Question

Consider a competitive industry comprised of 60 producers, all of whom have an identical short-run total cost curve: SRTC(q)= 64 + 2q^2 where q is the monthly output of a firm and $64 is the monthly fixed cost. Assume that $32 of the firm’s monthly $64 fixed cost can be avoided if the firm produces zero output in a month. The market demand for coal production is D(P) = 400 − 5P, where D(P) is monthly demand at price P . Derive the short run market supply curve in this market and determine the short-run equilibrium price.

Answer 1

Short run supply curve for a firm is given by P = MC where MC is the marginal cost.
So, MC = d(SRTC)/dq = d(64 + 2q^2)/dq = 4q
So, P = MC gives P = 4q
So, q = P/4 is the short run supply curve for an individual firm.

There are 60 producers so short run market supply curve is Q = 60q
So, Q = 60(P/4) = 15P

The short run market supply curve is Q = 15P
The market demand for coal production is D(P) = Q = 400 − 5P

At equilibrium, market supply = market demand
So, 15P = 400 − 5P
So, 15P + 5P = 400
So, 20P = 400
So, P = 400/20 = 20

Thus, the short run equilibrium price is $20.