Suppose there are 100 firms in a perfectly competitive industry. Each firm has a

Question

Suppose there are 100 firms in a perfectly competitive industry. Each firm has a U-shaped, long-run average cost curve that reaches a minimum of $10 at an output level of 8 units. Marginal costs are given by

MC(q)= q+2

and market demand is given by

Q=1000-20P

a. Find the long-run equilibrium in this market and determine the consumer and producer surplus (in this case, the areas of the triangles).

b. Suppose instead there was a single supplier whose marginal cost curve is

MC(Q) =(1/100)Q+2

i) From the above expression for market demand, determine the monopolist’s average revenue curve.

ii) From part (i), find the monopolist’s total revenue curve.

iii) Differentiate the expression in part (ii) to obtain the monopolist/s marginal revenue curve.

iv) From part (iii), what is the monopolist’s optimal supply?

v) Explain why this outcome is inefficient in comparison to the competitive outcome.

Explanation / Answer

a) Long run condition requires firms to operate at minimum of ATC and earn zero economic profit that implies P = ATC. Given these facts, P = $10, q = 8 units and industrial quantity is 800 units. Consumer surplus is equal to 1/2*(50-10)*800 = 16000. Producer surplus = 1/2*10*800 = 4000, Total surplus is 20,000.

b) AR is nothing but TR/Q which implies

Q = 1000 - 20P

P = 50 - 0.05Q

TR = 50Q - 0.05Q^2

AR = 50 - 0.05Q

This is the expression for AR curve.

ii) The TR curve is TR = 50Q - 0.05Q2

iii) Marginal revenue = d(TR)/dQ = 50 - 0.1Q

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