Question

4. To produce 16 units of output a firm can use either four workers (L) or two machines (K).  

a. Write down the production function q = f(L, K) that represents this production technology.

b. What is the firm’s MRTS?

c. Graph the isoquant associated with q = 32.  

Answer 1

(a) Since firm can use either 4L or 2K, workers and machines are substitutes and isoquant is linear.

Production function: q = 4L + 2K

(b) MRTS = MPL / MPK

MPL = q / L = 4

MPK = q / K = 2

MRTS = MPL / MPK = 4/2 = 2

(c) When q = 32,

32 = 4L + 2K

When L = 0, K = 32/2 = 16 (Vertical intercept) & when K = 0, L = 32/4 = 8 (Horizontal intercept).

In following graph, AB is the isoquant with above intercepts.