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.
