There are 60 firms in a competitive industry. The cost function of each of these firms is: TC = 3q^2 + 2q + 3 where TC is the total cost and q is the quantity produced by one firm.
The marginal cost function, corresponds to the above total cost function. MC = 6q + 2 where MC is the marginal cost function, and q is as before. The aggregate demand function is P = 20 - 1/5Q where P is the price per unit and Q is the aggregate quantity demanded.
a. Find the aggregate supply function. Explain.
b. At what price and quantity does this industry reach equilibrium? Explain.
c. What is the profit of the individual firm at the point of equilibrium? Explain.
d. Suppose now that 60 firms organize themselves into a monopoly. What is the equilibrium price and quantity? (The MR derived from the above demand function is MR = 20 - 2/5Q.
e. What is the profit of the monopoly? Explain and compare them to the profit of the industry when it was competitive.