear the transaction cost.

Barter Equilibria in the Vendor-Pays Environment
When the vendor is responsible for the transaction fee, each household will choose a set of visiting shoppers with whom its vendor is willing to trade-that is, a set of locations, lying in the counterclockwise direction from the home location, from which the household will accept goods in exchange for units of the home endowment.Consequently, each household will take as given the set of locations, lying in the clockwise direction from the home location, which are 'open' to its own shopperi.e., those locations around the atoll where other households have incurred the fixed cost to trade the goods which the shopper carries from the home location.
For the household located at i = 0, call the set of locations visited by the shopper t S and the set of locations from which the vendor accepts visitors t S ′ .Because the transaction cost increases with distance, and all goods are treated symmetrically in households' preferences, we may assume without loss of generality that the sets t S and t S ′ are each ‛connected' in the sense that t S consists of all locations 1 through t k for some t k and t S ′ consists of all locations and shoppers will never skip over a location to trade with one that is more distant; rather, they trade incrementally, choosing a set of adjacent locations and balancing the desire to eat each of the 1 N − non- home, differentiated goods against the transactions costs.

10
It is also clear that, because of the increasing transaction cost, taking as given t S , the household will always choose t S ′ such that t t S S ′ ∩ = ∅; simply put, it would be inefficient for the household to pay the fixed cost to include a location in t S ′ if that location is already open to the household's shopper in t S .
We let ( ) t A S ′ denote the total cost of trading goods from locations in t S ′ -that is, Now, suppose that all relative prices are unity, as they would be in a symmetric equilibrium; we establish this property in Appendix B. Under this assumption, the household's budget constraint can be ( ) ( ) ( ) We will construct an allocation where each household is maximizing its utility subject to its budget constraint, household choices are symmetric, and markets clear.
Since the good is nonstorable, and exchange of goods for goods is the only means of trade, each household's lifetime utility-maximization problem amounts to a static problem of maximizing momentary utility at each date.Given the household's preferences (1) and the budget constraint (3), the household's optimal consumption bundle will obey ( ) ( ) Taking as given t S , the household chooses , The implication is that consumption levels on the two sets are equated, and the budget constraint is satisfied with equality.The household's momentary utility can then be written in terms of t S and t S ′ as ( ) From ( 6 ( ) ( ) This is an integer-programming problem, the solution of which can be characterized by a set of inequalities.For our purposes in this paper, having very tight characterizations of equilibria is inessential for showing how equilibria either differ or do not differ across different environments.It is sufficient to note that a symmetric competitive equilibrium in the current environment, if one exists, is characterized by The critical feature of ( 7) is that the vendor chooses the distance for which they are willing to pay the transaction cost, taking the locations visited by the shopper as given.In doing so, the marginal cost of accepting a shopper from the next farthest location is equated with the marginal gain from consuming an additional variety.In equilibrium, consumption by each household from each of the 2 t k locations is given by ( )

Barter Equilibria in the Shopper-Pays Environment
Now suppose that it is the shopper who pays the fixed cost associated with any exchange, hence chooses the set of vendors with whom the household will trade.In this case, the typical household takes as given a set t S ′ of shoppers from other locations who will be visiting the home location, and chooses a set t S of locations which its shopper will visit.Again assume that all relative prices are unity, from which it follows that the household sets t t S S ′ ∩ = ∅and chooses constant consumption levels t c and t c ′ on the two sets.
The budget constraint again takes the form ( ) where ( ) A S is the sum of the transactions costs which the household incurs from shopping at the locations in t S .By way of comparison with the previous environment, note that the household's cost of visiting a set { } 1, 2,..., t k of locations in this environment would be identical to its cost of transacting with shoppers visiting from locations { } in the previous environment.
The household's momentary utility is again given It's immediate that we again have t t c c ′ = at an optimum.An argument similar to that above shows that t S takes the form{ } 1, 2,..., t k , and that the optimal choice of t k , given { } 1, 2,..., , is the solution to 11 Heuristically, one can get a feel for the equilibrium by imagining, for a moment, that there are a continuum of locations, in which case the household's maximization would give the following first-order condition: In a symmetric equilibrium t t k k ′ = and the common value t k would be characterized by Note that existence of a t k satisfying the last expression is essentially immediate from the assumptions that ( ) . a is nonnegative, continuous, and increasing, and such that ( ) for all k greater than some k ; the lefthand side is then increasing from a value of zero at 0, k = while the right-hand side is decreasing from a positive value at Consequently, a symmetric equilibrium is again characterized by ( ) ( ) and Note that the expressions in ( 7) and ( 8) are identical to equations ( 9) and (10).Since these equations completely characterize equilibria in the two environments, the analysis shows that the equilibrium outcomes are identical for the two versions of this barter model economy.More specifically, the representative household maximizes utility in equilibrium by choosing the same consumption bundlethat is, the same of consumption from each location and the same range of locations with which to trade.Hence, the vendor-pays economy is equivalent to the shopper-pays economy.This is a general feature of economies in which exchange is a trade of endowment goods for endowment goods.

