Question

Consider a competitive industry in which each firm has the following total cost function: c(q) = aq + 16q - 8q^2 + q^3. Market demand for the good is given by Q = 120 - 4p.

A. Derive the expressions for each firm's average cost and marginal cost as functions of q.
B. Verify that regardless of the value of the constant a, these curves meet at q = 4. Do they meet anywhere else?
C. What is the short-run supply curve of each firm? Explain.
D. Suppose that a = 10 and initially that there are 10 firms. Describe the long-run adjustments in the industry assuming any new firms have the same production costs.
E. Verify that there would be 15 firms in total in the long run if a equals the number of firms in the industry.

Answer 1

a. Average cost = a+16-8q+q^2

Marginal cost = a+16-16q+3q^3

b. If q=4, then average cost is equal to marginal cost=a

d. If a=10, then average cost and marginal cost is equal to 10

Step-by-step explanation:

Average cost is total cost divide by quantity. Put mathematically, Ac= Tc÷q, ac= (aq+16q-8q^2+q^3)÷q=a+16-8q+q^2

Marginal cost: it is additional cost incurred as a result of producing additional unit or quantity.

Mc= change in total cost divided by change in quantity

Mc= a+16-16q+3q^3

b. If q is equal to 4,then replacing 4 for a in both average cost function and marginal cost function,we arrive to a point where mc =ac=a,where a is a constant