Question

3. The table below shows the relationship between income and total utility for Jane. Use this to answer (a) and (b) below. Income Total Utility 5,000 10,000 15,000 20,000 25,000 30,000 12 30 36 40 42 (a) (b) Is Jane risk averse, risk neutral or risk loving? Explain Jane currently earns S15,000 in a riskless investment. Alternatively, she could invest in a project that has a 0.5 probability of yielding a S30,000 and a 0.5 probability of yielding $10,000. Should she alter her strategy and move her money into the more risky project? Explain your answer.

Answer 1

a)

Income	TU	MU
5000	12	----
10000	22	22 - 12 = 10
15000	30	30 - 22 = 8
20000	36	36 -30 = 6
25000	40	40-36 = 4
30000	42	42 - 40 = 2

Jane is a risk averse, as indicated by her declining marginal utility of income. A risk lover's marginal utility rises, while someone who is indifferent to risk has a constant marginal utility.

b)  Her expected utility under the project would be:

Expected Utility = 0.5*U(30,000) + 0.5*U(10,000)= 0.5(42) + 0.5(22)

Expected Utility = 32  

current utility = U(15000) = 30

Expected utility is more than current utility, so she should alter her strategy.