Tomato Versus Mustard Under a Cash Limit and Price Uncertainty
A farm household in Kota district has 1.0 ha irrigated land and ₹45,000 cash. It can grow tomato or mustard. Tomato: expected yield 40 t/ha, cost ₹1,10,000 (including hired harvesting and packing), and the harvest-time price is uncertain: 40% chance ₹12/kg, 40% chance ₹7/kg, 20% chance ₹3/kg. Mustard: expected yield 1.6 t/ha, cost ₹28,000, and the farmer can sell at the MSP of ₹5,650/qtl. Tomato needs six pickings and 60 hired labour-days; mustard needs 12 labour-days. The family has no cold storage and no contract buyer. A trader offers tomato at a fixed ₹6.50/kg for the whole crop if the farmer grades and packs, but payment is after 30 days. Credit costs 12% per annum for six months. The family has no off-farm income.
1. Calculate expected net returns for tomato and mustard, and the break-even price for tomato. Show the arithmetic.
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Tomato, 40,000 kg/ha:
- ₹12/kg: gross ₹4,80,000; net ₹4,80,000 − ₹1,10,000 = ₹3,70,000.
- ₹7/kg: gross ₹2,80,000; net ₹1,70,000.
- ₹3/kg: gross ₹1,20,000; net ₹10,000.
Expected net = 0.4 × ₹3,70,000 + 0.4 × ₹1,70,000 + 0.2 × ₹10,000 = ₹1,48,000 + ₹68,000 + ₹2,000 = ₹2,18,000/ha.
Break-even price = ₹1,10,000 ÷ 40,000 kg = ₹2.75/kg.
Mustard: 1.6 t = 16 qtl; gross = 16 × ₹5,650 = ₹90,400; net = ₹90,400 − ₹28,000 = ₹62,400/ha.
If tomato needs credit: cash gap = ₹1,10,000 − ₹45,000 = ₹65,000; interest for six months at 12% = ₹65,000 × 0.12 × 0.5 = ₹3,900. Credit-adjusted expected tomato net = ₹2,14,100/ha. Mustard fits within the ₹45,000 cash limit.
2. Given the cash limit and risk, recommend an area allocation and explain the trade-off.
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The cash limit is the binding constraint. Let x be tomato area: 1,10,000x + 28,000(1 − x) ≤ 45,000, so 82,000x ≤ 17,000 and x ≤ 0.207 ha. Without credit, he can plant at most about 0.2 ha tomato and 0.8 ha mustard: cost = ₹22,000 + ₹22,400 = ₹44,400, which fits. Expected net = 0.2 × ₹2,18,000 + 0.8 × ₹62,400 = ₹43,600 + ₹49,920 = ₹93,520. All mustard gives ₹62,400, so the small tomato block adds about ₹31,000 of expected value without borrowing.
If he borrows, he could plant more tomato, but the worst tomato outcome is only ₹10,000/ha before interest. A 0.5 ha tomato crop in a ₹3/kg year would leave little to repay. Recommended: 0.2 ha tomato, 0.8 ha mustard, with the tomato planted in two batches and graded. If a reliable buyer or credit is arranged, increase tomato to 0.3–0.4 ha, but keep at least half the area under mustard.
3. The trader offers a fixed ₹6.50/kg with payment after 30 days. Evaluate this offer and state the conditions under which you would accept it.
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The offer gives 40,000 × ₹6.50 = ₹2,60,000 gross and ₹1,50,000 net/ha. That is ₹68,000 below the expected ₹2,18,000, so it is not the best expected-value choice; it is an insurance price. It is well above the ₹2.75/kg break-even and above the ₹3/kg worst case, which is the main attraction for a farmer with no storage and no other buyer.
The 30-day payment delay matters. If he needs cash to pay harvest labour and repay credit, he should negotiate a partial advance or a shorter payment period. Accept if the market outlook is weak, if grading and packing costs are already included, and if the buyer is reliable. Reject or negotiate if he can sell graded tomatoes directly at above ₹6.50/kg, or if the delay would force him to borrow at a high rate. For a 0.2 ha block, the contract would reduce risk on a small, manageable tonnage.