Question

Save Homework: Chapter 5 Homework Score: 0 of 1 pt 6 of 15 (5 complete) HW Score: 20%, 3 of 15 pts X Exercise 8 Question Help As the owner of a family farm whose wealth is $300,000, you must choose between sitting this season out and investing $200,000 in a safe money market fund paying 7 percent option 1) or planting summer com (option 2). Planting costs $200,000, with a six-month time to harvest. If there is rain, planting summer com will yield $400,000 in revenues at harvest. If there is a drought, then planting will yield $50,000 in revenues. As a third choice (option 3), you can purchase AgriCorp drought-resistant com at a cost of $250,000 that will yield $400,000 in revenues at harvest if there is rain, and $300,000 in revenues if their is a drought. You are risk averse, and your preference for family wealth (W) is specified by the relationship UW) - VW The probability of a summer drought is 20 percent, while the probability of summer rain is 80 percent Which of the three options should you choose? Explain. You should choose V because it generates the highest

Answer 1

Solution :-

Total wealth (Investment) = $300000

• Option 1:-

Investment = $200,000

interest = 7%

Total wealth if option 1 = (30000 -200000) + 200000(1+.07)

Total wealth if option 1 = 314,000

U(W) =$\sqrt{W}$

U(W) = 560.35

• Option 2:-

Investment = 175000

Yield of 40000 with the probability 0.6

Yield of 50000 with the probability 0.4

Expected wealth = (300000-100000) + 0.6*400000 + 0.4*50000

Expected Wealth = 200000 + 260000

Expected Wealth = 460000

U(W) =$\sqrt{W}$

U(W) = 678.23

• Option 3:-

Investment = 250000

Yield of 400000 with the probability 0.6

Yield of 300000 with the probability 0.4

Expected wealth = (300000-250000) + 0.6*400000 + 0.4*300000

Expected Wealth = 50000 + 360000

Expected wealth = 410000

U(W) =$\sqrt{W}$

U(W) = 640.31

Hence, you should choose Option 2 because it generates the highest utility.