Question

True or False: You need to explain briefly your answers.

(a) (10pts) In the CAPM model, if a stock lies strictly below the budget line (recall that we label the standard deviation of a stock’s return on the x-axis and the mean of that on the y-axis), then it is for sure that no one will want to hold this stock in his optimal choice since there is always an alternative with less risk or greater expected return.

(b) (10pts)If apples are a normal good for a net supplier of apples, then it is possible that when the price of apples increases, his demand for apples increases as well.

(c) (10pts) Suppose there are two states of nature. State 1 occurs with Probability p1 and state 2 with p2 = 1 -p1. A consumer has the utility function of the following U(c1, c2, p1, p2) = c1^p1*c2^p2 where c1 is his consumption at state 1 and c2 is that at state 2. The consumer’s utility function takes the expected utility form.

(d) (10pts) Continue from above. Facing a risky income stream and the expected value of the same income stream, the consumer prefers the latter to the former.

Answer 1

a. True. Since persons want to minimize risk and also want to maximize their utility, thus if a stock lies below the budget line then no one will want to hold this stock in his optimal choice as they choose a bundle on the budget line rather than a bundle below the budget line.

b. True. As prices of apples increases, income of the supplier of apples will increase and in case of normal goods increase in income leads to increase in demand for a normal good.

c. True. the utility function can be written in expected utility form.

d. The person is risk averse person as the utility function is convex shaped. A risk averse person will prefer a risky income stream as compared to the expected value of the same income stream.Thus, the statement is false.