Question

3. Suppose that steel is produced by a competitive industry. Each firm in the industry has the following cost function: TC = 36+q?. The demand function is Q = 2520-10p a. Derive an expression for marginal cost? At what output is average cost minimized? What is the short run supply curve for this industry? Be as precise as you can. b. Suppose the government gives a subsidy of 11 to each firm in the industry. The subsidy is fixed and the government allows free entry. At what output is average cost minimized now? C. What happens to price, output per firm and economic profit for each firm for this industry in the short run. d. What happens to price, output per firm and economic profit for each firm in this industry in the long run after entry takes place.

Answer 1

a)

TC=36+q²

Marginal Cost=MC=dTC/dq=2q

Average Cost=TC/q=(36/q)+q

Average cost is minimized when MC=Average Cost i.e.

2q=(36/q)+q

q=36/q or q²=36 i.e. q=6

Average Cost is minimized at output=6

Let there be n number of firms in the industry in short run. For a competitive industry,

MC=p

2q=p

q=0.5p

It is a supply curve of individual firm. If there are n firms in industry, Market supply curve is given by

Qs=n*q=0.5np

b)

In case of subsidy, Cost function becomes

TC=25+q²-11=25+q²

Marginal Cost=MC=dTC/dq=2q

Average Cost=TC/q=(25/q)+q

Average cost is minimized when MC=Average Cost i.e.

2q=(25/q)+q

q=36/q or q²=25 i.e. q=5

Average Cost is minimized at output=5

c)

Marginal cost remains the same for each firm. Hence optimal output is unchanged for each of the firm in short run.

Price remains the same.

Since each firm is getting a subsidy of 11, profit will increase by 11.

d)

In long run, output of each firm=output that gives minimum ATC=5 units

In long run p=minimum ATC [(25/q)+q]

i.e.Long run price, p=(25/5)+5=10

Total Revenue=p*q=10*5=50

TC=25+q²=25+5²=50

Profit in long run=Total Revenue-Total Cost=25-25=0