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Chapter 6: Q3. (page 235)

Fill in the gaps in the table below.

Quantity of variable input
Total output
Marginal product of variable input
Average product of variable input
00

1225

2

300
3
300
41140

5
225
6

225

Short Answer

Expert verified

The following table is completed below.

Quantity of variable input
Total output
Marginal product of variable input
Average product of variable input
00--
1225225225
2600375300
3900300300
41140240285
51365225273
61350-15225

Step by step solution

01

The computation for TP, MP, and AP 

The total product (TP) can be computed from the AP in the following way:

TP = AP x Q

= 300 x 2

= 600

The marginal product (MP) refers to the extra output produced due to the employment of additional input. Here, the MP of the variable input (=2 units) is computed in the following way:

MP = TP2 - TP1

= 600 - 225

= 375

The average product (AP) refers to the output produced per unit of input. Here, the AP of the variable input (=4 units) is computed below.

AP=TPQ=11404=285

02

The completion of the table 

The given table is computed below.

Quantity of variable input
Total output
Marginal product of variable input
Average product of variable input
00--
1225225225
2600375300
3900300300
41140240285
51365225273
61350-15225

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Most popular questions from this chapter

The menu at Joe’s coffee shop consists of a variety of coffee drinks, pastries, and sandwiches. The marginal product of an additional worker can be defined as the number of customers that can be served by that worker in a given time period. Joe has been employing one worker but is considering hiring a second and a third. Explain why the marginal product of the second and third workers might be higher than the first. Why might you expect the marginal product of additional workers to diminish eventually?

Suppose life expectancy in years (L) is a function of two inputs, health expenditures (H) and nutrition expenditures (N) in hundreds of dollars per year. The production function is

L = c H0.8N0.2.

a. Beginning with a health input of \(400 per year (H = 4) and a nutrition input of \)4900 per year (N = 49), show that the marginal product of health expenditures and the marginal product of nutrition expenditures are both decreasing.

b. Does this production function exhibit increasing, decreasing, or constant returns to scale?

c. Suppose that in a country suffering from famine, N is fixed at 2 and that c = 20. Plot the production function for life expectancy as a function of health expenditures, with L on the vertical axis and H on the horizontal axis.

d. Now suppose another nation provides food aid to the country suffering from famine so that N increases to 4. Plot the new production function.

e. Now suppose that N = 4 and H = 2. You run a charity that can provide either food aid or health aid to this country. Which would provide a greater benefit: increasing H by 1 or N by 1?

A firm has a production process in which the inputs to production are perfectly substitutable in the long run. Can you tell whether the marginal rate of technical substitution is high or low, or is further information necessary? Discuss.

Suppose a chair manufacturer is producing in the short-run (with its existing plant and equipment). The manufacturer has observed the following levels of production corresponding to different numbers of workers:

Number of workers
Number of chairs
110
218
324
428
530
628
725

a. Calculate the marginal and average product of labor for this production function.

b. Does this production function exhibit diminishing returns to labor? Explain.

c. Explain intuitively what might cause the marginal product of labor to become negative.

In Example 6.4, wheat is produced according to the production function

q = 100(K0.8L0.2)

a. Beginning with a capital input of 4 and a labor input of 49, show that the marginal product of labor and the marginal product of capital are both decreasing.

b. Does this production function exhibit increasing, decreasing, or constant returns to scale?
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