Question

Suppose that the consumer is asked to contemplate a gamble with a probability of 60% of
winning Birr 10,000 with a utility of 10 utils, and a 40% probability of winning Birr 15,000 with
a utility of 12 utils.
A. What will be the expected income and expected utility of the consumer?
B. If the utility of this consumer from a risk free alternative which gives him an income equal
to the expected income of the risky alternative given above is equal to 11 utils, is this
consumer risk lover or risk averse? Why? Illustrate your answer with the help of a diagram

Answer 1

a.

The expected income will be, 

$Expected income = (60\%×10,000) + (40\%×15,000) \\=6,000 + 6,000\\= 12,000$

The expected utility will be, 

$Expected utility (E(u)) =(60\%×10) + (40\%×12)\\= 6 + 4.8 \\=10.8$

Therefore, expected income will be $12,000 and expected utility 10.8.

b.

The utility from risk free alternative that give the same income as risky alternative is 11 utils. This means, 

$E(u) < U(E(u)) \\10.8<11$

This shows that the consumer receives more utility with the same income given to him but with a certainty and risk free alternative, than with the same income but with risky alternative. This shows that the individual is risk averse in nature who wants to avoid risk.

A concave shape utility curve shows a risk-averse individual case.