Question

Hayden is a farmer deciding between two possible two crops to plant for the coming season: {corn, beans}. The two possible states of Nature are {good weather, bad weather}, and while beans are more weather resistant, corn is more profitable. If Hayden plants corn (a corn lottery, L_C), there will be 0.7 percent chance of good weather, yielding a gain of $20 mil. in profits, and a 0.3 percent chance of bad, yielding a loss of $8 mil. Planting beans (L_B) gives a 0.9 percent chance of good weather, resulting in $10 mil. in gains, and a 0.1 of bad, resulting in only a $2 mil. loss.

• a. Draw a decision tree to guide us.
• b. Which crop gives the highest expected utility, assuming Hayden gets direct utility from money? Show your calculations.

Answer 1

Corn has a higher expected utility.

Explanation:

Hayden faces two possibilities, each leading to two possible outcomes with different probabilities. We graph the scenario:

To get the expected utility of each crop, we add the multiplication of each probability by the monetary value of each outcome. For example, the expected utility of corn is the probability of good weather times the yield of good weather plus the probability of bad weather times the yield of bad weather. Therefore:

Expected utility of corn = 0.7 * 20 + 0.3 * (-8) = 11.6 mio

Expected utility of beans = 0.9 * 10 + 0.1 * (-2) = 8.8 mio

Therefore, corn has a higher expected utility.