Question

2. (10 points) You are the manager of a monopolistically competitive firm. The present demand curve you face is P = 100 – 4Q. Your cost function is C(Q) = 50 + 8.5Q².

a. (3 points) What level of output should you choose to maximize profits?

b. (2 points) What price should you charge?

c. (5 points) What will happen in your market in the long run? Explain.

Answer 1

We have the following information

Demand curve: P = 100 – 4Q; where P is price and Q is output

Cost function: C = 50 + 8.5Q²

Part a) In a monopolistically competitive market the equilibrium is attained at the point where the marginal cost (MC) is equal to the marginal revenue (MR)

Total Revenue (TR) = P × Q

TR = 100Q – 4Q²

MR = ΔTR/ΔQ = 100 – 8Q

MC = ΔC/ΔQ = 17Q

MR = MC

100 – 8Q = 17Q

25Q = 100

Equilibrium output = 4

P = 100 – 4Q

P = 100 – 16

Equilibrium price = P = 84

Part 3) In the long-run the situation will remain the same. In a monopolistically competitive market the long-run is made up of the combination of several identical short-run periods with the assumption that decisions in one period will not affect future periods and are also not affected by the past actions. This basically means that the decision which is optimum for any one period is also optimum for any other period.