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} = 0.25yi^{2} + 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**

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