Question 3: (10 Marks) Suppose utility is governed by the following function, U(x) = 100 - (x - 10)2

and that

0x10.

a) What can you say about the risk preference of this individual? ( 1 Mark)

b) Graph the utility function. (1 Mark)

Suppose the individual must choose between two options. The first option is to receive 7 units of x with

certainty. The second option is to receive 3 units with probability 1/3 or 9 units with probability 2/3.

c) Label the utility of the first option on your graph. (1 Mark)

d) Demonstrate mathematically that the expected utility of option 2 lies on the chord between u(x = 3) and

u(x = 9). (2 Marks)

e) Compute the utility of Option 1 and the expected utility of Option 2, and compare. (2 Marks)

f) Note that the first option, receiving 7 units, is the same as the expected value of the number of units

received from Option 2. How many of those 7 units would this individual be willing to give up in order to

avoid being given Option 2 in favor of receiving a fixed amount with certainty? (Assume that x can be

split into fractional numbers of units.) (2 Marks)

g) What is the risk premium? (1 Mark)