Question

Consider three choices A, B, C. Choice A gives $30 with probability 1/2 and $70 with probability 1/2. Choice B gives $50 with certainty. Choice C gives $40 with probability 1/2 and $70 with probability 1/2.

1. 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.

2. Carry out the same comparison as in (a) between choices (A,C) and (B,C) for a risk averse individual.

3. How do the conclusions in (a)-(b) change when the individual is risk neutral instead of risk averse?

Answer 1

1. Option (ii) prefers B over A. because he's a risk averse consumer he'll always choose sure bundle.

2. Between A and C he'll choose C by calculating expected payoffs.

expected payoff of A is 0.5*30+ 0.5*70 = 50

expected payoff of C is 0.5*40+ 0.5*70 = 55

Between B and C he'll choose B always because it's a sure bundle.

3. When consumer is risk neutral:

He'll choose C between (A,C) and (B,C) as expected payoff of C is higher than both A and B

expected payoff of A is 0.5*30+ 0.5*70 = 50

expected payoff of C is 0.5*40+ 0.5*70 = 55

expected payoff of B is 50

He'll be indifferent between A and B because both bundles give same payoff.

Expected payoff from A is 0.5*30 + 0.5*70 = 50

Expected payoff from B is 50 for sure.