Consider two farmers, Samantha and William. Samantha grows sweet potatoes, which tend to do well during dry seasons. William grows watermelons, which tend to do better during rainy seasons. If the weather is dry this year, Samantha will earn $100,000 and William will earn $10,000. If the weather is rainy this year, Samantha will earn $30,000 and William will earn $120,000. There is a 50 percent chance of dry weather and a 50 percent chance of rainy weather this year.Suppose Samantha and William are considering merging their farms. If they do merge, they will split their profits equally. Which of the following statements is true?Samantha will prefer to merge, but William will prefer to keep his farm separate.The expected value of William's earnings if the farms merge is $65,000.The expected value of William's earnings if they do not merge is $65,000.
A)III only
B)I and II only
C)II and III only
D)I, II, and III

Question

Quizplus · Accepted Answer

If they merge, William's expected earnings are (0.5 * 100,000 + 0.5 * 120,000) / 2 = 65,000. If they do not merge, William's expected earnings are (0.5 * 10,000 + 0.5 * 120,000) = 65,000. Therefore, William's expected earnings are the same whether or not they merge. Samantha, on the other hand, will earn more if they merge (expected earnings of 65,000) than if they do not merge (expected earnings of 50,000). Therefore, Samantha will prefer to merge, but William will prefer to keep his farm separate.

Consider Two Farmers, Samantha and William