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
3. Suppose that steel is produced by a competitive industry. Each firm in the industry has...
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