Answer to Question #277404 in Microeconomics for Ankit

Question

. In an industry with inverse demand curve p = 100 - 2Q there are four firms, each of which has a constant marginal cost given by MC = 20. If the firms form a profit-maximizing cartel and agree to operate subject to the constraint that each firm will produce the same output level, how much does each firm produce?

2. What is the duopoly Nash-Cournot equilibrium if the market demand function is Q = 1000 - 1000p and each firm’s marginal cost is 28¢ per unit?

Answer 1

Solution:

1.). Profit maximizing output: MR = MC

TR = P $\times$ Q = (100 – 2Q) $\times$ Q = 100Q – 2Q²

MR = $\frac{\partial TR} {\partial Q}$ = 100 – 4Q

MC = 20

100 – 4Q = 20

100 – 20 = 4Q

80 = 4Q

Q = 20

Each firm will produce = $\frac{20}{4}$ = 5 units

 

2.). Derive the inverse demand function:

P = 1 – $\frac{Q}{1000}$

TR = P $\times$ Q = (1 – $\frac{Q}{1000}$ ) $\times$ Q = Q – $\frac{Q^{2} }{1000}$

MR = $\frac{\partial TR} {\partial Q}$ = 1 – $\frac{Q}{500}$

MC = 28

Set MR = MC

1 – $\frac{Q}{500}$ = 28

Q = 13,500