Guaranteeing Existence of Symmetric Equilibria
Symmetric equilibria in the barter economy, when they exist, are identical regardless of whether the shopper or vendor pays the transaction cost-but do we know symmetric equilibria exist?Existence is straightforward to show with a continuum of locations, assuming only that the transaction cost function

( )
. a is nonnegative, continuous, increasing, and such that ( ) for all k greater than some k (see footnote 10 above).With a discrete set of locations, which we employ primarily for its simplicity in other regards, giving minimal assumptions on ( ) a i that guarantee existence is more difficult.Hence, we will simply assume that ( ), , a i e and α , in addition to the assumptions already made, are such that there exists a k with ( ) ( ) ( ) ( ) for all .
h That is, we assume the fixed-point problem implicit in (7)-or equivalently in (9)-has a solution.
13 12 Suppose that the transactions costs are borne according to the following rule: the seller pays ( ) θ ≤ ≤ It is fairly straightforward to show that the results, in terms of range of goods consumed ( ) k and the quantity of each good consumed ( ) c would be identical for any .θ 13 Given the complex nature of this joint assumption on ( ) . , , a e and α it behooves us to show that such ( ) ., , a e and α exist.Suppose there are four locations on the circle, 0,1, 2,3 i = We have in place all the pieces to verify that symmetric competitive equilibria exist, and have the properties described above-namely, that all relative prices are one and that allocations are invariant to the identity of party bearing the transaction cost.In sum, we can show: Proposition 1: In the barter economy, there exists a symmetric competitive equilibrium in which the location-specific goods trade at a relative price equal to one and the range of locations and the quantity are represented equivalently by equations ( 7) and (8) or equations ( 9) and (10).
Proof: The derivations of ( 7)-( 8) and ( 9)- (10) are given above, under the assumption that all relative prices are unity.That there exists a t k that solves (7) and ( 9) follows immediately from the assumption that ( ) . a obeys (11).All that remains to be shown then is that relative prices are in fact unity in the symmetric equilibrium.We prove that in Appendix B.

Payment System II: Fiat Money
In this section, we consider an environment in which there is a store of value, fiat money, which is the sole means of exchange.We are not trying to explain why money is superior to barter.In our frameworkwhere barter is not subject to double coincidence of wants problems or search frictions-money may be a superior medium of exchange owing to lower distance-related transactions costs.That is, the transaction cost function ( ) . a may be uniformly lower with money as the means of exchange.

