OLIGOPOLY 1.- Each of two firms, firms 1 and 2, has a cost function C(q) = 30q; the inverse demand function for the firms' output is p = 120-Q, where Q is the total output. Firms simultaneously choose their output and the market price is that at which demand exactly absorbs the total output (Cournot model).(a) Obtain the reaction function of a firm.(b) Map the function obtained in (a), and graphically represent the Cournot equilibrium in this market.(c) Repeat (b), this time analytically.(d) Now suppose that firm 1's cost function is C(q) = 45q instead, but firm 2's cost is unchanged. Analyze the new solution in the market.(e) Obtain the total surplus, consumer surplus, and industry profits in both cases, and compare. What is the effect of the worsening in firm 1's cost?

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Asked Oct 14, 2019
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OLIGOPOLY 1.- Each of two firms, firms 1 and 2, has a cost function C(q) = 30q; the inverse demand function for the firms' output is p = 120-Q, where Q is the total output. Firms simultaneously choose their output and the market price is that at which demand exactly absorbs the total output (Cournot model).
(a) Obtain the reaction function of a firm.
(b) Map the function obtained in (a), and graphically represent the Cournot equilibrium in this market.
(c) Repeat (b), this time analytically.
(d) Now suppose that firm 1's cost function is C(q) = 45q instead, but firm 2's cost is unchanged. Analyze the new solution in the market.
(e) Obtain the total surplus, consumer surplus, and industry profits in both cases, and compare. What is the effect of the worsening in firm 1's cost?

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Expert Answer

Step 1

Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and specify the other subparts (up to 3) you’d like answered.

Oligopoly: The market which has few sellers selling differentiated products.

Step 2

There are two firms in the market Firm 1 and Firm 2 with Cost function C(q) = 30q and inverse demand function p = 120-q, where q is the output produced.

The firms simultaneously choose their price and quantity at which market demand is equal to supply.

Step 3

The reaction function of the firm is given as below:

 

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p 120-q..(Market Demand Function) Q q1+q2

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