Consider a monopolistic competitive industry with 4 firms producing the same good. The (inverse) demand for the good is given as: p=30-Q where Q is total units of the good produced by the firms: Q =q₁. Each firm chooses their output qi to maximize profits. The cost of producing q units of output is the same for all firms: C(q) = 6qi for all i = 1, ..., 4. (a) Suppose all 4 firms choose their outputs at the same time (i.c., Cournot model), what will be the profit-maximizing outputs for each firm. [Note: Firms are iden- tical and face the same demand curve, hence model is symmetric] (b) Now consider a Stackelberg model in which 3 of the 4 firms (say, firms 1, 2 and 3) are already in the industry, hence act as Stackelberg leaders. That is, the 3 firms choose their outputs 91, 92, 93 at the same time in Stage 1 of the model. Then in Stage 2, the 4th firm (the follower) produces her output 9₁. Solve for the profit-maximizing quantitics 91, 92, 93, 94 in this Cournot-Stackelberg model. What is the total output Q and the price of the good?

Consider a monopolistic competitive industry with 4 firms producing the same good. The (inverse) demand for the good is given as: p=30-Q where Q is total units of the good produced by the firms: Q =q₁. Each firm chooses their output qi to maximize profits. The cost of producing q units of output is the same for all firms: C(q) = 6qi for all i = 1, ..., 4. (a) Suppose all 4 firms choose their outputs at the same time (i.c., Cournot model), what will be the profit-maximizing outputs for each firm. [Note: Firms are iden- tical and face the same demand curve, hence model is symmetric] (b) Now consider a Stackelberg model in which 3 of the 4 firms (say, firms 1, 2 and 3) are already in the industry, hence act as Stackelberg leaders. That is, the 3 firms choose their outputs 91, 92, 93 at the same time in Stage 1 of the model. Then in Stage 2, the 4th firm (the follower) produces her output 9₁. Solve for the profit-maximizing quantitics 91, 92, 93, 94 in this Cournot-Stackelberg model. What is the total output Q and the price of the good?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter14: Monopoly

Section: Chapter Questions

Problem 14.5P

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2. Consider a monopolistic competitive industry with 4 firms producing the same good. The (inverse) demand for the good is given as: p=30-Q where is total units of the good produced by the firms: Q = Eq. Each firm chooses their output qi to maximize profits. The cost of producing q units of output is the same for all firms: C(qi) = 6qi for all i = 1, ..., 4. (a) Suppose all 4 firms choose their outputs at the same time (i.c., Cournot model), what will be the profit-maximizing outputs for each firm. [Note: Firms are iden- tical and face the same demand curve, hence model is symmetric]