Introduction to Microlocal Analysis (L'Enseignement by Masaki Kashiwara

By Masaki Kashiwara

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Extra resources for Introduction to Microlocal Analysis (L'Enseignement Mathématique, # 32)

Example text

That yi < Sap, vi) Agent 1 could, while maintaining the same production-sales plan yi9 increase slightly his price without violating the constraint of the perceived demand curve, which would obviously increase profits, and that would contradict the profit maximization hypothesis. , he plans to satisfy all demand forthcoming at the price he sets. Of course in an equilibrium situation, such as is considered in later chapters, the pricemaker does actually satisfy all demands addressed to him. /, of the perceived demand curve.

Price Making Assume for the moment that the parameters TJ, of the perceived demand curve are known. The choice of the price p will then proceed along lines that are traditional in the theories of monopoly or monopolistic competition: In maximizing his objective function, the pricemaker takes into account parametric prices and quantity constraints on the markets where he does not set prices. In the markets where he decides on prices, however, sales must be less than or equal to the level given by the perceived demand curve, or, if he is a demander, purchases must be less than or equal to the level given by the perceived supply curve.

Z, ^ 0 -sik ^ zifc ^ dik k* h In other words, the effective demand on a market h corresponds to the exchange that maximizes utility, taking into account the constraints on the other markets. This definition, which we saw in Chapter 1, Section 4, integrates the spillover effects from the other markets. The solution of the program just given is unique, and we thus obtain a function. Repeating this program for all markets h = 1 , . . , / , we obtain a vector of effective demands ζί(ρ, d(, Si). We must immediately verify that this effective demand function leads to the optimal transaction, which results from the following proposi­ tion, proved in Appendix A: Proposition.

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