Chapter 11, Problem 5P

To determine

(a)

The marginal product of hat in the cases with three and four machines is to be determined.

Answer to Problem 5P

The marginal product of hat in the cases with three and four machines are shown below:

Labor (L)	Total Product (TP)	Marginal Product (MP)
1	8	8
2	18	10
3	30	12
4	45	15
5	57	12
6	67	10
7	72	5

Labor (L)	Total Product (TP)	Marginal Product (MP)
1	9	9
2	20	11
3	35	15
4	55	20
5	76	21
6	88	12
7	95	7

Explanation of Solution

Marginal Product is the addition to total product when an extra unit of labor is employed. It is calculated as follows.

  $M{P}_n=T{P}_n-T{P}_{n-1}$

Using the formula above, we calculate MP for 1^st level of employment as follows:

  $\begin{array}{l}M{P}_n=T{P}_n-T{P}_{n-1}\\ \Rightarrow M{P}_1=T{P}_1-T{P}_{1-1}\\ \Rightarrow M{P}_1=T{P}_1-T{P}_0\\ \Rightarrow M{P}_1=8-0\\ \Rightarrow \boxed{M{P}_1=8}\end{array}$

Similarly, we calculate MP for each level of employment in cases with three and four machines and MP schedule for both cases is shown below.

Labor (L)	Total Product (TP)	Marginal Product (MP)
1	8	8
2	18	10
3	30	12
4	45	15
5	57	12
6	67	10
7	72	5

Labor (L)	Total Product (TP)	Marginal Product (MP)
1	9	9
2	20	11
3	35	15
4	55	20
5	76	21
6	88	12
7	95	7

Economics Concept Introduction

Total Product (TP):

Total product is the total output that a firm produces by its production activities.

Marginal Product (MP):

Marginal Product is the addition to total product when an extra unit of a particular quantity.

To determine

(b)

The points at which the diminishing marginal product sets in with three machines and with four machines.

Answer to Problem 5P

The diminishing marginal product sets in with three machines at 5^th level of labor employment. The diminishing marginal product sets in with four machines at 6^th level of labor employment.

Explanation of Solution

We have the TP and MP schedule for the cases with three machines and four machines as follows:

Labor (L)	Total Product (TP)	Marginal Product (MP)
1	8	8
2	18	10
3	30	12
4	45	15
5	57	12
6	67	10
7	72	5

Labor (L)	Total Product (TP)	Marginal Product (MP)
1	9	9
2	20	11
3	35	15
4	55	20
5	76	21
6	88	12
7	95	7

In the first case, marginal product starts to fall from L=5. While, in the second case, marginal product starts to fall from L=6. Therefore, the diminishing marginal product sets in with three machines at 5^th level of labor employment and diminishing marginal product sets in with four machines at 6^th level of labor employment.

Economics Concept Introduction

Total Product (TP):

Total product is the total output that a firm produces by its production activities.

Marginal Product (MP):

Marginal Product is the addition to total product when an extra unit of a particular quantity.

To determine

(c)

The reasons why the points of diminishing marginal product are different in the two cases.

Explanation of Solution

Marginal Product is the addition to total product when an extra unit of labor is employed. Typically, marginal product first increases, reaches maximum, falls and finally becomes negative. In both the cases, the property of marginal product applies. However, the falling of marginal product is delayed with four machines because increasing one input (labor) with increase in another input (machines) makes marginal product higher. The marginal product of labor is higher at each step with four machines than that with three machines. Thus, with more number of machines, the diminishing returns to labor set in at a later stage. Therefore, the points of diminishing marginal product are different in the two cases.

Economics Concept Introduction

Total Product (TP):

Total product is the total output that a firm produces by its production activities.

Marginal Product (MP):

Marginal Product is the addition to total product when an extra unit of a particular quantity.