ABSTRACT
Rosse and Panzar (1977) and Panzar and Rosse (1987) formulate simple models for monopolistic, oligopolistic and perfectly competitive markets, and develop a test to discriminate between these market structures. This test is based on properties of a reduced-form revenue equation at the firm or bank level and uses a test statistic H , which, under certain assumptions, can serve as a measure of the competitive behavior of banks. The test is derived from a general banking market model, which determines equilibrium output and the equilibrium number of banks by maximizing profits at both the bank level and the industry level. This implies, first, that bank i maximizes its profits, where marginal revenue equals marginal cost:
R′i (Yi,n,Zi)−C ′i (Yi,wi,Ti) = 0 (11.1) Ri refers to revenues, Ci to costs, Yi to output, wi to a vector of m factor input prices, and Zi and Ti to vectors of exogenous variables that shift the bank’s revenue and cost functions, respectively; the subindex i refers to bank i; n is the number of banks; and the prime denotes first derivative with respect to output. Second, at the market level, it means that, in equilibrium, the zero profit constraint holds:
R∗i (Y ∗,n∗,Z)−C∗ (Y ∗,w,T ) = 0 (11.2)
Variables marked with an asterisk (∗) represent equilibrium values. Market power is measured by the extent to which a change in factor input prices (dwk,i) for k = 1, . . . ,m is reflected in the equilibrium revenues (dR∗i ), earned by bank i. Panzar and Rosse (P-R) define a measure of competition H as the sum of the elasticities of the reduced-form revenues with respect to factor prices:
H = m∑
(11.3)
The first market model of Panzar and Rosse (P-R) investigates monopoly. In their analysis, monopoly includes the case of price-taking competitive banks, as long as the prices they face are truly exogenous, that is, as long as their equilibrium
values are unaffected by changes in the other exogenous variables in the model. The empirical refutation of ‘monopoly’ constitutes a rejection of the assumption that the revenues of the banks in question are independent of the decisions made by their actual or potential rivals. P-R prove that under monopoly, an increase in input prices will increase marginal costs, reduce equilibrium output and subsequently reduce revenues; hence H will be zero or negative. This is a highly generalized result, requiring little beyond the profit maximization hypothesis itself. Along similar lines, Vesala (1995) proves that the same result holds for monopolistic competition without the threat of entry, that is, with a fixed number of banks. Thus, this case also falls under what we call monopoly or perfect collusion.
