Question

1.         You are given the following information about production for a company: Q = 200*K^.2L^.7.

a.         For units of labor = 0, 6, 12, 18, and 24, calculate the level of output associated with using a constant 4 units of capital.

b.         Calculate the marginal product of labor and average product of labor for each of the corresponding units of labor in a. Graph these.

c.         As capital becomes a variable input in the long-run, would tripling the amounts of both labor and capital result in output that is tripled, more than tripled, or less than tripled? Why?

2.         A company currently uses 10 units of labor and 4 units of capital in its production process and is able to produce 150 units of output per day.

a.         Provide an isoquant that shows imperfect substitution between labor and capital and label the values that are described on your graph.

b.         The company owner decides to use more capital and less labor in its production process. What should happen to the marginal product of capital relative to the marginal product of labor? Use intuition and math to explain your answer.

c.         How would your isoquant change in part a. if capital and labor were perfect substitutes in production? Illustrate this on your graph and explain the change.

d.         Re-answer your question to part b. if capital and labor are perfect substitutes.

           

3.         Suppose a firm has the short-run cost function C = q² + 5q + 125

a.         Draw a graph of this firm’s total cost curve on one graph and its marginal cost, average total cost and average variable cost curves on another graph, below the first one.

b.         If the firm’s fixed costs increase by $70, how would this affect the firm’s cost curves that you have graphed in part a.? Explain the effect on EACH of them.

4.         Two companies, X and Y, are competitors in the same industry, but company X is more efficient at using its resources than company Y.

a.         If the MRTS is the same in the production processes of both companies, show and discuss how the isoquants will be different for company X than they are for company Y.

b.         Both companies can hire labor at the same wage, w, but company X is able to pay a lower rent per unit on its capital. Show and discuss how these company’s relative uses of labor and capital will be different from one another and why.

Answer 1

(a) Given, K= 4

For L=0

Q=200*4^0.2*0^0.7

Q=0

Using same way by putting K=4 and other values of L, we can calculate Q(output).

K	L	Q
4	0	0
4	6	925.01
4	12	1502.69
4	18	1995.87
4	24	2441.12

(b) Marginal Product of labor is the increase in the output from a unit increase in labor.

MPL=(Q₁-Q₀)/(L₁-L₀)

For the first one MPL = (925.01-0)/(6-0) = 154.17

Similarly all other values will be calculated for MPL

Average Product Labor is the total output divided by the number of labor units employed to produce that output.

APL = Q₁/L₁

So, for first APL= 925.01 / 6 = 154.17

Similarly all other values will be calculated for APL.

K	L	Q	MPL	APL
4	0	0
4	6	925.01	154.17	154.17
4	12	1502.69	96.28	125.22
4	18	1995.87	82.20	110.88
4	24	2441.12	74.21	101.71

(c) The output will be less than tripled because the given production function exhibits the decreasing return to scale.

We add up the powers of K and L which is less than 1. (0.2+0.7<1)