WAEC Economics 2020 (Theory)

The table below shows the workers engaged by an agricultural firm over a period of time. Study it and answer the questions that follow;

Number of workers	Total product	Marginal product	Average product
0	0	0	0
1	20	20	20
2	50	30	z
3	70	20	23.3
4	80	y	20
5	80	0	16
6	x	-9.8	11.7

(a) Calculate the values of X, Y, and Z.

(b) At what level of employment of labour does the firm experience:

i. Increasing returns

ii. decreasing returns

ii. negative returns

(c) State the law of diminishing returns

(d) i. On a graph sheet, draw the total product and marginal product curves.

ii. State any two relationships between the two curves in (d)(i) above

SOLUTION

Let's solve this step by step.

First, we'll fill in the missing values for 

𝑥 𝑦 and 𝑧

Given data:

Total product is the total output produced by a given number of workers.

Marginal product is the additional output produced when one more worker is employed.

Average product is the total output per worker.

Using the definitions:

For 𝑥 

TP = AP x L

TP = 11.7 X 6 

TP = 70.2

For 𝑦

Y = MP

MP = 80 - 70 (this is done to find the changes in TP for 4 workers)

MP = 10

y = 10

For 𝑧

 we need to find the average product at 2 workers. 

Average product (AP) is Total Product (TP) divided by the number of workers, so 

𝑧 = 𝑇𝑃 / 2

z = 50/2

z = 25

Now, let's address the second part of the question:

(b) At what level of employment of labor does the firm experience:

i. Increasing returns: Increasing returns occur when each additional worker contributes more to total output than the worker before. This corresponds to the phase where the marginal product of labor is increasing. Looking at the marginal product column, this occurs from 1 to 2 workers, because the marginal product increases from 20 to 30.

ii. decreasing returns: Decreasing returns occur when each additional worker contributes less to total output than the worker before. This corresponds to the phase where the marginal product of labor is decreasing. Looking at the marginal product column, this occurs from 3 to 5 workers, because the marginal product decreases from 20 to 0.

iii. negative returns: Negative returns occur when each additional worker actually decreases total output. This corresponds to the phase where the marginal product of labor is negative. Looking at the marginal product column, this occurs when the marginal product is negative, which happens at 6 workers.

So, to summarize:

Increasing returns: 1 to 2 workers

Decreasing returns: 3 to 5 workers

Negative returns: 6 workers