Question

Facing a lottery that yields £0 and £100 with equal probability, a risk averse consumer will:

a. Prefer any certain win to playing the lottery;

b. Prefer a certain win of 50 pounds to playing the lottery;

c. Prefer to play the lottery to any certain win of x pounds, with 0 < x < 50;

d. Be indifferent between playing a lottery and receiving a certain win of 50 pounds;

Answer 1

The answer to the question is OPTION B, that is, Prefer a certain win of 50 pounds to playing the lottery.

A risk-averse person has a diminishing marginal utility of income and hence prefers a certain income to a lottery with the same expected income but with variance (risk) around this quantity.

To show the preferences of a risk-averse person, I will show you the diagram:

  

With income on X-axis and Utility on Y axis, note that, as money income of the individual increases from 10 to 20 points, his total utility increases by 20 points (that is from 45 units to 65) and when his money increases from 20 to 30 points, his total utility increases by only 10 points (that is from 65 to 75 units). The increase in utility is, therefore decreasing, as indicated by the CONCAVE shape of the Utility function