Question

Question 1 Consider three choices A, B, C. Choice A gives $60 with certainty. Choice B gives $30 with probability 1/2 and $90 with probability 1/2. Choice C gives $40 with probability 1/2 and $90 with probability 1/2. (a) [2 points] For a risk averse individual, determine if the individual (i) prefers A over B, or (ii) prefers B over A, or (iii) more information on the individual's risk attitude is needed to compare A,B for the individual. (b) [4 points] Carry out the same comparison as in (a) between choices (A,C) and (B,C) for a risk-averse individual. (c) [3 points] How do the conclusions in (a)-(b) change when the individual is risk neutral instead of risk averse?

Answer 1

One thing to remember:

The utility of a risk-averse individual is U(y)= (y)^1/2 as the individual keeps on investing additional wealth (y), their marginal utility of wealth declines.

The utility of a risk-neutral individual is U(y)= y as the individual keeps on investing additional wealth (y), their marginal utility of wealth remains constant.

Utilities in case of Risk-averse individual:-

A:- (60)^1/2= 7.74

B:- 0.5 (30)^1/2 + 0.5 (90)^1/2= 7.47

C:- 0.5 (40)^1/2 + 0.5 (90)^1/2= 7.9

(I) A will be preferred over B, (ii) C will be preferred over A and B too. So C>A>B.

Utilities in case of Risk-neutral individual:-

A:- 60

B:- 0.5 (30) + 0.5 (90)= 60

C:- 0.5 (40) + 0.5 (90)= 65

(i) A person will be indifferent between A and B, (ii) C will be preferred over A and B too. So C>A=B.