Allocating Three Hectares Between Tomato and Cabbage
Mr Dube has 3 ha of irrigated land, $4,000 of working capital and family labour equivalent to 1,400 person-days for the season. Fixed costs are $1,800 whatever he grows. Extension budgets per hectare give: tomato - gross income $6,000, variable costs $4,000 of which $2,000 is cash (seed, fertiliser, sprays, hired spray operators), and 600 person-days of labour; cabbage - gross income $3,500, variable costs $2,000 of which $1,000 is cash, and 400 person-days. His record book shows 32 boxes of tomatoes sold at $18 a box, but he is certain that 40 boxes left the field on the buyer's truck and he cannot find receipts for the rest.
1. Explain why the best plan does not put all the land into tomato, even though tomato earns the higher gross margin per hectare, and why it does not put all the land into cabbage either.
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Why not all tomato. Tomato earns the higher gross margin per hectare but it demands $2,000 of cash per hectare and 600 person-days. With only $4,000, the largest tomato area is 2 ha, which leaves 1 ha of land and 200 person-days doing nothing. The gross margin falls to $4,000 - a thousand dollars below the mixed plan. The scarce resource is cash, not land.
Why not all cabbage. Cabbage is more efficient in the use of the limiting resources: it returns $1.50 of gross margin per dollar of cash against $1.00 for tomato, and $3.75 per person-day against $3.33. Growing 3 ha of cabbage therefore looks attractive and uses all the land, but it uses only $3,000 of the $4,000 and 1,200 of the 1,400 person-days. Land is the only thing that is fully used, and land is not his scarcest resource.
The logic of the mix. Each hectare switched from cabbage to tomato adds $500 of gross margin but consumes an extra $1,000 of cash and 200 extra person-days. Starting from 3 ha of cabbage, he has exactly $1,000 and 200 person-days spare, so exactly one hectare can be switched. At that point every resource is fully used and no further switch is possible.
A secondary reason is risk: one hectare of tomato spreads price and disease risk without giving up the safer cabbage income.
2. What is the effect of the eight unrecorded boxes on his figures, and what record-keeping changes should he make?
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The size of the error. Eight boxes at $18 = $144 of gross income missing from the book. If this happened on the 1 ha tomato block in the plan above, his recorded tomato gross income would be $5,856 instead of $6,000, understating the tomato gross margin by about 7%. Repeated over several crops and several seasons, that error is large enough to make tomato look less profitable than it is, and could push him into the wrong cropping plan.
Wider consequences.
- He cannot prove his turnover to a bank, so any loan application for irrigation or a borehole is weakened.
- If the boxes were sold but the money was not banked, the missing cash is invisible and working capital for the next crop disappears.
- Without receipts he cannot check whether the buyer paid the agreed price or short-paid him.
Changes to make.
- A sales book ruled with date, buyer, quantity, unit price, amount and signature of the buyer, completed at the point of loading, not at the end of the week.
- A duplicate delivery note left with the buyer, so both parties hold a copy.
- A daily field diary for labour, sprays, fertiliser and harvest, cross-checked against the sales book at the end of each crop.
- A simple cash book kept separately from household money, reconciled monthly.
The rule is that a box leaves the field only when a line is written and signed; memory is not a record.