Question

The relationship between income and total utility (TU) for 2 investors (Alan and Bob) is as follows:

  Alan                               Bob

Income      TU            Income     TU

5,000         14            5,000        6

10,000       24           10,000       14

15,000       32           15,000       24

20,000       38           20,000       36

25,000       43           25,000       52

30,000       47           30,000       72

35,000       49           35,000       100

Each investor has been confronted with the following three investment opportunities.  The first opportunity is an investment which pays €15,000 risk free.  Opportunity two offers a 0.4 probability of a €25,000 payment and a 0.6 probability of paying €10,000.  The final investment will either pay €35,000 with a probability of 0.25 or €5,000 with a probability of 0.75.

The expected value of the third opportunity is

5,000

35,000

10,000

12,500

The expected utility of the second opportunity for Alan is

		31.6
		43
		24
		12

Answer 1

1). To calculate the expected value multiply the probability of each given outcome by its expected value and add them together -

€35,000 × 0.25 +  €5,000 × 0.75

= 8750 + 3750

=  €12,500 .

So, the correct answer is 12500.

2). Expected utility of the second opportunity for Alan is -

= 0.4 U(25,000) + 0.6 U(10,000)

= 0.4 × 43 + 0.6 × 24

= 17.2 + 14.4

= 31.6 .

So, the correct answer is 31.6 .