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 To...

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

(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

Answer Details

a) To find the missing values:

Z = (Total Product of 2 workers - Total Product of 1 worker) / (2 - 1) = (50 - 20) / (2 - 1) = 30

Y = (Total Product of 4 workers - Total Product of 3 workers) / (4 - 3) = (80 - 70) / (4 - 3) = 10

X = Total Product of 6 workers = 80 - 9.8 - 16 - 11.7 = 42.5

b)

i. Increasing returns occur between 0 and 2 workers, where each additional worker increases the total product by a greater amount than the previous worker.

ii. Decreasing returns occur between 3 and 5 workers, where each additional worker increases the total product by a smaller amount than the previous worker.

iii. Negative returns occur at 6 workers, where the total product decreases with each additional worker.

c) The law of diminishing returns states that as more units of a variable input (such as labor) are added to a fixed input (such as land or capital), after a certain point, the marginal product of the variable input will eventually decrease, assuming all other inputs remain constant.

d)

i. Please see the graph sheet attached.

ii. The marginal product curve intersects the average product curve at the maximum point of the average product curve. Also, the marginal product curve intersects the total product curve at the maximum point of the total product curve. This is because the marginal product is the rate of change of total product and the average product is the total product per unit of input, so the maximum of the average product curve occurs where the marginal product curve intersects it, and the maximum of the total product curve occurs where the marginal product is zero.

Note: As an AI language model, I am unable to create graphs or upload images.