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
Explanation
(a) X = TP \(_{6}\) x Q\(_{6}\)
= 11.7 x 8
= 70.2
OR
TP\(_{5}\) + MP\(_{6}\)
= 80 + (-9.8)
= 70.2
Y = MP\(_{4}\) =
\(\frac{TP_4 -TP_3}{4 - 3}\)
= \(\frac{80 - 70}{1}\)
= 10
Z = AP\(_{2}\) = TP\(_{2}\) + Q
= \(\frac{50}{2}\)
= 25
(b) i. Increasing returns: 1 - 2 units of labour.
ii. Decreasing returns: 3 - 4 units of labour
iii. Negative returns: 6 units of labour
(c) The law of diminishing returns states that as more and more units of a variable factor are combined with a fixed input, the marginal product increases and after a certain point begins to decline.
(d) i.
ii. From the graph, as the variable input labour increases i.e up to 2 units of labour. At 3 units of labour, TP still increases, but MP attains a maximum of 30 and begins to fall. As MP falls up to 5 units of labour, TP has reached its maximum at 80. When MP turns negative, TP begins to fall to 70.2.