Question

Find the long-run supply function of a perfectly competitive firm for each cost function given below:

(b) c(q)= q^1.5+ 8q^0.5 for all q >0.

Suppose the long-run market demand curve is p = 100 - Q.
(a) Find the long-run market equilibrium.
(b) What are the values of consumers’ and producers’ surplus

Answer 1

(a) In long run, Price = MC = AC

MC = dc(q)/dq = 1.5q^0.5 + (4/q^0.5)

AC = c(q/)q = q^0.5 + (8/q^0.5)

Equating MC and AC,

1.5q^0.5 + (4/q^0.5) = q^0.5 + (8/q^0.5)

q^0.5 = (4/q^0.5)

q = 4

Price = AC = (4)^0.5 + [8 / (4)^0.5] = 2 + (8/2) = 2 + 4 = 6

From market demand function,

6 = 100 - Q

Q = 94 (Long run industry output)

(b)

From demand function, when Q = 0, p = 100 (reservation price)

Consumer surplus (CS) = Area between demand curve and market price = (1/2) x (100 - 6) x 94 = 47 x 94 = 4,418

Producer surplus = Area between supply curve (MC) and market price = 0 (Since Market price = MC)