Duopoly and menu costs. (This is adapted from CaminaI 1987.) Consider two firms producing imperfect substitutes. Both firms can produce at zero marginal cost. The demand for the good produced by firm i is given by Now suppose that both firms enter the period with price p., which is the Nash equilibrium price for some value of a, a·. They know b and c. They each observe the value of a for the period, and each firm must independently quote a price for the period. If it wants to quote a price different from p, it must pay a cost k. Otherwise, it pays nothing. Once prices are quoted, demand is allocated, demand determines produdion, and profits are realized. (b) Compute the set of values of a (around a) for which not to adjust prices is a Nash equilibrium. (c) Compute the set of values of a (around a*) for which to adjust prices is a Nash equilibrium. (d) Check that all equilibria are symmetric and therefore that there are no other equilibria than the ones computed above. (e) If only Pareto optimal equilibria (in the sense of equilibria for which no other equilibrium exists with profits higher for one firm and not lower for the other) are observed, discuss the following statement: "Duopolistic prices are more sensitive to positive shocks than to negative shocks of the same magnitude."

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Duopoly and menu costs. (This is adapted from CaminaI 1987.) Consider two firms producing imperfect substitutes. Both firms can produce at zero marginal cost. The demand for the good produced by firm i is given by

Now suppose that both firms enter the period with price p., which is the Nash equilibrium price for some value of a, a·. They know b and c. They each observe the value of a for the period, and each firm must independently quote a price for the period. If it wants to quote a price different from p^*, it must pay a cost k. Otherwise, it pays nothing. Once prices are quoted, demand is allocated, demand determines produdion, and profits are realized.

(b) Compute the set of values of a (around a^*) for which not to adjust prices is a Nash equilibrium.

(d) Check that all equilibria are symmetric and therefore that there are no other equilibria than the ones computed above.

(e) If only Pareto optimal equilibria (in the sense of equilibria for which no other equilibrium exists with profits higher for one firm and not lower for the other) are observed, discuss the following statement: "Duopolistic prices are more sensitive to positive shocks than to negative shocks of the same magnitude."

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