Question

2. Suppose that a person produces their own consumption good, G, using a production function G=3L, where L is the amount of labour time used. The person has 24 units of labor time available to them. Free time, denoted F, is the amount of time not used for labour.

a. Compute the average product of labour and show that it is constant.

b. Draw the set of feasible combinations of G and F, with F on the horizontal axis.

c. Compute the MRT in this situation, and find the opportunity cost of free time in terms of G.

d. What is the value of the person’s MRS at their most preferred attainable combination of G and F?

e. Illustrate the most preferred attainable combination of G and F on a diagram that shows the feasible set and an indifference curve.

Answer 1

Answer:

a. Average Product of Labour= Quantity Produced/ Labour Employed

= G/L

= 3*L/L

Average Product of Labour= 3

b.

c. MRT= Slope Of Production Possibility Frontier

= 72/24

MRT= 3

Opportunity Cost of F = Quantity Of G Produced/ Labour Used

= 3

Therefore, for an additional unit of free time, the consumer sacrifices 3 units of G.

d. The most preferred combination is where the MRS is equal to MRT, i.e the rate at which the consumer values the good relative to his free time is the same as the rate at which he can produce the good by sacrificing his free time.

Therefore, the most preferred combination will be when the MRS =3 (MRT).

e. The most desireable combination is at the point where the indifference curve intersects the production possibilty line. It is represented by Point A.