Question

Consider a market where the demand is given by Y = 2, 400 − 200p (i.e., the inverse demand is p = 12 − 0.005Y)

Assume for the moment that this market is perfectly competitive. In the short-run, there are 50 identical firms operating in this market with cost function c (yi) = 0.25yi^ 2 + 100. Find

i. an individual firm's supply function,

ii. the industry supply function,

iii. the market price and the total quantity sold in the market,

iv. the individual firm's level of production, and

v. the individual firm's profit.

Answer 1

Y = 2400 − 200P

c(yi) = TC_i = 0.25yi² + 100

so, MC_i = dTC_i/dy_i = 0.5y_i

n = 50

(i) Individual firm's supply function is given by:

P = MC_i

P = 0.5y_i

y_i = P/0.5

y_i = 2P

(ii) The industry supply function is given by:

Y = ny_i

Y = 50(2P)

Y = 100P

(iii) The market equilibrium occurs where market demand equals market supply:

2400 - 200P = 100P

300P = 2400

P = 8

and Y = 100(8)

Y = 800

(iv) The individual firm's level of production is:

Y = ny_i

800 = 50y_i

y_i = 800/50

y_i = 16

(v) Individual firm's profits are:

Profit = TR_i - TC_i

At P = 8 and y_i = 16,

TR_i = P * y_i = 8 * 16 = 128

TC_i = 0.25(16)² + 100 = 164

Profit = 128 - 164

Profit = -36