M. Pingle J. of Economic Behavior Org. 41 2000 3–26 9
A special case is the case where m = 0. With a zero markup, wholesale and retail prices would be equal and ρ
1
= ρ
2
. Case 3 would hold only if by chance MRSy
1
,y
2
= ρ
1
= ρ
2
, meaning all subjects would almost surely find trading through the store more attractive
than self-sufficiency. To be viable with this zero markup, the store would have to be able to operate without incurring any costs and would be restricted to earning zero profits. This
special case is that implicitly assumed in standard general equilibrium model where trade is mediated exclusively by a price system.
Here, a more general case is considered by assuming that the store-owner must pay costs equal to C
1
≥ 0 units of Good 1 and C
2
≥ 0 units of Good 2 to operate the store. After paying these costs and meeting all of the trading desires of its customers, the store owner is allowed
to keep any remaining inventory as profits. As the costs C
1
and C
2
increase from zero, the markup must also increase in order for the store to be viable. The increase in the markup
would make Case 3 no trade through the store more likely and would reduce the volume of trade through the store under cases 1 and 2. That is, increases in the costs of providing
intermediation reduce the extent to which self-sufficient subjects can benefit from mediated trade.
An increase in the wholesale price ratio q
1
q
2
increases both ρ
1
and ρ
2
. This causes all subjects trading with the store to reduce their consumption of Good 1 and increase their
consumption of Good 2. Subjects under Case 1 sell more Good 1 to the store, while subjects under Case 2 buy less Good 1 from the store. Conversely, subjects under Case 1 buy more
Good 2 from the store, while subjects under Case 2 sell less Good 2 to the store.
An increase in the decision cost level D decreases the optimal consumption levels of both goods, implying a reduction in mediated trade.
5. Opening a store
In the experiment, no store exists at the outset. If intermediation is to occur, it must arise endogenously. As an alternative to barter or trading through an existing store if one were
in existence, subjects could attempt to open a store. The store attracts inventories of the two goods by paying the wholesale prices q
1
and q
2
. Out of this inventory, the store must first deliver to subjects their desired purchases of Goods 1 and 2. With a positive markup, it is conceivable that the store could generate excess
supplies of each good. Let the functions E
1
m,q
1
q
2
and E
2
m,q
1
q
2
denote the excess supplies as they depend upon the markup m and the wholesale price ratio q
1
q
2
. Out of these excess supplies, the store must pay its operating costs C
1
and C
2
. Thus, after it pays its costs and meets all of the subjects’ trading desires, the store’s remaining inventories of
the two goods can be represented by I
1
= E
1
m,q
1
q
2
− C
1
and I
2
= E
2
m,q
1
q
2
− C
2
. To obtain explicit representations for E
1
m,q
1
q
2
and E
1
m,q
1
q
2
, consider some addi- tional simplifying assumptions. Suppose 1 trading through the store is the only alternative
to self-sufficiency; 2 all subjects optimize with D = 0, and 3 the number of type A sub- jects, n
A
, is equal to the number of Type B subjects, n
B
, so that n = 2n
A
= 2n
B
gives the number of subjects in the economy. It then follows that the store’s inventories I
1
and I
2
are given by the functions
10 M. Pingle J. of Economic Behavior Org. 41 2000 3–26
I
1
n, m, q
1
q
2
, C
1
= n
2 y
A 1
+ y
B 1
2 −
1 2q
1
q
2
y
A 2
[1 + m] + y
B 2
[1 + m] − C
1
and I
2
n, m, q
1
q
2
, C
2
= n
2 y
A 2
+ y
B 2
2 −
q
1
q
2
2 y
B 1
[1 + m] + y
A 1
[1 + m] − C
2
. Note that I
1
and I
2
are not monotonic functions of the markup m. When the markup increases, Type A subjects sell less Good 1 to the store, while Type B subjects sell less
Good 2. These responses reduce the store’s inventories of each good. However, the store’s inventories of each good are enhanced by the fact that Type A subjects buy less Good 2 from
the store, while Type B subjects buy less Good 1. The partial derivative ∂I
1
∂m indicates that an increase in the markup generates an increase in I
1
when m q
y
A 1
y
B 1
− 1, with I
1
decreasing for larger markups. Similarly, the partial derivative ∂I
2
∂m indicates that an increase in the markup generates an increase in I
2
when m q
y
B 2
y
A 2
− 1, with I
2
decreasing for larger markups. The store’s most pressing problem is viability, which requires I
1
≥ 0 and I
2
≥ 0. Note that if m = 0 and q
1
q
2
= 1, then E
1
= 0 and E
2
= 0 so that I
1
= −C
1
and I
2
= −C
2
. In this case, the store is viable only if C
1
= 0 and C
2
= 0. This outcome is the standard general equilibrium solution. However, if there are costs to operating the store, then the store cannot be viable
with a zero markup. When C
1
0 or C
2
0, the store must generate an excess supply of one of the good without generating an excess demand for the other good. Note that E
1
is an increasing function of q
1
q
2,
while E
2
is decreasing. Thus, as q
1
q
2
increases from q
1
q
2
= 1 with m = 0, E
2
becomes negative. Conversely, as q
1
q
2
decreases from q
1
q
2
= 1 with m = 0, E
1
becomes negative. Therefore, as long as m = 0, there is no adjustment the store can make in the wholesale price ratio so that it can cover either C
1
0 or C
2
0. For a given wholesale price ratio q
1
q
2
, E
1
and E
2
increase as m increases from zero. Thus, there must exist a range of markup levels where the store can at least pay portions of
any positive operating costs C
1
and C
2
. However, because E
1
and E
2
are decreasing in m once the critical markup levels given above are reached, there is no guarantee that a viable
markup level exists for a given population n of subjects. Yet, as long as q
1
q
2
and m are set so that E
1
and E
2
are positive, the store must eventually become viable as the population of subjects increases. Mathematically, this follows from
the fact that I
1
and I
2
are each increasing in n as long as E
1
and E
2
are each positive. The intuition is that, if the number of transactions is large enough, any level of operating costs
can be covered by the store if the store is netting a positive return on each transaction. Since the store-owner can consume the remaining inventories I
1
and I
2
, store ownership is potentially lucrative. Given his or her own post-production bundle y
1
,y
2
, a subject seeking to open a store could move beyond the viability goal and choose m and q
1
q
2
so as to maximize U = U
1
y
1
− D + I
1
+ U
2
y
2
+ I
2
, where D is the decision cost required to first produce and then solve this problem. In the absence of competition among stores, this would
determine the economy’s markup level and wholesale price ratio. Note that this monopoly solution is the same as the standard general equilibrium solution if D = C
1
= C
2
= 0.
M. Pingle J. of Economic Behavior Org. 41 2000 3–26 11
Recognizing the potential for competition, another approach to determining the markup and wholesale price ratio would be to assume that the store-owner would act so that no other
store-owner could viably enter the market. This ‘contestable markets’ solution would imply that m and q
1
q
2
are set for a given population of n subjects so that E
1
= C
1
and E
2
= C
2
. Note that this contestable markets solution is the same as the standard general equilibrium
solution if D = C
1
= C
2
= 0.
6. Experimental procedure
