Cost function of a firm is given,
In the long run equilibrium the firms earn zero economic profit thus the price is equal to minimum ATC. We are required to minimize the ATC.
Differentiating ATC wrt q we get
The first order condition of minimization is that the first derivative must be equal to zero.
Again differentiating ATC wrt q
The SOC of minimization. Is that the second derivative must be a positive number. As we can see both condition is satisfied. Hence, ATC will be minimum at q = 5 units.
Minimum ATC = $ 11 per unit
A. Long run equilibrium price = $ 11 per unit.
The long run supply curve is constant and parallel to the horizontal axis.
B. Given, Q = 111 - P
Q = 111 - 11 = 100
Market demand = 100 units.
Quantity supplied by each firm, q = 5 (calculated above)
Number of firms in long run = 20.
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