Long-run equilibrium in a competitive market with per unit transaction costs.
A competitive equilibrium in a market with transaction costs is defined in the same way as a market without transaction costs, but with full prices now playing an adjustment role. The full prices paid by buyers and received by sellers now adjust until the quantity demanded at the buyer's full price is equal to the quantity supplied at the seller's net realised selling price, with the additional property that the amount of money that is exchanged (that is, the two money prices) must be equal. In other words,
and these prices adjust until QS = QD.
To illustrate, let us continue with our simple example of linear demand and supply curves. To find the competitive or market clearing equilibrium, we equate demand with supply, and set the money prices equal to a single money price that is common between the two sides of the market:
Thus, if PSf = P>M = P*, we have:
This means that PD = P* +tD = a +12 +ts and Ps = P* - tS = -—12—^.
The equilibrium is illustrated in Figure 1.3.1.
The analysis of competitive markets with per unit transaction costs is similar to the analysis of specific commodity taxation in competitive markets, with a few subtle but important differences. Most notably, although a tax collects revenue, activities which consumers and producers regard as transaction costs may not. For example, if market transaction involve search, waiting in queues, or travel then there may be little or no revenue collected from any economic actor as a result of such activity. Nevertheless, the analytical similarities between per unit transaction costs and specific taxes lead to several very interesting and important conclusions:
Figure 1.3.1 Long-run competitive equilibrium in a market with per unit transaction costs
- • First, in terms of equilibrium market quantities, what matters is not the individual transaction costs faced on each side of the market, but the sum of these transaction costs. In other words, if the sum of the transaction costs does not change, then the equilibrium market quantities do not change, and economic welfare does not change.
- • Second, (as with taxation) the economic incidence of the transaction costs is independent of the physical or legal incidence of the transaction costs. The former describes the extent to which each party is affected in economic terms by transaction costs; the latter is the extent to which each party is physically burdened by transaction costs.
- • Third, the less elastic side of the market bears the larger fraction of the economic burden of transaction costs, and this fraction is independent of the physical incidence of transaction costs.
To see the first two results, suppose that only buyers physically face transaction costs of tD, but that these costs are equal to the sum t illustrated in Figure 1.3.2. In this diagram, buyers face transaction costs of tD = t which are equal to the sum of the transaction costs in Figure 1.3.1. Note that the market quantity does not change: the transaction costs t simply drive a wedge between the full buyer and the money price that they pay. Since the size of the overall wedge is assumed not to change, the market quantity does not change either.
Figure 1.3.2 Only buyers face transaction costs equal to t
Figure 1.3.3 Only sellers face transaction costs of t > 0
Now consider the opposite situation, in which only sellers face transaction costs of t. This situation is illustrated in Figure 1.3.3. In this figure, sellers face transaction costs of tS = t which are equal to the sum of the transaction costs in Figure 1.3.1. Note that once again, the market quantity does not change: the transaction costs t again simply drive a wedge between the full buyer and the money price that they pay. Since the size of the overall wedge is assumed not to change, the market quantity does not change. The sum of the transaction costs do not change, then the equilibrium market quantities do not change, and economic welfare does not change.
Figure 1.3.4 Transaction cost incidence when the supply curve is perfectly elastic
Note also that in Figure 1.3.2 and Figure 1.3.3 the physical incidence of the transaction costs differed completely. And yet the economic incidence of the transaction costs did not change: the well-being of both buyers and sellers was the same in each situation. This illustrates the second point above.
To see the third result, consider Figure 1.3.4 above. In this diagram we consider the original situation in which the seller physically bears the burden of the transaction costs t, and then compare this to the situation where the seller's marginal cost curve is perfectly elastic. Even though the seller physically pays the transaction costs t, the buyer bears the entire economic burden when the seller's supply curve is perfectly elastic.
Tax incidence analysis also provides us with an exact formula for predicting the economic incidence of changes in transaction costs when those changes are sufficiently small. Let t be the sum of the transaction costs. Let PD and PS be the full buyer price and net realised seller price respectively. By definition we have PD = PS +1, and in a competitive equilibrium we have:
Differentiating with respect to t, and noting that in an equilibrium markets clear, we have:
At the point where transaction costs are zero, we have PS = PD and QS = QD and so this formula collapses to:
dQD PD dQS PS
where ?D =—D^ and ?S = S. — are the price elasticities of demand
D dPD Qd S dPs Qs P
and supply respectively. Since —D = —^ +1, we also have:
Further, since the terms -dPS/dt and dPD/dt add to 1, each expression can be interpreted as the fraction of the burden borne by each side of the market. If, for example, the supply curve is perfectly
elastic as in Figure 1.3.4, then ?s = ~ and so D = lim s— = 1 and
dP ? dt ?s -?s -?d
= lim^^^ = 0.
dt ?s ?s - ?d
184.108.40.206.3 The influence of transaction costs on the money prices paid by consumers. We are now in a position to analyse the effect of transaction costs on the money price that is exchanged between buyers and sellers. Recall that:
where PD is the full price, PDM is the money price, and tD are the additional per unit transaction costs incurred by the buyer. This means that:
and so, holding tS constant, we have:
This inequality states that an increase in tD, holding tS constant, reduces the money price paid by buyers. Similarly, a reduction in tD, holding tS constant, increases the money price paid by buyers.
This result is illustrated in Figure 1.3.5 below, where tS is held constant but tD falls to tD < tD. The money price is initially P. The transaction costs are initially tD and tS, and are identical to the transaction costs in Figure 1.3.1 above. The full price paid by buyers is PD = PM + tD =
рМ + tD = PS + tS + tD.
Now suppose that transaction costs faced by buyers fall to t'D < tD. The new full price paid by buyers is PD = PS + tS + tD, and the new money price is P' = PD- t'D> P. The full price paid by consumers falls, but the money price paid by consumers rises. As expression (1.7) indicates, money prices always respond to changes in buyer transaction costs in this way.
If we were to ignore transaction costs and full prices and instead focus only on money prices, then a situation like Figure 1.3.5 would present great difficulties. Money prices would rise (which, in the absence of a consideration of transaction costs, would indicate that consumers would be worse off), but quantity demanded would also
Figure 1.3.5 A reduction in the transaction costs faced by buyers increases the money price paid rise. Failing to account for transaction costs would therefore give a very misleading picture of changes in both economic behaviour and economic welfare.
What about the effect of changes in the transaction costs faced by sellers? Recall that PM = PD - tD. Thus, holding tD constant, we have:
Thus, holding tD constant, an increase in tS increases the money price paid by buyers. Combining all of these results, we can state the following. If both tD and tS increase at the same time, then:
- • The full price paid by consumers must rise (unless demand is perfectly elastic); and
- • The effect on the money price paid by consumers is ambiguous, and is given by:
This is a weighted average of the change in the transaction costs faced by the buyer and the seller. The first term is negative, but the second term is positive. The overall effect on the money price depends on the relative elasticities of supply and demand, and the size of the change in the transaction costs faced by both buyers and sellers.