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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 marginal product of labor in the production of computer chips is 50 chips per hour. The marginal rate of technical substitution of hours of labor for hours of machine capital is 1/4. What is the marginal product of capital?

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?

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?

For each of the following examples, draw a representative isoquant. What can you say about the marginal rate of technical substitution in each case?

a. A firm can hire only full-time employees to produce its output, or it can hire some combination of fulltime and part-time employees. For each full-time worker let go, the firm must hire an increasing number of temporary employees to maintain the same level of output.

b. A firm finds that it can always trade two units of labor for one unit of capital and still keep output constant.

c. A firm requires exactly two full-time workers to operate each piece of machinery in the factory

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.
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