# Economic power and market efficiency

The preceding sections have shown that the power structure in the commodity market determines the price and, consequently, the distribution of benefits. Then, under what power structure can a particular price combination be reached, and does this combination lead to Pareto optimal utility for the participants?

Consumer choice theory shows that given the price, a consumer can always choose a consumption bundle to realize maximum utility under budget constraints. This logic ignores the fact that consumers are not always passive price takers. Consumers are at least able to affect the price in certain commodity markets. Consumers have different degrees of influence on different commodities. In commodity markets, it is more common to have unequal power and dispersed prices than one price. Under the premise that consumers have unequal power, if the allocation of power changes among consumers, the price also changes, which, in turn, results in a new consumption bundle. Will this change lead to Pareto improvement in the allocation of utility?

When an economic agent influences price formation, instead of choosing a consumption bundle directly, the agent will attempt to affect the price determination first and then select the bundle after the price is determined. To change the price is actually to change budget constraints. The greater the economic power, the stronger the ability to influence the price; then, the budget line will be shifted more toward the right-hand side. Hence, the individual utility level corresponding to the optimal consumption bundle will be higher. Meanwhile, the same consumer will experience changes in power in different markets, which will affect the slope of the budget line. Consequently, the agent’s consumption structure is going to change. This implies the possibility of improvement; that is, every consumer’s utility will be raised by adjusting the allocation of power in all markets for all consumers. Such adjustments continue until there is no room for further improvement given a particular power structure. Such a structure will be the most efficient one in a commodity market. We illustrate this point with the following example.

Suppose there are *m* goods, and *n* consumers in the market.

Consumer / (/ = 1,2...,«) has the economic power of *R _{ik}* in commodity market

*к (к -*where the price he pays for the commodity is

*P _{jk} *

*=*

*P*(

_{k}*R*). Following the analysis in the preceding sections of this chapter,

_{ik}*P _{k} [Ri_{k})* is monotonically decreasing. This means, the more power consumer /' has in commodity market

*к,*the lower the price he pays for commodity

*к.*Consumer

*i’s*problem is how to maximize his utility £/, through choosing different consumption bundles (ai,a'2,...,a„,) given the income constraint /,

The Lagrangian function for the above optimization problem is as follows,

where Я is the Lagrangian multiplier. If bundle *x** maximizes consumer *i’s *utility, given the budget constraint, then it follows from the first-order conditions that,

That is, for any two goods, *к* and /, the following equation holds,

Equation (5.22) states that consumer / always chooses the bundle that maximizes his utility, which makes the marginal rate of substation between the two goods equal to the price ratio.

Following the same logic, consumer *j* will choose the bundle*y** that makes

If consumer /' and *j* have equal power, that is, *R,k =Rjk* and *R,/ = Rg,* then it follows that *Pk {Rjk) = P/< (Rjk)* ^{an(}J *P,(Ru) = Pi(Rji).* It can be derived from (5.22) and (5.23) that

Equation (5.24) states that if consumers *i* and *j* have equal power in every market, the allocation of commodities will reach Pareto optimality under the guidance of maximizing their own utility. On the contrary, if the consumers have unequal power in a certain market, the marginal rates of substitution will not be equal. Hence, there will be one possible result; that is, they will take *x* and *у** as initial endowments to make further exchanges, which will raise the utility of at least one side. In this case, Pareto improvement is attained. Therefore, equal power among consumers *i* and *j* in every market is the necessary and sufficient condition for Pareto optimality.

# Notes

- 1 Chinese books and audiovisual products usually have only a single printed specification.
- 2 It should be noted that the auction price given by the auctioneer does not represent a price offer. Its one-dimensional function is to remind bidders to start bidding above this auction price. The truly binding bidding behavior starts with the bidder’s bidding.
- 3 Because when the negotiation cost isn’t zero, there is always a moment that one party either accepts or rejects and leaves. The tougher the attitude of S, the greater the probability that В leaves the table will be.
- 4 Obtained via the maximum distribution formula of multi-dimensional random variable.
- 5 Based on the maximum distribution formula of multi-dimensional random

variable. _{dy} n -O

6 The partial derivative of Уо with respect to *m*: —-2- =———*Щ-* < 0.

*dm* (1 *+ m) ^{z}*