Abstract
The chapter presents an evolutionary model of a product differentiated industry and proves that the monopolistically competitive equilibrium will arrive as a long run outcome even though firms are totally irrational. In this evolutionary model, firms are totally irrational in the sense that firms enter the industry regardless of the existence of profits; firms’ outputs are randomly determined rather than generated from profit maximization problems; and firms exit the industry if their wealth is negative. The model concludes that the industry converges in probability to the monopolistically competitive equilibrium as the size of each firm becomes sufficiently small, as entry costs become sufficiently small and as time gets sufficiently large. The firms that remain in the industry in the long run are those producing output at the tangency of the demand curve to the average cost curve. Furthermore, in the long run, no potential entrant can make a positive profit by entry.
This chapter is based on my article published in European Economic Review 53(5): 512–526, 2009.
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Notes
- 1.
As noted by Arrow (1986, p. s391), the knowledge requirements under a monopoly are very demanding. “The demand curve is more complex than a price. It involves knowing about the behavior of others. Measuring a demand curve is usually thought of as a job for an econometrician. We have the curious situation that scientific analysis imputes scientific behavior to its subjects.”
- 2.
Certainly, there are two possible extreme assumptions with respect to firms’ behavior. One is complete rationality and the other is no rationality. Other behavioral traits such as adaptive behavior would lie in between. The chapter abandons all rationality on the firms’ part to illustrate and highlight the impact of a very irrational world on the long run aggregate market. Even when we remove the plank of rationality and replace this with total irrationality, the traditional monopolistic competition equilibrium emerges. This is very compelling and reinforces the idea that even without rationality, natural selection forces lead to a monopolistically competitive equilibrium. Purposive maximization of profits is not required.  Undoubtedly, allowing adaptive behavior on the firm side will also lead to convergence; however, the speed of convergence is faster.
- 3.
The average cost function could be U-shaped but the relevant part of the average cost curve for this model is the downward sloping part of the average cost curve.
- 4.
Using wealth as the selection criterion means that for a firm to survive, the firm upon entry must cover its entry cost in addition to its variable costs. However, this condition could be relaxed to allow for a firm to continue its operations as long as it recovers some part (say dk (for some d < 1)) of its entry costs in addition to its variable cost, upon entry. This relaxation of the survival condition on entry does not change the results of the chapter (as the only change in the proofs would be that the wealth at the end of entry period would be modified to subtract off dk rather than k).
- 5.
It should be noted that a part of the distribution of surviving firms’ average costs at time 15,000 lies to the right of the corresponding price distribution. With wealth being used as the selection criterion, it may take a while for firms with higher average costs than current prices to leave the industry.
- 6.
Since (3.25) suggests that \(\alpha < \frac{k-2{\epsilon }^{{\prime}}} {Ab\overline{q}}\), with ε′ = 0. 005, k = 0. 025 and with \(A = 4,b = 0.05\) and \(\overline{q} = 1.75,\) this would mean that for convergence, α < 0. 043.
- 7.
Due to the nonconvergence of price, many more firms with a greater variation of average costs, are surviving at time period 15,000.
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Luo, G.Y. (2012). Evolution, Irrationality, and Monopolistically Competitive Equilibrium. In: Evolutionary Foundations of Equilibria in Irrational Markets. Studies in Economic Theory, vol 28. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0712-6_3
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