If the cost function is given, the marginal cost is the derivative of the cost function.

C(Q) = 50 + 12Q + 2Q^2

Find MC

MC(Q) = 12 + 4Q

a. The perfect competition equilibrium is where price is equal to marginal cost. Set price equal to marginal cost and solve for quantity.

In perfect competition set P=MC

12 + 4Q = 120

4Q = 108

Q = 27

The firm should produce 27 units

b. In perfect competition the best price is the market price so the firm should charge a price of $120.

c. The total revenue is equal to the equilibrium price multiplied by the equilibrium quantity. Plug the equilibrium quantity into the cost function to find the total cost. The profit is equal to the total revenue minus the total cost.

Total revenue = P * Q

TR = $120 * 27 = $3,240

C(27) = 50 + 12(27) + 2(27^2) = $50 + $324 + $1,458 = $1,832

Profit = $3,240 - $1,832 = $1,408

The profit is $1,408

d. Since there is economic profit in the short run, entry to the market has to be anticipated by the firm, the firm will end up making zero economic profit in the long run.