1.7. In Section 1.2.B, we analyzed the Bertrand duopoly modelwith differentiated products. The case of homogeneous products yields a stark conclusion. Suppose that the quantity that con-sumers demand from firm i is a − p; when pi < Pj, 0 when pi > Pj,and (a − p¡)/2 when p; = pj. Suppose also that there are no fixedcosts and that marginal costs are constant at c, where c < a. Showthat if the firms choose prices simultaneously, then the uniqueNash equilibrium is that both firms charge the price c.

The profit for Firm i =a-pipi-c if pi<pj= 0 if…

Answered: Nash equilibrium is that both firms…

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Nash equilibrium is that both firms charge the price c.

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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Question

1.7. In Section 1.2.B, we analyzed the Bertrand duopoly model
with differentiated products. The case of homogeneous products

yields a stark conclusion. Suppose that the quantity that con-
sumers demand from firm i is a − p; when pi < Pj, 0 when pi > Pj,
and (a − p¡)/2 when p; = pj. Suppose also that there are no fixed
costs and that marginal costs are constant at c, where c < a. Show
that if the firms choose prices simultaneously, then the unique
Nash equilibrium is that both firms charge the price c.

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