Imagine that a local retail market is monopolistically competitive. Each firm (a
ID: 1250457 • Letter: I
Question
Imagine that a local retail market is monopolistically competitive. Each firm (and potential entrant) is identical and faces a marginal cost that is independent of output and is equal to $100 per unit. Each firm has an annual fixed cost of $300 000 per month. Because each active firm perceives itself facing a price elasticity of demand equal to -2, the inverse price elasticity condition implies that the profit maximizing price for each firm is (P – 100) / P = ½ or P = 200. If each firm charges an equal price they will evenly split the overall market demand of 96 000 units per month.a) How many firms will operate in this market at a long-run equilibrium?
b) How would your answer change if each firm faced a price elasticity of demand of -4/3 and charged a profit maximizing price of $400 per unit?
Explanation / Answer
a. First we check that the pricing condition for monopolists are met: MR=MC. TR= 200Q MR= P(1+ 1/PED)= 200(0.5)=100 , where PED = price elasticity of demand MC= 100 So, MR=MC holds. All you need to do next is equalize total revenue with cost to see where the firms will break even. Monopolistic competition implies that as soon as there are positive profits to be made under monopolistic pricing, more firms will enter the market. So in the long run equilibrium this condition will be satisfied: TR= C TR= 200Q C= 100Q + 300,000 200Q=100Q + 300,000 Q=3,000 That means that demand needed for one firm to make zero profits is 3,000. If we now divide 96,000 by 3,000 we get 32, which is the number of firms that will be active in the market in the long run equilibrium. b. Again, we calculate the number of firms active in the market. TR= C TR= 400Q C= 100Q + 300,000 400Q=100Q + 300,000 Q=1,000 So, with a profit maximizing price of 400, the individual firm realizes zero profits with a demand of 1,000. Since total demand is 96,000, there will be 96 firms active in the market in the long run equilibrium.