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...
Question 1 Report
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
Answer Details
(a) Completed table
| Number of workers | Total product (TP) | Marginal product (MP) | Average product (AP) |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 1 | 20 | 20 | 20 |
| 2 | 50 | 30 | 25 (Z) |
| 3 | 70 | 20 | 23.3 |
| 4 | 80 | 10 (Y) | 20 |
| 5 | 80 | 0 | 16 |
| 6 | 70.2 (X) | -9.8 | 11.7 |
Calculations
\[Z=AP_2=\frac{TP_2}{2}=\frac{50}{2}=25\]
\[Y=MP_4=TP_4-TP_3=80-70=10\]
\[X=TP_6=TP_5+MP_6=80+(-9.8)=70.2\]
Therefore: \(X=70.2\), \(Y=10\), and \(Z=25\).
(b)
- Increasing returns: from 1 to 2 units of labour, as marginal product rises from 20 to 30.
- Decreasing returns: from 3 to 4 units of labour, as marginal product falls from 20 to 10 while total product continues to rise.
- Negative returns: at 6 units of labour, where marginal product is \(-9.8\) and total product falls.
(c) Law of diminishing returns
As successive units of a variable factor are added to fixed factors of production, the marginal product of the variable factor will initially increase, but after a certain point it begins to decline.
(d)(i) Total product and marginal product curves
(d)(ii) Relationships between total product and marginal product
- When marginal product is positive, total product rises. When marginal product is zero at the fifth worker, total product remains at its maximum level of 80 units.
- When marginal product becomes negative at the sixth worker, total product falls from 80 units to 70.2 units.
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