The table below relates to the application of fertilizer to a fixed area of land and the production of maize. Use the table to answer the questions that fol...
Question 1 Report
The table below relates to the application of fertilizer to a fixed area of land and the production of maize. Use the table to answer the questions that follow.
| Tones of fertilizer Applied | Total production in Bags | Marginal product |
| 0 | 1,000 | - |
| 1 | 1,100 | 100 |
| 2 | 1,250 | 150 |
| 3 | 1,500 | 250 |
| 4 | - | 400 |
| 5 | - | 250 |
| 6 | - | 125 |
| 7 | 2,350 | - |
| 8 | 2,380 | - |
| 9 | 2,330 | - |
(a) What will be the total output of maize when no fertilizer is applied to the land?
(b) Calculate the total product after the application of the following quantities of fertilizer:
(i) 4 tonnes;
(ii) 5 tonnes;
(iii) 6 tonnes.
(c) Calculate the marginal product after the application of the following quantities of fertilizer:
(i) 7 tonnes;
(ii) 8 tonnes;
(iii) 9 tonnes.
(d) (i) After what level of the application of fertilizer does diminishing marginal returns occur?
(ii) After what level of fertilizer application will the total output decrease?
Answer Details
Total product (TP) and marginal product (MP) are linked by \(MP_n=TP_n-TP_{n-1}\), so \(TP_n=TP_{n-1}+MP_n\). Using this to fill the gaps:
| Fertilizer (tonnes) | Total Product (bags) | Marginal Product |
|---|---|---|
| 0 | 1,000 | - |
| 1 | 1,100 | 100 |
| 2 | 1,250 | 150 |
| 3 | 1,500 | 250 |
| 4 | 1,900 | 400 |
| 5 | 2,150 | 250 |
| 6 | 2,275 | 125 |
| 7 | 2,350 | 75 |
| 8 | 2,380 | 30 |
| 9 | 2,330 | -50 |
(a) With no fertilizer applied the total output is 1,000 bags.
(b) Total product: (i) at 4 tonnes, \(1{,}500+400=1{,}900\) bags; (ii) at 5 tonnes, \(1{,}900+250=2{,}150\) bags; (iii) at 6 tonnes, \(2{,}150+125=2{,}275\) bags.
(c) Marginal product: (i) at 7 tonnes, \(2{,}350-2{,}275=75\) bags; (ii) at 8 tonnes, \(2{,}380-2{,}350=30\) bags; (iii) at 9 tonnes, \(2{,}330-2{,}380=-50\) bags.
(d)(i) Marginal product rises up to 4 tonnes (MP = 400) and then falls, so diminishing marginal returns set in after the 4th tonne of fertilizer.
(d)(ii) Total output is highest at 8 tonnes (2,380 bags) and then falls, so total output begins to decrease after the 8th tonne of fertilizer.
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