Question

1, Consider a perfectly competitive market characterized by the following components where Q refers to the entire market output, P refers to the market price, and q refers to an individual firm’s output. Assume that all firms are identical and have the same technological capabilities.

Market Demand; P = 52.5 – 0.30Q / Market Supply; P = 5 + 0.20Q / An Individual Firm’s Total Cost; TC = 64 + 5q + q²

A, Determine the market output, an individual firm’s output, and the number of firms in the short run equilibrium.

B, Determine the market output, an individual firm’s output, and the number of firms in the long run equilibrium.

Answer 1

A )

P = 52.5 - 0.30Q

P = 5 + 0.20Q

Market equilibrium is given by the equality of market demand and market supply

52.5 - 0.30Q = 5 + 0.20Q

52.5 - 5 = 0.20Q + 0.30Q

47.5 = 0.5Q

Q = 95  

P = 5 + 0.20(95)

P = 5 + 19

P = 24

The equilibrium market price is P = 24 and equilibrium market output is Q = 95

TC = 64 + 5q + q²  

MC = 5 + 2q

A firm's output, in the short-run, is given by P = MC

24 = 5 + 2q

24 - 5 = 2q  

19 = 2q  

q = 9.5  

An individual firm's output is q = 9.5

Number of firms n = Q/q = 95/9.5 = 10  

B)

TC = 64 + 5q + q²  

MC = 5 + 2q

AC = TC/q  

= ( 64 + 5q + q² )/q  

= 64/q + 5 + q

AC = 64/q + 5 + q

In the long-run equilibrium P = MC = AC

MC = AC

5 + 2q = 64/q + 5 + q

5 + 2q - 5 - q = 64/q

q = 64/q

q² = 64  

q = 8

The long-run equilibrium output produced by an individual firm is q = 8

P = MC

P = 5 + 2q

P = 5 + 2(8)

P = 21

The long-run equilibrium market price is P = 21

Market demand function is

P = 52.5 - 0.30Q

21 = 52.5 - 0.30Q

0.30Q = 52.5 - 21

0.30Q = 31.5

Q = 105

The long-run market output is Q = 105

Number of firms n = Q/q = 105/8 = 13.125