Question

A hamburger company produces hamburgers according to the production function Q = F(K,L) = 4K + 8L. 2 a. How many hamburgers are produced when K = 2 and L = 3? b. If the wage rate is $60 per hour and the rental rate on capital is $20 per hour, what is the cost-minimizing input mix for producing 32 units of hamburgers? c. How does your answer to part b change if the wage rate decreases to $20 per hour but the rental rate on capital remains at $20 per hour?

Answer 1

(a)

Q = (4 x 2) + (8 x 3) = 8 + 24 = 32

(b)

Total cost (C) = wL + rK = 60L + 20K

A linear production function means that L and K are substitutes and in optimal bundle, only one input will be used.

When Q = 32,

32 = 4K + 8L

When K = 0, L = 32/8 = 4 and C = 60 x 4 + 0 = 240

When L = 0, K = 32/4 = 8 and C = 0 + 20 x 8 = 160

Since cost is lower when L = 0 and K = 8, this is optimal input mix.

(c)

C = 20L + 20K

When Q = 32,

32 = 4K + 8L

When K = 0, L = 32/8 = 4 and C = 20 x 4 + 0 = 80

When L = 0, K = 32/4 = 8 and C = 0 + 20 x 8 = 160

Since cost is lower when L = 4 and K = 0, this is optimal input mix.