14
As usual, we assume that fiat money is intrinsically useless and noncounterfeitable.Let the stock of money be constant over time.Trade takes place as before, with shoppers from each household moving clockwise around the atoll.In this economy however, all trades take the form of shoppers offering cash to vendors in exchange for goods.Note that in this environment, a household only consumes goods lying in the shopper's direction of travel from the home location.
As in exchanges in which the endowment goods are used as payment, we assume that there is a fixed cost that is related to the distance between two potential traders.We consider the same two cases: either the shopper or vendor pays a fixed fee to trade with persons that live j locations away.
In this economy, the separation of the shopper-vendor pair at the start of each period presents a timing issue.The vendor must offer the home-good for cash while the shopper uses the household's previously accumulated cash balances to finance the pair's current-period consumption.At the end of the period, the vendor gives the shopper the proceeds from this period's sales to finance next-period's consumption.De facto, a cash-in-advance condition arises.
Analogous to our notation of the last section, let t S and t S ′ denote, respectively, the set of locations to which the shopper will carry cash to exchange for goods and the set of locations from which other households' shoppers will visit bearing cash to exchange for the home endowment good.If the shopper is responsible for the cost of verifying that the goods received satisfy the conditions for trade, the household chooses the set t S of locations to visit, and takes as given the set t S ′ of visitors.In this case, for the 14 We use the same notation for the transactions cost throughout, and make similar assumptions regarding its nonnegativity and dependence on distance, but we do not assume that the properties of the function ( ) . a here are identical to those presented for ( ) . a in the section describing the barter economy.Our focus is on comparing equilibrium allocations across the two environments; that is, whether the monetary equilibria under vendor-pays or shopper-pays rules display the same invariance as they do in the barter economy.~ 14 ~ household at location zero, trading at a set of locations t S incurs a cost of ( ) ( ) , where ( ) a i is again increasing in i , with ( ) for k small, and ( ) Conversely, if the vendor pays the distance-related fixed cost associated with any potential trading partner, the household chooses the set t S ′ of shoppers from whom the household's vendor will accept cash in exchange for the home good and takes as given the set t S of markets to which the shopper carries money.
In this case, the household would incur a cost ( ) , which comes out of the pair's endowment of the home good.In either case, assuming that the de facto cash-in-advance constraint is binding, the household's money balances at the start of the next period will be the nominal value of the household's endowment, less transactions costs.
Without loss of generality, again suppose the relative prices of goods are equal to unity.The household starts the period with a quantity of real cash balances, denoted by t m .Given the set t S of markets to which the household carries cash, consumption on that set-which will be uniform given unit relative pricesobeys: .
This is the household's cash-in-advance constraint: purchases of current consumption by the shopper must be financed with previously accumulated cash balances.Assuming that (12) binds, the household's real money balances in the subsequent period are given by either , , depending on whether the household incurs the transaction costs through shopping (13) or vending (14)  12), as an equality, into the household's momentary utility function (1), gives the following expression for the household's within-period utility, in terms of t S and t m : .
We then can cast the household's lifetime utility-maximization problem as one of the following two dynamic programs, depending on whether we are in the shopper-pays or the vendor-pays environment: The t z in these Bellman equations denotes the vector of all exogenous variables which condition the household's decision at each date, in particular the price level t p .The character of equilibria in the two environments hinges on the very different natures of the solutions to these two problems.

Monetary Equilibria in the Shopper-Pays Environment
Consider ( 16) first, which corresponds to the `‛shopper pays' environment.Assuming t S takes the form { } 1, 2,...,

S k =
; in other words, we have an interval in the direction of travel from the home location to some t k then the Bellman equation ( 16) becomes ( ) ( ) Note that changing t k results in both costs and benefits to the household-the household's momentary utility is increasing in the range of locations visited by the shopper, but a greater range of locations comes at the cost of smaller real cash balances for next period.An optimal choice of t k balances these effects.Of course, the maximization on the right-hand side of this Bellman equation is an integer-programming problem, as t k is restricted to integer values.It would be straightforward to add enough additional structure to fully characterize a solution; however, as in our analysis of the barter economy, having very tight characterizations of equilibria is not important for demonstrating how, in broad terms, equilibria differ across different environments.
Even without explicitly solving this problem, we can draw some conclusions about the character of the solution.The most important feature to note is that there is no explicit dependence of the household's problem on t S ′ , the set of visitors to the home location.This follows from the faceless nature of the household's monetary transactions-its endowment net of transactions costs is worth ( ) independent of the identity of the buyers who purchase it.This feature of transactions using money proves to be important for comparing the nature of equilibria in the shopper-pays versus vendor-pays environments.
As in our analysis of the barter economy, further intuition can be gained by assuming for a moment, that locations are continuous, so that the problem is not integer-constrained.If the value function is differentiable, the first-order condition for the right-hand-side maximization is ( ) ( ) .
Note that the last equality follows from the fact that ( )

