Choosing a Maize Variety Under Uncertain Rainfall
A farmer in a semi-arid district has 2 hectares of sandy loam and plans to plant maize. Records from the last ten seasons show rainfall of 280, 310, 295, 340, 260, 300, 330, 250, 315 and 290 mm, all falling within a 90-day window. Two varieties are available. Variety A matures in 120 days and yields 4.5 t/ha when rainfall exceeds 350 mm, but only 1.8 t/ha below 300 mm. Variety B matures in 85 days and yields 3.0 t/ha under 300-350 mm and 2.2 t/ha below 300 mm. Seed for A costs P250/ha and for B P180/ha. The farmer has P600 for seed and cannot irrigate. Last season he planted A and harvested 1.6 t/ha.
1. Using the rainfall record, calculate the probability that each variety will face its low-yield condition, and recommend a variety with justification.
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Count seasons below 300 mm: 280, 295, 260, 250 and 290 = 5 of 10 seasons, so 50%. Variety A drops to 1.8 t/ha in exactly those seasons. Variety B's low condition (below 300 mm) also occurs 50% of the time, but its penalty is smaller (2.2 vs 3.0 t/ha). Expected yield for A = (0.5 x 4.5) + (0.5 x 1.8) = 2.25 + 0.9 = 3.15 t/ha. Expected yield for B = (0.5 x 3.0) + (0.5 x 2.2) = 1.5 + 1.1 = 2.6 t/ha. On average A looks better, but the median season is below 300 mm, and the worst case for A (1.8 t/ha) is far below B's worst case. Since the farmer cannot irrigate and has limited capital, B reduces downside risk. Seed cost also favours B: P180 x 2 ha = P360 versus P500 for A, leaving P240 spare. Recommend B for risk-averse production, or A only if the farmer can absorb a 1.8 t/ha season.
2. The farmer says he will simply plant the variety with the highest average yield. Critique this decision rule.
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The average across ten seasons is not the same as the yield in the coming season. A single season is a one-off event, so the farmer experiences either the high or low outcome, not the average. A's average is inflated by the 350 mm-plus seasons, which occurred only in 2 of 10 years (340 and 330 mm are below 350, so actually zero seasons exceeded 350 mm). Re-checking: no season exceeded 350 mm, so A would have yielded 1.8 t/ha every year in this record, giving an average of 1.8 t/ha, not 3.15 t/ha. This is a crucial correction: the farmer must check whether the high-yield threshold is ever met. Since it is not, A is strictly worse. The lesson is that decision rules must be applied to the actual distribution, not to a hypothetical average that assumes conditions the record never shows.
3. Suggest two management practices that could raise the achievable yield of the chosen variety without irrigation.
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First, early planting at the onset of reliable rains extends the effective growing period and lets the crop use early moisture; for an 85-day variety this can shift grain filling into a period with better residual moisture. Second, soil moisture conservation through mulching or tied ridges reduces evaporation and concentrates runoff, which matters on sandy loam with low water-holding capacity. A third option is adding organic matter (compost or manure) to improve water retention and nutrient supply. These practices do not change rainfall but improve the fraction of it available to the crop, narrowing the gap between potential and actual yield.