Principles Of Microeconomics
Principles Of Microeconomics
13th Edition
ISBN: 9780135162170
Author: CASE, Karl E., Fair, Ray C., Oster, Sharon M.
Publisher: Pearson,
Question
Book Icon
Chapter 10, Problem 4.1P

(a)

To determine

Which process will be employed.

(a)

Expert Solution
Check Mark

Explanation of Solution

The total variable cost incurred for each process can be calculated using the following equation:

Total variable cost=((Price of capital×Quantity of capital)+(Price of labor×Quantity of labor)) (1)

Given the cost of capital per unit is $5, and the cost of labor per unit is $3. Process 1 requires 5 units of labor and 2 units of capital. Process 2 requires 3 units of labor and 3 units of capital. Process 3 requires 1 unit of labor and 6 units of capital.

Substitute the respective values in Equation 1 to calculate the total variable cost incurred in process 1, which is calculated as follows:

Total variable cost=(5×2)+(3×5)=10+15=25

The total variable cost of process 1 is $25.

Table 1 shows the total variable cost of the three processes calculated using Equation 1.

Table 1

Quantity of capitalQuantity of laborTotal variable cost
Process 125 $                25.00
Process 233 $                24.00
Process 361 $                33.00

Since the cheapest cost of production is for process 2, the process to be employed is process 2.

Economics Concept Introduction

Total Variable Cost:  Total variable cost is defined as the cost that depends on the level of production or output of a firm.

(b)

To determine

The total variable cost curve.

(b)

Expert Solution
Check Mark

Explanation of Solution

Figure 1 shows the total variable cost curve.

Principles Of Microeconomics, Chapter 10, Problem 4.1P

The horizontal axis of Figure 1 measures the quantity of output, and the vertical axis measures the cost. The total variable cost curve is an upward sloping curve as the cost increases the output increases. TVC shows the total variable cost when the cost of capital is $5, and cost of labor is $3 per unit. TVC shows the total variable cost when the cost of capital is $7, and the cost of labor is $3 per unit.

Economics Concept Introduction

Total Variable Cost:  Total variable cost is defined as the cost that depends on the level of production or output of a firm.

(c)

To determine

The demand for capital and labor.

(c)

Expert Solution
Check Mark

Explanation of Solution

Since 1 unit of output requires 3 units of capital and 3 units of labor using process 1, the amount of capital and labor required to produce any quantity of output can be calculated using Equations 2 and 3.

Amount of capital required=3×Quantity (2)

Amount of labor required=3×Quantity (3)

Substitute the respective values in Equation 2 to calculate the quantity of capital required to produce 25 units of output, which is calculated as follows:

Amount of capital required=3×25=75

The amount of capital required to produce 25 units of output is 75.

Similarly, the amount of labor required to produce 25 units of output can be calculated using Equation 3 as follows:

Amount of labor required=3×25=75

The amount of labor required to produce 25 units of output is 75.

The total variable cost incurred to produce 25 units of output using process 2 can be calculated using Equation 1 as follows:

Total variable cost=(5×75)+(3×75)=375+225=600

Thus, the total variable cost to produce 25 units of output is $600.

Table 1 shows the quantity of capital and labor required to produce various levels of output through process 1, which is calculated using Equations (1), (2), and (3).

Table 1

Quantity of outputAmount of capital requiredAmount of labor requiredTotal variable cost
257575 $              600.00
50150150 $           1,200.00
100300300 $           2,400.00
Economics Concept Introduction

Total Variable Cost:  Total variable cost is defined as the cost that depends on the level of production or output of a firm.

(d)

To determine

The demand for capital and labor.

(d)

Expert Solution
Check Mark

Explanation of Solution

When the cost of capital increases to $7, the total variable cost incurred in process 1 can be calculated by substituting the values in Equation 1 as follows:

Substitute the respective values in Equation 1 to calculate the total variable cost incurred in process 1, which is calculated as follows:

Total variable cost=(7×2)+(3×5)=14+15=29

The total variable cost of process 1 is $29.

Table 3 shows the total variable cost of the three processes, which are calculated using Equation (1).

Table 3

Quantity of capitalQuantity of laborTotal variable cost
Process 125 $                29.00
Process 233 $                30.00
Process 361 $                45.00

When the cost of capital increases to $7, the process to be chosen is process 1, as it is the cheapest.

Since 1 unit of output requires 2 units of capital and 5 units of labor using process 1, the amount of capital and labor required to produce any quantity of output can be calculated using Equations 4 and 5.

Amount of capital required=2×Quantity (4)

Amount of labor required=5×Quantity (5)

Substitute the respective values in Equation (4) to calculate the quantity of capital required to produce 25 units of output, which is calculated as follows:

Amount of capital required=2×25=50

The amount of capital required to produce 25 units of output is 50.

Similarly, the amount of labor required to produce 25 units of output can be calculated using Equation (5) as follows:

Amount of labor required=5×25=125

The amount of labor required to produce 25 units of output is 125.

The total variable cost incurred to produce 25 units of output using process 1 can be calculated using Equation 1 as follows:

Total variable cost=(7×50)+(3×125)=350+375=725

Thus, the total variable cost to produce 25 units of output is $725.

Table 4 shows the quantity of capital and labor required to produce various levels of output through process 1, which is calculated using Equations (1), (4), and (5).

Table 4

Quantity of outputAmount of capital requiredAmount of labor requiredTotal variable cost
2550125 $              725.00
50100250 $           1,450.00
100200500 $           2,900.00
Economics Concept Introduction

Total Variable Cost:  Total variable cost is defined as the cost that depends on the level of production or output of a firm.

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