Answer to Question #282077 in Microeconomics for Xyz

Question

1) A market has an inverse demand curve and five firms, each of which has a constant marginal cost of 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 = 4,000 - 400p, and each firm's marginal cost is $0.28 per unit?

Answer 1

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 = 10 – $\frac{Q}{400}$

TR = P $\times$ Q = (10 – $\frac{Q}{400}$ ) $\times$ Q = 10Q – $\frac{Q^{2} }{400}$

MR = $\frac{\partial TR} {\partial Q}$ = 10 – $\frac{2Q}{400}$

MC = 28

Set MR = MC

10 – $\frac{Q}{400}$ = 0.28

Q = 3,888