As the owner of a family farm whose wealth is $250,000, you must choose between sitting this sea- son out and investing last year's earnings ($200,000) in a safe money market fund paying 5.0 percent or planting summer corn. Planting costs $200,000, with a six-month time to harvest. If there is rain, planting summer corn will yield $500,000 in revenues at har- vest. If there is a drought, planting will yield $50,000 in revenues. As a third choice, you can purchase AgriCorp drought-resistant summer corn at a cost of $250,000 that will yield $500,000 in revenues at har- vest if there is rain, and $350,000 in revenues if there is a drought.
You are risk averse, and your preference for family wealth (W) is specified by the relationship U(W) = 1W. The probability of a summer drought is 0.30, while the probability of summer rain is 0.70.
Which of the three options should you choose? Explain.