Chapter 11, Problem 8PA

Subpart (a):

To determine

Marginal productivity and its relevance.

Explanation of Solution

In this given scenario, fisherman is the only variable factor. When other things remain the same increasing the number of fisherman leads to reduce the productivity which is known as diminishing marginal productivity.

In the fish firm, all the factors can be varied according to the requirement. Thus, marginal productivity is constant for the fisherman in the firm.

Economics Concept Introduction

Concept introduction:

Marginal product: Marginal product refers to an additional product in the total product due to a change in one unit of labor.

Diminishing marginal product: Diminishing marginal productivity refers to the increase in output at a slower rate as an additional unit of input increases.

Subpart (b):

To determine

Number of fishing person.

Explanation of Solution

Minimum number of fish should catch is 2 per day. The number of fisherman fishing in the lake can be calculated as follows.

$\begin{array}{c}\text{Number of person fishing}=\text{6}-\text{Minimum number of fish need to catch}\\ =6-2\\ =4\end{array}$

Thus, the number of fisherman catching fish in the lake is 4. Remaining one fisherman is working in the firm. Total number of fish catching is 10 units $\left(2\times 5\right)$.

Subpart (c):

To determine

Marginal productivity and its relevance.

Explanation of Solution

Total number of fish can be calculated as follows.

$\text{Total catching fish}=\text{Number of person}\times \text{Catching fish per person}$ (1)

Substitute the respective values in equation (1) to calculate the total number of fish at 1 unit of fisher man.

$\begin{array}{c}\text{Total catching fish}=\text{1}\times \text{5}\\ =5\end{array}$

Total fish is 5 units.

Marginal productivity can be calculated as follows.

$\text{Marginal productivity}=\frac{{\text{Total fish}}_{\text{Present}}-{\text{Total fish}}_{\text{Previous}}}{{\text{Total fisherman}}_{\text{Present}}-{\text{Total fisherman}}_{\text{Previous}}}$ (2)

Substitute the respective values in equation (2) to calculate the marginal productivity of fish at 2 unit of fisher man.

$\begin{array}{c}\text{Total catching fish}=\frac{8-5}{2-1}\\ =\frac{3}{1}\\ =1\end{array}$

Total fish is 5 units.

Table -1 shows the marginal productivity of fisher in the lake that obtained by using equation (1).

Table -1

Total fisherman(a)	Catching fish per person $\left(6-\text{N}\right)$ (b)	Total fish	Marginal productivity
1	5	5	-
2	4	8	3
3	3	9	1
4	2	8	–1
5	1	5	–3

Profit maximizing output is occurred at the point where the marginal revenue is equal to or greater than the marginal cost. Since marginal productivity is closer to 2 at the number of fisherman is 2, two fishers should be catch the fish in lake. Remaining 3 fishermen should work in the farm. And remaining 3 people should produce fish the farm. Total production of fish can be calculated as follows.

$\begin{array}{c}\text{Total fish}=\left(\begin{array}{l}\left({\text{Total fisher man}}_{\text{Lake}}\times {\text{Catching fish per person}}_{\text{Lake}}\right)\\ +\left({\text{Total fisher man}}_{\text{Farm}}\times {\text{Catching fish per person}}_{\text{Farm}}\right)\end{array}\right)\\ =\left(2\times 4\right)+\left(3\times 2\right)\\ =8+6\\ =14\end{array}$

Thus, total number of fish is 14.

Economics Concept Introduction

Concept introduction:

Marginal product: Marginal product refers to an additional product in the total product due to a change in one unit of labor.

Diminishing marginal product: Diminishing marginal productivity refers to the increase in output at a slower rate as an additional unit of input increases.

Subpart (d):

To determine

Marginal productivity and its relevance.

Explanation of Solution

The value of tax should be equal to the marginal productivity of the fisherman. The marginal productivity of fishermen is 2 (Fisherman produces fish in the farm). Thus, the tax should be equal to $2. The marginal productivity for fisher man who working in the lake is equal to or greater than the tax amount $2. Thus, two fisher man catching fish in lake and rest of the fisherman produces fish in the farm.

Economics Concept Introduction

Concept introduction:

Marginal product: Marginal product refers to an additional product in the total product due to a change in one unit of labor.

Diminishing marginal product: Diminishing marginal productivity refers to the increase in output at a slower rate as an additional unit of input increases.

Subpart (e):

To determine

Number of fish per person

Explanation of Solution

Number of fish per person as per the policy can be calculated as follows.

$\begin{array}{c}\text{Number of fish per person}=\frac{\text{Total fish}}{\text{Total fisherman}}\\ =\frac{14}{5}\\ =2.8\end{array}$

Thus, one fisherman gets 2.8 units of fish.

The person work in the farm produces only 32 units of fish and now receives additional 0.8 units of fish. On the other hand, the fisherman who works in the lake catches 4 per person. Now they are losing 1.2 units of fish. The policy makers opinion is that if there is no restriction, then fisherman in the lake would catch only 2 units of fish per fisherman.