Monetary Equilibria in the Vendor-Pays Environment
Now, consider (17), the dynamic program which the household faces in the vendor-pays environment.The key differences between the problems described by ( 16) and ( 17) are that in the latter, the t S entering the household's one-period reward-the set of locations which are open to the household's shopper-is taken as given, while the quantity of real balances the household takes into the subsequent period now depends on the household's choice of t S ′ , the set of locations from which the household will accept cash in exchange for the home endowment.That is, the range of goods available to the household's shopper depends on other households' decisions as to whether or not to incur the cost of transacting with the shopper, while the household's vendor makes a similar decision regarding transacting with other households' shoppers.
then this problem can be written as ( ) ( ) This problem has a simple solution.With t k taken is given, and the household's next-period money balances are decreasing in t k ′ , the household chooses the smallest possible set on which to sell its endowment.That is, the household will set 1, − offering its endowment in exchange for cash only to shoppers from the nearest adjacent location.
The assumption of price-taking behavior means that the vendor can sell any amount of the home good at t p dollars per unit on any t S ′ .Given that the verification cost ( ) to the shopper from location 1 N − .In other words, vend the whole endowment to the shopper from next door.In a symmetric equilibrium-with all households following this same logic-everyone exchanges with and consumes only the goods of the households at their nearest neighboring location.This stark outcome highlights what it means for fiat money to serve as a generally acceptable medium of exchange.The problem seems to be the combination of having the person who accepts money in exchange for goods being responsible for paying the transaction cost, together with the idea of money as generalized purchasing power-that is, indifference by the household as to the identity (or home goods) of the bearer.In other words, the vendor specializes in acquiring one good-fiat money-that does not directly enter into the household's utility function.If the shopper paid the transaction cost-as we saw above in money economy in which the shopper pays, the utility gained from a greater variety of goods would be weighed against the cost of added variety.In contrast, in the environment in which the vendor pays the transaction costs, the vendor does not observe (or care about) any variety of goods.In the absence of acquiring goods that directly enter into the household's utility function, it is not surprising that the vendor eschews variety, trading with shoppers that minimize the total transaction costs paid by the household.If the household can sell ∑ on any set , t S ′ then the household would want to make t S ′ a singleton. 15 inspection, it is obvious that the equilibrium outcomes for the vendor-pays case are not identical to those in the shopper-pays case when fiat money is present.In short, it matters who pays the fixed costs.In the monetary version of this economy, we have equilibria that can be radically different depending on which party to a transaction bears the cost.Moreover, the following proposition compares the welfare outcomes associated with the two monetary economies.Let ( ) ; that is, welfare in the vendor-pays environment cannot exceed welfare in the shopper-pays environment.
Proposition 2 simply states that the lifetime utility of the representative household can never be less in the shopper-pays equilibrium than it is in the vendor-pays equilibrium.Note that the shopper could always choose to consume the good of just the next-door neighbor.So, if the household in the shopper-pays case chooses a range of goods such that 1, k > it follows that welfare is strictly greater under the shopper-pays case than under the vendor-pays case.
The intuition is straightforward.The cost to the shopper from going to an additional location, call it the th k , is twofold.First, there is the marginal utility foregone from consuming less at each of the first 1 k − locations so that the shopper can acquire some goods at the th k .Second, there is the marginal utility foregone because some goods are used up by transaction costs at the th k location.To offset these two marginal costs, there is the marginal utility associated with quantities from the new location.As long as the marginal benefit exceeds the sum of the two marginal costs, welfare is higher.Hence, if the shopper chooses multiple locations, it follows that total welfare is greater by buying at these locations than if the shopper were to stop after trading with the first location.
~ 18 ~ Shoppers specialize in the acquiring goods while the vendor specializes in acquiring what is, in effect, an intermediate good.Money is an intermediate good used by the household to acquire final goods.Because households at different locations do not coordinate, under vendor-pays rules each household tries to maximize its acquisition of the intermediate good by minimizing its transactions costs; taking the actions of all households together, this behavior condemns all shoppers to the smallest possible choice of varieties.

