A Corn Farmer Is Considering Two Alternatives For Selling

A Corn Farmer Is Considering Two Alternatives For Selling His Crop Th

A corn farmer is considering two alternatives for selling his crop. The first is a contract where he can sell the rights to the future crop at planting. The second is to sell the crop after harvest. At harvest, the farmer estimates that the price of corn will be $10 per bushel with probability 0.5 and $12 per bushel with probability 0.5. The farmer is risk-averse and is willing to pay $50,000 to avoid the risk of damage to the crop while it is growing (e.g., from a tornado or flood).

If the farmer uses pesticides, he expects a crop of 60,000 bushels; if he does not use pesticides, he expects a crop of 55,000 bushels. The cost of pesticides is $20,000. The other costs associated with planting and harvesting the crop total $450,000.

Paper For Above instruction

The decision-making process of farmers regarding their crop sales involves analyzing risk factors, costs, and potential profits. In particular, the choice between pre-harvest contractual agreements and post-harvest sales requires a thorough understanding of expected revenues, risk aversion, and market conditions. This paper examines the farmer's options, focusing on profitability, the valuation of crop rights, and the implications of risk aversion, providing insights grounded in economic theories and real-world agricultural practices.

Analysis of Immediate Sale (Post-Harvest Sale)

The farmer's expected profit from selling the crop after harvest hinges on the anticipated revenues and associated costs. If the farmer uses pesticides, the expected crop yield is anticipated at 60,000 bushels, with additional costs of $20,000 for pesticides and $450,000 for planting and harvesting, totaling $470,000. Without pesticides, the expected yield drops to 55,000 bushels, but pesticide costs are avoided, and total costs would be $430,000.

Calculating the revenue for each scenario based on the probabilistic price distribution:

• At a price of $10 per bushel (probability 0.5): revenue = 60,000 bushels × $10 = $600,000 (with pesticides); 55,000 bushels × $10 = $550,000 (without pesticides).
• At a price of $12 per bushel (probability 0.5): revenue = 60,000 bushels × $12 = $720,000 (with pesticides); 55,000 bushels × $12 = $660,000 (without pesticides).

Expected Profit With Pesticides

Expected revenue = 0.5 × $600,000 + 0.5 × $720,000 = $660,000.

Net profit = expected revenue - total costs = $660,000 - $470,000 = $190,000.

Expected Profit Without Pesticides

Expected revenue = 0.5 × $550,000 + 0.5 × $660,000 = $605,000.

Net profit = expected revenue - total costs = $605,000 - $430,000 = $175,000.

Considering the farmer's risk aversion and the potential damage, the expected profits suggest that pesticides increase expected profit marginally from $175,000 to $190,000, but also introduce additional risk mitigation, which the farmer values at $50,000. Therefore, the farmer would prefer using pesticides, gaining an expected profit of $190,000, acknowledging his risk-averse nature.

Valuation of the Crop Rights for an External Buyer

The maximum price an outside purchaser would pay for the right to the future crop hinges upon the farmer’s expected profit and the risk premium associated with the operations. Given the farmer's risk aversion and valuation for risk mitigation ($50,000), an ideal valuation would consider the expected profit adjusted for risk preferences. Assuming the buyer cannot monitor the farmer post-sale, and considering the probabilistic prices, the most accurate valuation encompasses the expected revenue less farmer’s risk aversion adjustment.

The expected revenue from the crop, as calculated, is $660,000 with pesticides. The buyer, unable to monitor, would base his offer on the expected value, minus an appropriate risk premium. Given the risk-averse nature and the farmer’s valuation, the buyer’s maximum willingness-to-pay could approximate the farmer’s expected profit adjusted for risk, about $190,000 or slightly higher depending on the market's risk premium.

Comparison of Sale Prior to Planting Versus After Harvest

The choice between selling rights prior to planting or selling after harvest depends significantly on the farmer’s risk appetite. Selling rights before planting (a forward contract) reduces exposure to market price fluctuations but might yield a lower price reflecting risk premiums, whereas selling after harvest offers potential upside but involves price risk.

Risk aversion suggests that the farmer prefers certainty and might hence favor selling rights at planting if the offer covers his expected profit plus risk premium. However, given the analysis, the expected profit from post-harvest sale ($190,000) exceeds the net benefit of fixed contractual prices if the market prices are favorable or if the farmer values flexibility and market participation. If risk premiums are accounted for, the farmer might prefer to sell rights in advance if the upfront payment compensates adequately for potential variability and his risk aversion.

Conclusion

Overall, the analysis indicates that the farmer benefits from using pesticides due to increased expected yield and profit, aligning with his risk-averse stance and safety valuation. The valuation of crop rights for a third party must consider the farmer’s expected profit, risk premium, and inability to monitor post-sale, with a maximum willingness-to-pay around his expected profit threshold. Finally, the decision between selling rights prior to planting versus post-harvest sale critically hinges on the farmer’s risk preferences, market conditions, and contractual agreements. Employing risk management strategies aligned with the farmer's preferences can optimize profitability and risk mitigation.

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