Question 3 (20 points)

In class discussions about uncertainty we assumed that the utility levels in each state of nature depends on c, which we might interpret as some aggregate con- sumption and we expressed utility as U(c). Now, lets extend this to a case where the utility level depends on consumption of two goods (this was the type of utility we used mainly in this course).

Ben is a farmer who grows wheat and barley. However, his harvest is uncertain. If weather is good, he gets 200 lbs of wheat and 200 lbs of barley. If weather is bad, he gets only 100 lbs of wheat and 100 lbs of barley. His utility in each state of nature is U(w,b) = w1/4b3/4, where w and b represent his consumption of wheat and barley, respectively. Prices of wheat and barley are $1 in both state of nature. The probability of good weather is .

Question 3 Part a

Express Bens expected utility function. (Hint: find Bens optimal consumption in each state of nature first)

Question 3 Part b

Lets assume = 0.5. Knowing that bad weather reduces his harvest, Ben contemplates to purchase an insurance. He can purchase an insurance at a cost of 20 cents for each $1 worth of coverage. So, for each $1 of insurance premium he will receive $5 in bad weather. How much insurance would Ben purchase?

help on all!! thanks

Question 3 ( 20 points) In class discussions about uncertainty we assumed that the utility levels in each state of nature depends on c, which we might interpret as some aggregate consumption and we expressed utility as U(c). Now, let's extend this to a case where the utility level depends on consumption of two goods (this was the type of utility we used mainly in this course). Ben is a farmer who grows wheat and barley. However, his harvest is uncertain. If weather is good, he gets 200lbs of wheat and 200lbs of barley. If weather is bad, he gets only 100lbs of wheat and 100lbs of barley. His utility in each state of nature is U(w,b)=w1/4b3/4, where w and b represent his consumption of wheat and barley, respectively. Prices of wheat and barley are $1 in both state of nature. The probability of good weather is . Question 3 Part a Express Ben's expected utility function. (Hint: find Ben's optimal consumption in each state of nature first) Question 3 Part b Let's assume =0.5. Knowing that bad weather reduces his harvest, Ben contemplates to purchase an insurance. He can purchase an insurance at a cost of 20 cents for each $1 worth of coverage. So, for each $1 of insurance premium he will receive $5 in bad weather. How much insurance would Ben purchase