Answer to Question #248520 in Microeconomics for msuma

Question

Assume the following demand and cost function of a monopolistically

competitive firm:

P = 100 − 0.2Q

TC = 30Q − 5Q

2 + Q3

i. Determine the long run equilibrium price and output of a

monopolistically competitive firm.

ii. How is monopoly solution (price and output) different from that of

monopolistic competitive solution (price and output)?

iii. Find out the perfect competitive solution (price and output) and

compare the results with monopoly and monopolistically

competitive solution (price and output)

iv. Why do results vary from perfect competition to monopolistic

competition to monopoly?

Answer 1

i

 In long run monopolistically competitive firm behave as perfect competition and in long run profit is zero for perfect competition

Profit = Revenue - Total cost 

0 = Revenue - total cost

Price = Avg. cost 

$100 − 0.2Q = 25 \\ 0.2Q = 75\\ Q = 375............(1)\\ P = 100 - 0.2\times(375)\\ P = 100 - 75\\ P =\$25.............(2)$

ii

Profit = Revenue -Total cost

$Revenue = Price\times Quantity \\ Revenue = (100-0.2Q)\times Q\\ Revenue = 100Q - 0.2Q^2\\ Total \space cost = 30Q - 5Q\\ Profit = 100Q - 0.2Q^2 - 30Q + 5Q\\ Profit = 100Q - 0.2Q^2 -25Q\\ Profit = 75Q - 0.2Q^2\\ At \space profit \space max. \\ 0 = 75 - 0.4Q\\ \frac{75}{0.4 }= Q\\ Q = 187.5..............(3)\\ P = 100 - 37.5\\ P = \$62.5.................(4)$

In short-run monopoly and monopolistically competitive produce same output at same price

iii

In short-run monopoly and monopolistically competitive produce same output at same price but in long run monopolistically competitive firm work as perfect competition and produce zero profit 

iv

In perfect competition, the firms are price takers while in Monopoly the firms are price makers and in this case monopolies have a single seller. Monopolistic competition is an intermediate between perfect competition and monopoly where it has at least 2 firms but not a large number of sellers.