Plantain Contract on a Fixed-Land Farm
A 50-hectare family farm in the Centre Region of Cameroon grows plantain and groundnuts. Each hectare of plantain yields 8 tonnes and sells for 120,000 FCFA per tonne; each hectare of groundnuts yields 1.2 tonnes and sells for 450,000 FCFA per tonne. The family has 4,200 worker-days available per season. Plantain requires 60 worker-days per hectare; groundnuts require 90. The farm currently allocates 20 hectares to plantain and 30 to groundnuts. A trader offers a forward contract for 60 tonnes of plantain at a premium price of 150,000 FCFA per tonne, but only if the farm can deliver the extra output next season. The family cannot borrow to hire more labour, and land is already fully used. The groundnut price is expected to rise by 15% before planting decisions are finalised.
1. Calculate the opportunity cost, in tonnes of groundnuts and in FCFA, of producing the 60 tonnes of plantain needed to fulfil the trader's contract. Show your working and state any assumption.
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60 tonnes ÷ 8 tonnes per hectare = 7.5 hectares of plantain. Those hectares must come out of groundnuts, so groundnut output falls by 7.5 × 1.2 = 9 tonnes. At the current price, the value forgone is 9 × 450,000 = 4,050,000 FCFA. If the expected 15% rise occurs before planting, the relevant price is 450,000 × 1.15 = 517,500 FCFA/t, so opportunity cost = 9 × 517,500 = 4,657,500 FCFA. Contract revenue is 60 × 150,000 = 9,000,000 FCFA. The labour check: 7.5 ha of plantain needs 450 worker-days; the groundnuts no longer grown would have used 675 worker-days; net labour use falls by 225 days, so the 4,200-day constraint is not violated. Assumption: the 60 tonnes are additional output, not just existing plantain diverted to the premium buyer, and yields are certain.
2. Explain why the farm's production possibility frontier between plantain and groundnuts is likely to be bowed outward rather than a straight line. What does this imply about the opportunity cost of the first and last hectares switched?
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The PPF is likely bowed outward because the farm's land and labour are not equally suited to both crops. Some plots are better drained or closer to the homestead for plantain, while others are better for groundnuts. As the family shifts the first hectares, it gives up groundnuts grown on land that is relatively poor for plantain, so the opportunity cost is low. As more land is switched, it must use plots where groundnuts were highly productive, so each extra tonne of plantain costs more groundnuts. That is increasing opportunity cost. A straight-line PPF would imply constant opportunity cost, which is plausible only if all hectares and workers were identical. The bowed shape means the farm should not specialise completely; the optimal mix depends on prices and on where the marginal cost equals the marginal benefit.
3. Advise the family whether to accept the contract. Consider the expected 15% groundnut price rise and the labour constraint. Would your advice change if the trader required 100 tonnes?
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Accepting is worthwhile if the extra revenue exceeds the opportunity cost. At the expected groundnut price, the net gain is 9,000,000 − 4,657,500 = 4,342,500 FCFA, and the labour constraint is satisfied, so the contract looks attractive. But the family should check delivery risk, whether the premium applies to all 60 tonnes, and whether the groundnut price rise is certain. If the trader demanded 100 tonnes, the land requirement is 100 ÷ 8 = 12.5 ha. Groundnuts forgone = 15 t, worth 7,762,500 FCFA at the higher price; revenue = 15,000,000 FCFA; net gain = 7,237,500 FCFA. Labour: plantain uses 750 days, groundnuts release 1,125 days, so net labour falls by 375 days. The 100-tonne contract is still feasible and more profitable in this calculation. The main risk is yield loss or a much larger groundnut price rise; the contract breaks even only if the groundnut price reaches about 1,000,000 FCFA/t.