Question

Consider the firm with production function given by q = f(L,K) = Lź Kả.lfw== = 1, what is the producer surplus to the seller when the market price is $3? (round your answer to the nearest decimal place if necessary)

Answer 1

Production function is Q = (KL)^1/3

MRTS = K/L and w/r = 1/1 = 1

At optimum input choice MRTS = w/r or K/L = 1.

This gives K = L and so Q = (L)^2/3 or L = Q^1.5 and K = Q^1.5

Cost function is C = 1L + 1K

C = Q^1.5 + Q^1.5

C = 2Q^1.5

Marginal cost = 3Q

At P = 3, Q is 1 This is because P = MC is used.

Producer surplus = 0.5*(price – minimum MC)*Q

Hence PS = 0.5*(3 – 0)*1 = $1.5

Producer surplus is $1.50