We assume that the utility levels in each state of nature depend on c, which we...

 

Transcribed Image Text:

We assume that the utility levels in each state of nature depend on c, which we might interpret as some aggregate consumption and we express utility as U(c). Now, let's extend this to a case where the utility level depends on consumption of two goods). Ethan 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) = w^1/4b^3/4, 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 T. Question 3 Part a Express Ethan's expected utility function. (Hint: find Ethan's optimal consumption in each state of nature first) Question 3 Part b Let's assume TT = 0.5. Knowing that bad weather reduces his harvest, Ethan 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 Ethan purchase? We assume that the utility levels in each state of nature depend on c, which we might interpret as some aggregate consumption and we express utility as U(c). Now, let's extend this to a case where the utility level depends on consumption of two goods). Ethan 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) = w^1/4b^3/4, 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 T. Question 3 Part a Express Ethan's expected utility function. (Hint: find Ethan's optimal consumption in each state of nature first) Question 3 Part b Let's assume TT = 0.5. Knowing that bad weather reduces his harvest, Ethan 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 Ethan purchase?