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 Q+2 100

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

ii) Frompart(i),findthemonopolist’stotalrevenuecurve.

iii) If the monopolist’s marginal revenue curve is MR(Q) = 50 ? Q , what is 10

its optimal supply?

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

outcome.

Answer 1

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. Long run price is minimum of AC which is $10 per unit. At this price, Q = 1000 – 20*10 = 800 units. Each firm produces 8 units and so there are 800/8 = 100 firms in the long run.

CS = 0.5*(max price – current price)*current qty = 0.5*(50 – 10)*800 = $16000.

Market supply is

P = q + 2

q = P – 2

Qs = 100q = 100P – 200.

PS = 0.5*(current price – minimum price)*qty = 0.5*(10 – 2)*800 = $3200

b. i) AR = Inverse demand function

20P = 1000 – Q

P = 1000/20 – Q/20

P = 50 – Q/20

ii) TR = PQ = 50Q – Q^2/20

iii) Use MR = MC

50 – Q = Q + 2

48 = 2Q

Q = 24 units.

iv) This outcome is inefficient as there is a deadweight loss and the total surplus is not maximized.