Division of Research August 1984 Graduate School of Business Administration The University of Michigan PRICE FIXING ABOVE COMPETITIVE EQUILIBRIUM Working Paper No. 386 Lu Wang FOR DISCUSSION PURPOSES ONLY None of this material is to be quoted or reproduced without the expressed permission of the Division of Research.

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PRICE FIXING ABOVE COMPETITIVE EQUILIBRIUM Lu Wang Assistant Professor of Finance School of Management The University of Michigan-Dearborn

This paper intends to make a modification of the following familiar dia gram: P D S \ I Sur lus K P. C that is, a purely competitive industry constrained with a price fixing, with the price p fixed above its market-clearing level Pc. This paper argues that the. surplus IK shown in the above diagram can not be sustained over'time; since the industry will not supply a quantity as much as pK, incurring a marginal cost MC = p yet finding that they really are not able to sell all of the quantity pfK to realize the p for each of the units they have produced. But the industry will not supply so few units as pI, either; since the now realizable unit price p > MC and thus there is an incentive for each firm to supply more in order to maximize its profit. From the above two considerations, we see that pK is too much and yet p I is too less; thus, intuitively, the equilibrium state can only be settled somewhere between points I and K.

2 So we are searching for a point J lying between I and K, or in other words, P < < I = 1. This proportion (I) should serve as the probability for each PK PJ PI PJ unit to be sold in the market, because of the assumption of homogeneous product from pure competition. It then follows that. (-P) is the expected P PJ unit price (i.e., expected average revenue) p for each unit produced. Furthermore, this expected average revenue p should also be the expected marginal revenue; since -- as firms in free pure competition perceive their individual variations of the quantity supplied not to influence the market - determined price, so do competitive firms under price fixing P perceive their individual variations of the quantity supplied not to influence the market-determined proportion of quantity sold to quantity supplied (-I); i.e., firms take (P) as given and see P () = PJ PJ PJ P both as the expected average revenue and as the expected marginal revenue for ~=_ PI each unit they produce. As such,the equilibrium condition is p =p.( ) = MC PJ (which, as usual, is a function of the quantity supplied ~J ). In other words, we want to solve the equation p.L ) = MC(PJ) for pJ. That particular rJ* is PJ the equilibrium industry quantity supplied, with the resultant IJ* = pJ* - p being the equilibrium market excess supply. Now, in addition to the above algebra, the geometry of determining pj* from.(PI) = MC(pJ) could also be done as follows: PJ Transposing pJ to the other side of the equation, we have pJ MC(pJ) = p ' pI = the fixed total market revenue due to the price fixing. This suggests that we draw rV a rectangular hyperbola starting the point I; this 'effectual demand curve D' will intersect the industry's supply curve S at a point H, which will determine pJ*. That is,

I 0 -3 - P D S I J* (={(PQ): P<P & PQ=P;'rI=the fixed total market revenuej ) O --- —- Q* The above analysis is attributed to the existing rich airline studies. Following Yance [2], the equilibrium condition for a carrier under price regulation p is that p = the marginal cost seat sold MC (marginal cost seat supplied) a-(marginal load factor) dS MC D (the average load factor) x S. LD) (the capacity elasticity of demand) S D as S 3D For an oligopolistic industry, due to the mutual dependence recognized, (S ) cl. But for a purely competitive industry (without mutual dependence recognized), S 2D (D a-) = 1, that is, the individual carrier takes the observed average load factor (D) as given and believes that its incremental quantity supplied AS will bring about a proportional increase in AD, i.e., A - D (Schmalensee [1]). ' '"A S S Hence, p (D) = MC, which is the concluding point of the above analysis. Finally, we note that, like any other proposition of a static equilibrium point, no dynamic discussion is made here.

-4 -REFERENCES [1] Schmalensee, R., "Comparative Static Properties of Regulated Airline Oligopolies," The Bell Journal of Economics, Autumn 1977. [2] Yance, J.V., "Nonprice Competition in Jet Aircraft Capacity," The Journal of Industrial Economics, December 1972.