Choosing the Nitrogen Dose on a Bulandshahr Wheat Field
Ramesh Singh farms 2.0 ha of irrigated wheat in Bulandshahr district, Uttar Pradesh. Last rabi the block extension officer ran a nitrogen trial on his field, holding all other inputs constant: 0 kg N/ha gave 25 quintals, 40 kg gave 32, 80 kg gave 37, 120 kg gave 40, 160 kg gave 41 and 200 kg gave 40 quintals per hectare. Urea (46 per cent N) costs ₹270 per 50 kg bag in the local market and wheat is selling at ₹2,200 per quintal. Ramesh has ₹18,000 of working capital earmarked for fertilizer and one assured 10-day irrigation slot after the second top dressing; the pump set can reach only the whole 2.0 ha at one time. His neighbour, who applied 200 kg N/ha, harvested 41 quintals and insists that since yield is highest at that dose, 200 kg is the right amount. Ramesh is also being offered ₹6,000 of credit at 12 per cent annual interest by a local supplier for extra urea, and he wants a defensible figure before he books the bags.
1. From the trial data, work out the marginal product and marginal value product of each 40 kg increment of nitrogen, compare them with the marginal factor cost, and state the profit-maximising dose for Ramesh's 2.0 ha.
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First convert the input price to a per-kg-N basis: ₹270 per 50 kg urea ÷ 0.46 = ₹587 per kg of N, i.e. ₹11.74 per kg N. Wheat at ₹2,200/qtl is ₹22 per kg of grain.
| Increment (kg N/ha) | Extra yield (qtl/ha) | MP (kg grain per kg N) | MVP (₹ per kg N) |
|---|---|---|---|
| 0 → 40 | 7 | 17.5 | 385 |
| 40 → 80 | 5 | 12.5 | 275 |
| 80 → 120 | 3 | 7.5 | 165 |
| 120 → 160 | 1 | 2.5 | 55 |
| 160 → 200 | −1 | −2.5 | −55 |
Every increment up to 160 kg N/ha has an MVP far above the MFC of ₹11.74; the 160 → 200 increment has a negative MVP. So the optimum is 160 kg N/ha, which is 160 ÷ 0.46 = 348 kg urea per hectare, i.e. 7 bags (350 kg) per hectare, or 14 bags for 2.0 ha, costing about ₹3,780.
Check the alternatives: at 160 kg N/ha the return is 41 × ₹2,200 = ₹90,200; at 200 kg N/ha it is 40 × ₹2,200 = ₹88,000, so the higher dose earns ₹2,200 less while spending about ₹470 more on urea. The rational choice is 160 kg N/ha, not 200.
2. Explain to the neighbour why the highest yield is not the most profitable dose, using the three stages of the law of diminishing returns and locating the trial data within them.
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The law of diminishing marginal returns says that as more of one variable input is applied to fixed land and other fixed inputs, the extra output per extra unit of input eventually falls. Three stages are distinguished by the behaviour of the average product and the marginal product.
In Stage I the average product is still rising and the marginal product is above the average product; adding input raises output per unit of input, so it always pays to go further. Stage II runs from the point where average product peaks to the point where marginal product becomes zero, which is exactly where total product peaks. Stage III begins when marginal product turns negative and total product actually falls.
In this trial the average product falls from the very first increment (0.80, 0.46, 0.33, 0.26 and 0.20 qtl per kg N), so Stage I is essentially already over and the data lie in Stage II. Total product peaks at about 160 kg N/ha, where marginal product reaches zero; beyond that we enter Stage III, and the fall from 41 to 40 quintals at 200 kg shows it. Because the extra grain from the last increment is worth less than the extra urea, profit peaks before yield does. A rational farmer stops inside Stage II where marginal value product equals marginal factor cost, not where the yield column is highest. The neighbour's 200 kg dose produces one quintal less.
3. Should Ramesh borrow ₹6,000 at 12 per cent to buy extra urea? Identify the real binding constraint in his situation and the practical advice you would give.
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The marginal arithmetic favours the last profitable increment: 40 kg N/ha above 120 kg costs about ₹470 of urea, and even with three months' interest at 12 per cent (about ₹14) it returns roughly ₹2,200 of extra grain. So on returns alone, borrowing is justified.
But the binding constraint is not capital. For 2.0 ha Ramesh needs 14 bags × ₹270 = ₹3,780, well within his ₹18,000 working-capital envelope. Taking a 12 per cent supplier loan is unnecessary and, worse, supplier credit often ties him to a particular brand and price. The genuinely scarce resources are irrigation water and the single 10-day slot: the pump can wet the whole 2.0 ha only once, so a large single dose risks volatilisation and leaching losses if rain does not follow.
The advice is: buy 14 bags from his own funds, split the 160 kg N/ha into the two remaining top dressings and time the larger share immediately before the assured irrigation, place the fertilizer in moist soil or incorporate it, and keep the ₹6,000 credit line unused as a buffer for harvesting or a spray. If he insists on a bigger dose, the trial data still show a loss beyond 160 kg N/ha. Excess nitrogen would also raise lodging risk and cost.