Eco 550 Check Your Understanding 7 and 8

Chapter 7

1. In the Deep Creek Mining Company example described in this chapter (Table 7.1), suppose again that labor is the variable input and capital is the fixed input. Specifically, assume that the firm owns a piece of equipment having a 500-bhp rating.

A. Complete the following table:

[pic]

B. Plot the (i) total product, (ii) marginal product, and (iii) average product functions

C. [pic]

D. Determine the boundaries of the three stages of production.

Stage 1 0-5 Increasing rate in TPx

Stage 2 5-9 decreasing rate in TPx

Stage 3 9-11 negative rate in TPx

6. Consider the following short-run production function (where L = variable input, Q = output):

Q= 10L-0.5L^2

Suppose the output can be sold for $10 per unit. Also assume that the firm can obtain as much of the

Variable input (L) as it needs at $20 per unit.

A. Determine the marginal revenue product function.

R = P*Q =10*(10X-0.5) = 100X - 5X2

MR = R’ = 100 – 10X

B. Determine the marginal factor cost function.

TC = Cx*X = 20X

MC = 20

C. Determine the optimal value of L, given that the objective is to maximize profits.

MR = MC

100 – 10X = 20

X=8

8. Based on the production function parameter estimates reported in Table 7.4:

Which industry (or industries) appears to exhibit decreasing returns to scale? (Ignore the issue of statistical significance.)

Petroleum 0.947

Primary Metal 0.958

Sum of Elasticities less than 1

Which industry comes closest to exhibiting constant returns to scale?

Textiles 1.004

Sum of Elasticites closest to 1

In which industry will a given percentage increase in capital results in the largest percentage increase in output?

Stone, Clay, etc.

Capital Elasticity is greatest at 0.632

In what industry will a given percentage increase in production workers result in the largest percentage increase in output?

Furniture

Production Worker Elasticity is greatest at...