Vose SoftwareModelChoice decision tree · Agriculture and food
Agricultural Crop Planning Decision
Should a 500-acre farm plant corn, plant soybeans, split the land 50/50 or lease it out?
From the model’s decision tree
Best first decision: Plant Corn
The expected value of each first option when every later decision is also made well (the tree rolled back).
| First decision | Expected value | |
|---|---|---|
| Plant Corn | $61,350 | ✔ best |
| Plant Soybeans | $59,412 | |
| Split 50/50 | $59,300 | |
| Lease Land | $45,000 |
| Measure | Value |
|---|---|
| Expected value of the best strategy | $61,350 |
| Chance of a loss on the best strategy | 14.0% |
| Best outcome on the best strategy | $195,000 |
| Worst outcome on the best strategy | −$70,000 |
S-curve (cumulative probability) of Plant Corn from the saved simulation.
The decision
A 500-acre farm in the Midwest must decide what to plant for the upcoming growing season. The farmer faces two layers of uncertainty: weather conditions during the growing season and commodity prices at harvest time.
Unlike financial investments, agricultural decisions have a unique feature: weather and price risks are partially correlated. A widespread drought reduces supply and tends to push prices higher, partially offsetting yield losses.
Objective
Maximize expected net profit. This model illustrates the classic diversification vs. concentration tradeoff and the value of mid-season adaptive decisions (irrigation) in agriculture.
The options
- Option 1: Plant Corn
Higher cost ($85K for seed, fertilizer, fuel) but higher revenue potential. Corn is more sensitive to weather extremes. If drought hits, the farmer can choose to irrigate (extra $25K) or accept reduced yield.
- Option 2: Plant Soybeans
Lower cost ($60K) and more drought-tolerant, but lower revenue ceiling. Soybeans are a safer choice with less variance in outcomes.
- Option 3: Split 50/50
Diversify by planting half corn, half soybeans ($72.5K). This hedges against both weather and price risk but limits upside potential.
- Option 4: Lease the Land
Lease all 500 acres to another farmer for a guaranteed $45,000. Zero risk but foregoes all upside.
The decision tree
The tree has 2 decisions, 10 chance events and 28 outcomes. The best path is open: at every decision the best choice is marked, and the expected value beside each branch counts every cash flow from the start. Open any other branch to see what follows it.
DecisionChance event+$ cash flow on the branch
Plant Corn −$85,000expected $61,350 ✔ best
Chance: Growing Season Weather25% Ideal Conditionsexpected $121,000
Chance: Corn Price (Ideal Yield)- 20% High Price +$280,000payoff $195,000
- 50% Normal Price +$210,000payoff $125,000
- 30% Low Price +$150,000payoff $65,000
45% Normal Conditionsexpected $70,000
Chance: Corn Price (Normal Yield)- 25% High Price +$200,000payoff $115,000
- 50% Normal Price +$155,000payoff $70,000
- 25% Low Price +$110,000payoff $25,000
20% Droughtexpected $33,000
Decision: Drought ResponseIrrigate (Extra Cost) −$25,000expected $33,000 ✔ best
Chance: Irrigated Corn Price- 30% High Price +$180,000payoff $70,000
- 50% Normal Price +$140,000payoff $30,000
- 20% Low Price +$95,000payoff −$15,000
Accept Reduced Yieldexpected −$3,500
Chance: Corn Price (Drought Yield)- 35% High Price +$120,000payoff $35,000
- 45% Normal Price +$70,000payoff −$15,000
- 20% Low Price +$40,000payoff −$45,000
- 10% Flooding +$15,000payoff −$70,000
Plant Soybeans −$60,000expected $59,412
Chance: Growing Season Weather25% Ideal Conditionsexpected $110,000
Chance: Soybean Price (Ideal)- 25% High Price +$220,000payoff $160,000
- 50% Normal Price +$170,000payoff $110,000
- 25% Low Price +$120,000payoff $60,000
45% Normal Conditionsexpected $71,250
Chance: Soybean Price (Normal)- 25% High Price +$175,000payoff $115,000
- 50% Normal Price +$130,000payoff $70,000
- 25% Low Price +$90,000payoff $30,000
20% Droughtexpected $19,250
Chance: Soybean Price (Drought)- 30% High Price +$110,000payoff $50,000
- 45% Normal Price +$75,000payoff $15,000
- 25% Low Price +$50,000payoff −$10,000
- 10% Flooding +$20,000payoff −$40,000
Split 50/50 −$72,500expected $59,300
Chance: Growing Season Weather- 25% Ideal Conditions +$195,000payoff $122,500
- 45% Normal Conditions +$145,000payoff $72,500
- 20% Drought +$80,000payoff $7,500
- 10% Flooding +$18,000payoff −$54,500
- Lease Land +$45,000payoff $45,000
Change the numbers. Open the workbook with ModelChoice, change a probability or a cost in the tree, and the best decision updates at once.
Key assumptions
| Assumption | Value | Notes |
|---|---|---|
| Farm Size | 500 acres | All tillable, no pasture |
| Corn Planting Cost | $85,000 | Seed, fertilizer, chemicals, fuel, labor |
| Soybean Planting Cost | $60,000 | Lower input costs than corn |
| Irrigation Cost (Drought) | $25,000 | Pumping, equipment rental |
| Ideal Weather Probability | 25% | Warm, adequate rain, no early frost |
| Normal Weather Probability | 45% | Typical growing season |
| Drought Probability | 20% | Below-normal rainfall, heat stress |
| Flooding Probability | 10% | Excessive spring/summer rain |
| Corn Revenue Range | $15K - $280K | Flood loss to ideal yield + high price |
| Soybean Revenue Range | $20K - $220K | Narrower range, more drought-tolerant |
| Land Lease Income | $45,000 | Guaranteed, $90/acre cash rent |
The figures are illustrative: the companies and numbers are invented for teaching.
Try it in ModelChoice
- Strategy Table. Compare all crop strategies with risk-return frontier
- Sensitivity Analysis. How do commodity prices and weather odds affect the decision?
- Risk Profile. Is the guaranteed lease income worth the foregone expected profit?
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Further reading
Download the workbook and open it with ModelChoice. The free trial opens every example.
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An illustrative example: the figures are invented for teaching. Last updated 9 October 2026.