Question

Suppose a firm has the production function, Q = 12KL. It has a contract to produce 144 units of output per day. One way to do is to use 3 units of capital (K) and 4 units of labor (L). Suppose a unit of labor costs $2 (wage = w) while a unit of capital costs $3 (r).

What is the slope of the isocost line? A) 2/3 B) 1/4 C) 1/3 D) 3/2

At this combination of inputs, is the firm producing the given output target of 144 units as cheaply as possible?

A) Yes, it is producing the target of 144 units at minimum cost.

B) No, it is not producing the target of 144 units at minimum cost.

C) We do not have sufficient information to find out whether the firm is producing the target as cheaply as possible.

D) Given the production function, it is not possible for the firm to choose any other input combination, regardless of the cost of production.

Answer 1

1)

Q = 12KL

w = 2

r = 3

slope of isocost line = w/r  

= 2/3

2)

Q = 12KL

Q/L = MP_L = 12K

Q/K = MP_K = 12L

MRTS = MP_L/MP_K  

= 12K/12L

= K/L   

K = 3 and L = 4

MRTS at (L = 4, K = 3)

MRTS = 3/4

at optimal choice or minimum cost condition

MRTS = w/r

MRTS = 3/4

w/r = 2/3

which means MRTS w/r

Hence firm is not producing the target of 144 units at minimum cost.