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3. You are the owner of a family farm of 100 acres whose wealth is $1,000,000. You must choose between three alternative investments for the next three years: i) investing this amount in a safe money market fund paying an interest rate of 2.5% quarterly, i) planting corn every year in the 100 acres and invest the remaining amount in the safe money market fund, or ili) planting wheat every year in the 100 acres and invest the remaining amount in the safe money market fund. Assume that you are only allowed to invest in the safe money market fund at the beginning of the period. The annual interest rate is 5% and the probability of a drought period is 0.40, while the probability of a wet period is 0.60. The expected annual costs and revenues under the two scenarios for both crops during the three year period are presented in Table 2. Table 2. Payoff table for different crops (payoff expressed in AUD per acre) Year 1 Year 2 Year 3 Corn Revenue (Dry) Revenue (Wet) Cost 10,200 12,000 10,000 10,200 12,000 10,000 10,200 12,000 10,000 Wheat Revenue (Dry) Revenue (Wet) Cost 7,500 6,500 6,000 7,500 6,500 6,000 7,500 6,500 6,000 Source: Adapted from Barry and Ellinger (2012). You are risk averse, and your preference for family wealth (W) is specified by the relationship U(w) ( 5 1. Present the appropriate calculations for each alternative. (15 Marks) 2. Which of the three alternative investments should you choose