Mechanisms to Improve the Vendor-Pays Equilibrium
One question immediately arises.If the shopper-pays case Pareto dominates the vendor-pays case, is there a way to re-shape the household's problem so that the dominant equilibrium of the former environment obtains in the latter?The problem analogous to the textbook prisoner's dilemma: When the vendor pays, there is no incentive to unilaterally accept shoppers from locations more distant than the ( ) location (the location immediately next door to location 0).This is true regardless of the variety of locations open to the household's shopper.As in the prisoner's dilemma, though, a mechanism enforcing cooperation can improve the equilibrium outcome.
To illustrate this point, it is straightforward to show that there exists such a mechanism-the enforcement of symmetric trade rights-that eliminates the inefficiency of the vendor-pays setting with money.The following proposition formalizes this point. .
To prove this point, we begin by describing an environment in which an intermediary can costlessly enforce a welfare improving symmetric equilibrium.
Under the mechanism we have in mind, a household submits the choice it plans to make for the set under its control, and the intermediary dictates the set outside the household's control in a symmetric way.From the standpoint of a representative household at location 0 in the shopper-pays environment, for example, if the household submits { } 1, 2,..., k as the set of locations it will pay the transaction cost to shop at, the mechanism would dictate { } , 1,..., 1 N k N k N − − + − as the locations the household's vendor will accept cash from.In the vendor-pays environment, if the household submits − + − as the set of locations it will pay the transaction cost to accept cash from, the mechanism would dictate { } 1, 2,..., k′ as the set of locations open to the household's shopper.
Households in either environment maximize utility taking the mechanism into account.
Clearly, the mechanism adds nothing to the shopper-pays environment: the household is indifferent to the locations it gets cash from, so telling it who to accept cash from imposes no constraint.The household's maximization given the mechanism is equivalent to choosing both k-locations its shopper will visit-and k′-locations that can use cash at the home location-subject to the constraint k = k′.That is, the household's problem, given the enforcement of symmetric trading rights, is equivalent to ( ) ( ) . . .
As the reader can see, the sole difference between the problem with and without the intermediary is clear; there is an additional constraint which guarantees symmetry in trading ranges.Note, too, that t k ′ does not appear in the Bellman equation for the shopper-pays case.The implication is that the constraint is costlessly satisfied in the monetary economy in which the shopper-pays the transaction cost.In other words, it is a matter of indifference to the household whether it sells to the set defined by Because the shopper bears the transactions cost, the vendor's action in accumulating fiat money is costless to the representative household.Since the households are otherwise identical across locations, no shopper from farther away than t k locations will trade with the location-0 vendor, just as no location-0 shopper will trade with a vendor farther than t k locations away.Thus, in equilibria, t t k k ′ = , and the choice is the same as it was for the shopper-pays setting without an intermediary.
While the mechanism adds nothing to the shopper-pays environment, it makes a great deal of difference for the vendor-pays environment.The equilibrium that arises in that environment will now be identical to the one that obtains in the shopper-pays case.Here again the problem faced by the household can be thought of as a choice of k′ -that is, locations it incurs the transactions cost to sell to-and k - locations its shopper will visit-subject to the constraint .

k k′ =
The constraint is no longer costlessly satisfied, as both k and k′ enter into the household's Bellman equation: . . .
With the equality constraint, it is straightforward to substitute t k for t k ′ or vice versa in the Bellman equation.Thus, the problem can either be written as ( ) ( ) Clearly, the maximization will yield the same choice of locations that the representative location household will accept or visit.Indeed, as one can see from the latter representation of the unconstrained Bellman equation, the vendor-pays case will yield the same outcome as the shopper-pays case.Thus, the existence of the intermediary is sufficient to eliminate the difference between the two cases.

