Because entry into the market is free, and Oligopolist currently exists in a con

Question

Because entry into the market is free, and Oligopolist currently exists in a contestable market where all firms are identical. The Oligopolist's total cost curve is given by: TC=10x-2x^2+2x^3 and market demand is given by: X=20-P.

A. write the equations for the Average Total Cost (ATC) curve and the Marginal Cost (MC) curve.
B.What price has to prevail in the market to prevent firms from entering? That is, at what price does the Oligopolist earn zero profits? How much output does a single firm produce?
C. How much output does the market demand at the market price?
D. How many firms are needed to meet this level of demand?

Explanation / Answer

This question is about to expire so I only had time to do part A and some of B. I hope it is helpful...

A. ATC = TC/x

ATC = 10-2x+2x2

MC = dc/dx

MC = 10 - 4x + 6x2

B. Profit equals 0 when price intersects with ATC so first we need to invert the demand function as such:

X=20-P

P = 20 + X

(now set this equal to ATC)

20 + X = 10 - 2x + 2x2

I'm not really sure where to go from here, I would have to look it up but I'm out of time.

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