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.

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

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

x=3

step-by-step explanation:

this is really simple i saw that there was only one term (5x) and thought if that was 15 what would i have to multiply everything else to get it there? well if 5x became 15 then x would have to be 3 so plug the 3 in the x for the other equations and you get 15 for the other ones. so there you go. : )

answer///video, because samuel can show his work in real time and be better understood;