Question

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

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.

Y = 2400 − 200P

c(yi) = TCi = 0.25yi2 + 100

so, MCi = dTCi/dyi = 0.5yi

n = 50

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

P = MCi

P = 0.5yi

yi = P/0.5

yi = 2P

(ii) The industry supply function is given by:

Y = nyi

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 = nyi

800 = 50yi

yi = 800/50

yi = 16

(v) Individual firm's profits are:

Profit = TRi - TCi

At P = 8 and yi = 16,

TRi = P * yi = 8 * 16 = 128

TCi = 0.25(16)2 + 100 = 164

Profit = 128 - 164

Profit = -36