Let's break down the problem and solve it step by step, as requested. --- ## GIVEN DATA - **Corn:** - Value if Rebecca copdusts: $33,000 - Value if not: $27,000 - **Wheat:** - Value if Rebecca copdusts: $45,000 - Value if not: $15,000 - **Soybeans:** - Value if Rebecca copdusts: $50,000 - Value if not: $ - Probability Rebecca can copdust: \( p = \frac{2}{3} \) - Probability Rebecca cannot copdust: \( 1-p = \frac{1}{3} \) - Cost to Ned for Rebecca's service: $3,000 --- (a) Efficient Crop for Ned to Plant Calculate **Expected Value (EV)** for each crop, accounting for probabilities and cost. ### **Corn:** \[ \text{EV}_\text{corn} = p \cdot 33,000 + (1-p) \cdot 27,000 - 3,000 \] \[ = \frac{2}{3} \cdot 33,000 + \frac{1}{3} \cdot 27,000 - 3,000 \] \[ = 22,000 + 9,000 - 3,000 = 28,000 \] ### **Wheat:** \[ \text{EV}_\text{wheat} = p \cdot 45,000 + (1-p) \cdot 15,000 - 3,000 \] \[ = \frac{2}{3} \cdot 45,000 + \frac{1}{3} \cdot 15,000 - 3,000 \] \[ = 30,000 + 5,000 - 3,000 = 32,000 \] ### **Soybeans:** \[ \text{EV}_\text{soy} = p \cdot 50,000 + (1-p) \cdot - 3,000 \] \[ = \frac{2}{3} \cdot 50,000 + \frac{1}{3} \cdot - 3,000 \] \[ = 33,333.33 + - 3,000 = 30,333.33 \] ### **Conclusion:** - **Wheat** gives the highest expected value: **$32,000** - **Efficient for Ned to plant wheat.** --- ## (b) If Ned Plants Corn - Value with copdust: $33,000 - Value without: $27,000 - **Benefit from performance:** $33,000 - $27,000 = $6,000 - **Expectation damages if Rebecca breaches:** $6,000 --- ## (c) If Ned Plants Wheat - Value with copdust: $45,000 - Value without: $15,000 - **Benefit from performance:** $45,000 - $15,000 = $30,000 - **Expectation damages if Rebecca breaches:** $30,000 --- ## (d) If Ned Plants Soybeans - Value with copdust: $50,000 - Value without: $ - **Benefit from performance:** $50,000 - $ = $50,000 - **Expectation damages if Rebecca breaches:** $50,000 --- ## (e) Damages Limited to Corn If damages are limited to what Ned would have lost with corn: - Max expectation damages = $33,000 - $27,000 = $6,000 (the corn difference) - **Ned would choose to plant wheat (EV: $32,000), but if damages are limited to $6,000, the risk of planting wheat or soybeans is not properly compensated.** - **Ned would likely choose to plant corn.** --- ## (e) (continued): Damages Cover Actual Loss If Rebecca must cover Ned's actual loss (so even if he plants wheat/soybeans, gets the full loss), Ned will always choose the crop with the highest expected value, **wheat**. --- ## (1) When is it Efficient for Rebecca to Breach? It is efficient for Rebecca to breach only if her cost of performing exceeds the benefit to Ned from her performance (i.e., the *increase in value* from her service). - For corn: Breach if cost > $6,000 - For wheat: Breach if cost > $30,000 - For soybeans: Breach if cost > $50,000 --- ## (f) Under Rule in (d): Is Rebecca Likely to Breach Efficiently? **No.** If damages are always $6,000 (corn), Rebecca will breach too often on wheat/soybeans—she may breach even when her cost is less than the benefit to Ned, resulting in *inefficient breaches*. --- ## (g) Under Rule in (e): Would Rebecca Invest Efficient Amount? **Yes.** If damages = actual loss, Rebecca internalizes the full benefit to Ned, so she will breach only if her cost exceeds the benefit—leads to efficient performance/breach. --- ## **Summary Table** | Crop | EV (copdust) | EV (no copdust) | Efficient? | Expectation Damages | Under (d) | Under (e) | |----------|--------------|------------------|------------|---------------------|-----------|-----------| | Corn | $33,000 | $27,000 | No | $6,000 | Plant corn| Plant wheat| | Wheat | $45,000 | $15,000 | Yes | $30,000 | Plant corn| Plant wheat| | Soybeans | $50,000 | $ | No | $50,000 | Plant corn| Plant wheat| --- ## **Final Answers** ### (a) Efficient crop: **Wheat** ### (b) Corn, benefit: **$6,000**, damages: **$6,000** ### (c) Wheat, benefit: **$30,000**, damages: **$30,000** ### (d) Soybeans, benefit: **$50,000**, damages: **$50,000** ### (e) If damages limited to corn: **Plant corn** ### (e) If damages cover actual losses: **Plant wheat** ### (1) Efficient for Rebecca to breach if cost > benefit to Ned of performance. ### (f) Under (d), Rebecca breaches too often and not efficiently. ### (g) Under (e), Rebecca breaches efficiently. --- Let me know if you need further breakdowns or calculations!

Expected Value (EV) is the weighted average of possible outcomes, calculated by multiplying each outcome by its probability, reflecting the anticipated value of a decision.

### (b) If Ned Plants Corn - **Value with Copdust:** $33,000 - **Value without Copdust:** $27,000 - **Benefit from Performance:** \[ 33,000 - 27,000 = 6,000 \] - **Expectation Damages if Rebecca Breaches:** $6,000 ### (c) If Ned Plants Wheat - **Value with Copdust:** $45,000 - **Value without Copdust:** $15,000 - **Benefit from Performance:** \[ 45,000 - 15,000 = 30,000 \] - **Expectation Damages if Rebecca Breaches:** $30,000 ### (d) If Ned Plants Soybeans - **Value with Copdust:** $50,000 - **Value without Copdust:** $0 (worthless) - **Benefit from Performance:** \[ 50,000 - 0 = 50,000 \] - **Expectation Damages if Rebecca Breaches:** $50,000 --- These calculations reflect the potential financial outcomes for Ned based on whether Rebecca successfully cropdusts or breaches the contract. Each crop has different values and associated risks, influencing Ned's decision-making.

Under Rule (e), if Rebecca is liable for Ned's actual losses, she fully accounts for the financial impact of her performance. This incentivizes her to invest efficiently in maintaining her cropdusting capability, ensuring she only breaches the contract when her costs outweigh the benefits to Ned, promoting optimal decision-making.