Discussion
In this paper, we specify a simple general equilibrium model with differentiated consumption goods in which traders face a fixed fee to acquire goods.The fixed fee is strictly increasing in the variety of goods consumed.To help illustrate the household decision problem, we treat each household as consisting of two individuals, each performing a specific activity.We consider two cases distinguished by which party to a transaction is responsible for bearing the fixed fee.We consider each experiment in two different payment systems: barter and money.The household objective is always to maximize lifetime welfare.Variety is desired by the household.In the barter system, the household faces a basic trade-off-to obtain greater variety, the household must pay a higher transaction cost.In the vendor-pays case, the shopper's actions are taken as given, and we solve for the equilibrium that the vendor chooses.In the shopper-pays case, the vendor's actions are taken as given and we solve for the equilibrium that the shopper chooses.In each version, the household's problem is written as if one person is choosing the locations and quantities, taking the location the other party will visit as given.This structure plays a critical role in our results.We ask whether the equilibrium is invariant to which party is responsible for the transaction cost when we analyze the problems under different payment arrangements.We focus on symmetric equilibrium.
Our key results are: 1.In barter economies-i.e., ones in which goods are exchanged for goods-the equilibria are the same whether shoppers or vendors are responsible for paying the transaction costs.
2. This invariance fails in monetary economies-the equilibria are different in that households will consume a wider range of the differentiated products when the shopper pays the transaction costs than when the vendor pays the costs.
3.Moreover, the two equilibria are Pareto ranked with the shopper-pays equilibrium welfaredominating the vendor-pays equilibrium.If a third-party intermediary could enforce a symmetric trading range, the coordination failure across the two experiments would be resolved, so .
First, the payment system does matter.The equilibrium in the two versions of the monetary economies are different and owe chiefly to two factors.First, money is an intermediate good, and, in effect, the vendor specializes in producing the intermediate good for the household.The vendor puts no value on the variety available to other households' shoppers, and thus-in the environment where the vendor pays the transaction cost-maximizes the household's purchase of the intermediate good, money, by minimizing the range of locations the household sells the home good to.In contrast, the shopper specializes in acquiring the final consumption good.To achieve this goal, the shopper maximizes household welfare by acquiring a wider range of goods with the money available.Thus, in the environment in which shoppers bear the transaction cost, the shopper balances the marginal benefit of greater variety against the marginal transaction cost, taking the quantity of the intermediate good as given.It follows that money creates a different outcome for the same objective function.No such distinction emerges when both parties are directly acquiring final consumption goods, which is what is happening in the barter environment.Unlike other papers that have highlighted production specialization, producation specialization is already built into our model economy.Rather our results characterize specialization within an economic unit.
Second, welfare is generally not the same in the two monetary economies.The two monetary equilibria are Pareto ranked, with household welfare not greater in the vendor-pays environment.In that sense, the equilibrium in the vendor-pays environment has the flavor of a coordination failure.We show that an institutional arrangement that governs the actions in the economic unit can enforce symmetric trading rights, thus elimination any inefficiency associated with the vendor-pays economy.In our view, the existence of monetary settlement is the source of within-unit specialization.As such, the payment system can, in part, account for the governance structures that exist in economic units comprised of agents within the unit that are specialists.
The nature of our results does have some potential implications for analyzing trade patterns.On a historical front, our results suggest that the evolution from barter economies to monetary economies in ancient days involved consideration of both production specialization and trade specialization.
Next, note that relative prices are related by ( ) ( ) 5)   which implies that in a symmetric equilibrium, the relative price paid by the vendor for a good brought from i locations away is the inverse of the relative price paid by a shopper for a good purchased i locations away.By substituting (B.5) into (B.4),relative prices for a symmetric equilibrium must then obey ( ) ( ) ( ) ( ) p i ≠ If, however, 1, α > then each term i is nonpositive for ( ) 0, p i > and strictly negative for ( ) 1. p i ≠ Thus, for any 0 α > , only ( ) 1 p i = for all i satisfies (B.6).
To verify this claim, note that each term in the sum has the form where ( ) α > we know that x x α − and 2 1 x − are both strictly positive (if 1) x > or strictly negative (if 1).
x < Thus, the left-hand side of inequality (B.9) is less than zero for any 1, x ≠ implying that ( ) Finally, for any 0, α > it is easy to show that inequalities (B.7) and (B.9) hold as equalities when 1. z x = = Thus, the material balance condition for a symmetric equilibrium is satisfied if and only if all relative prices are such that ( ) 1 p i = for all .i

Proposition 2 :
computed for the vendor-pays and shopper-pays cases, respectively.In the two monetary economies, (

Proposition 3 :
With a costless intermediary to enforce symmetric trade rights, ( t Producers and consumers simply have different factors that they consider when assessing the benefits of what variety 1In a symmetric equilibrium, all households choose the same number of locations to visit (so k k′ = ), so that ( ) , p l l i + and ( ) , q l l i − depend only on .iConsequently, we suppress the dependence on l without loss each term i in (B.6) nonnegative for all ( ) 0 p i > and strictly positive for ( )1.
we have, for all positive z and x ( ) ( ) ( )(), what the vendor is going to choose.We will focus on equilibrium allocations with this type of friction present in all of our analyses.
pays, consider the vendor solves the problem, communicates costlessly to the shopper, who then knows how many locations are willing to trade with the shopper.In this illustration, when the vendor solves for t S ′ it simultaneously solves for t S .By taking t S as given, we are implicitly treating the shopper as being Jim Dolmas & Joseph H. Haslag ~ 10 ~ oblivious to Note that the number of goods each household consumes is 2 .
t k 11