Question

Find the short-run supply function of a perfectly competitive firm for the given short-run cost functions - (a) c(q) = q 1.5 + 8q 0.5 + 16 for all q ? 0. Suppose there are ten identical firms in the industry. The short-run market demand curve is p = 100 ? Q. (a) Find the short-run market equilibrium for part (a) (b) What is the value of consumers’ and producers’ surplus for part (a)

Answer 1

1. a) For a perfectly competitive firm, the supply curve is the portion of its marginal cost curve lying above the minimum average variable cost curve.

Hence, C(q) = q^1.5 + 8q ^0.5 + 16

Now, differentiating this wrt q, we have

MC = C'(q) = 1.5*q^0.5 + 4*q^-0.5

Hence, MC is  

which is also the supply curve.

2. a) Demand is p = 100 - q (assuming the ? is -)

Supply =

At equilibrium, Demand = supply

Hence,

Hence, q = 21.63 = 22 units

Price = 100 - Q = 100 - 22 = $78

b) Consumer surplus = 0.5*(100 - 78)*(22) = 242

Producer surplus = 0.5* (22)*22 = 242