Chapter 72, Problem 2FRQ

a)

To determine

The MPL of the 4th worker when the wage is $10 per day and the price of pencils is $1.

Answer to Problem 2FRQ

The MPL of the 4^th worker is 20.

Explanation of Solution

Q (labor)	Q (pencil)	Marginal product of labor
0	0	0
1	40	40
2	90	50
3	120	30
4	140	20
5	150	10
6	160	10
7	166	6

MPL (Marginal product of labor) of the 4th worker

  $\begin{array}{l}\text{= }\left({\text{TP}}_{\text{n-1}}{\text{-TP}}_{\text{n}}\right)\hfill \\ \text{= 140-120}\hfill \\ \text{= 20}\hfill \end{array}$

Here,

TP_n-1 is the total product of labor at the 4^th unit and TP_n is the total product at the 3^rd unit.

Therefore, the MPL (Marginal product of labor) of the 4th worker is 20.

Economics Concept Introduction

Introduction: The change in extra output caused by adding one additional unit of the input factor to the current factors of inputs, such as labor and capital, is referred to as the marginal product of an input or a factor of input.

b)

To determine

The MP per dollar of the 5th worker when the wage is $10 per day and the price of pencils is $1

Explanation of Solution

Q (labor)	Q (pencil)	Marginal product of labor	Marginal product per dollar (wage is $10)
0	0	0	0
1	40	40	4
2	90	50	5
3	120	30	3
4	140	20	2
5	150	10	1
6	160	10	1
7	166	6	0.6

Marginal product per dollar for the 5^th worker:

  $\begin{array}{l}\text{= }\frac{\text{ Marginal product of labor }}{\text{wage rate}}\hfill \\ \text{= }\frac{\text{10}}{\text{10}}\hfill \\ \text{= 1}\hfill \end{array}$

Because the wage rate is $10, therefore, the MP per dollar of the 5th worker would be 1.

Economics Concept Introduction

Introduction: The change in extra output caused by adding one additional unit of the input factor to the current factors of inputs, such as labor and capital, is referred to as the marginal product of an input or a factor of input.

c)

To determine

The number of workers that the firm would hire if it employed every worker at the marginal product per dollar each worker is greater than or equal to 1 pencil per dollar

Explanation of Solution

Q (labor)	Q (pencil)	Marginal product of labor	Marginal product per dollar (wage is $10)
0	0	0	0
1	40	40	4
2	90	50	5
3	120	30	3
4	140	20	2
5	150	10	1
6	160	10	1
7	166	6	0.6

When a firm hires 6 workers, the marginal product per dollar would be:

  $\begin{array}{l}\text{= }\frac{\text{ Marginal product of labor }}{\text{wage rate}}\hfill \\ \text{= }\frac{\text{10}}{\text{10}}\hfill \\ \text{= 1}\hfill \end{array}$

The firm hires 6 workers if it employed every worker at the marginal product per dollar each worker is greater than or equal to 1 pencil per dollar because by hiring 6 workers, the marginal product of labor per dollar is not less than the pencil rate per dollar.

Economics Concept Introduction

Introduction: The change in extra output caused by adding one additional unit of the input factor to the current factors of inputs, such as labor and capital, is referred to as the marginal product of an input or a factor of input.

d)

To determine

Whether the firm minimizes its cost if the marginal product per dollar spent on labor is 1 pencil per dollar, the marginal product of the last unit of capital hired is 100 pencils per dollar, and the rental rate is $50 per day.

Explanation of Solution

No, the firm is not following the cost-minimization rule because the marginal product per dollar spent on capital is more than the labor as:

  $\begin{array}{l}\begin{array}{l}\text{= }\frac{\text{100}}{\text{\$50}}\hfill \\ \text{= 2 pencils per dollar}\hfill \\ \hfill \end{array}\hfill \end{array}$

Here, the marginal product per dollar spent on labor is less than the marginal product per dollar spent on capital which is $2 whereas, the marginal product per dollar spent on labor is $1

Economics Concept Introduction

Introduction: The change in extra output caused by adding one additional unit of the input factor to the current factors of inputs, such as labor and capital, is referred to as the marginal product of an input or a factor of input.