Question

Suppose that a decision maker’s utility as a function of her wealth, x, is given by U(x) = ln (2x) (where ln is the natural logarithm). The decision maker now has $10,000 and two possible decisions. For Alternative 1, she loses $1000 for certain. For Alternative 2, she gains $500 with probability 0.8 and loses $2,000 with probability 0.2. Which alternative should she choose and what is her expected utility (rounded to 2 decimals)?

a.She should choose Alternative 1. Her expected utility is 9.10.

b.She is indifferent between both alternatives.

c.She should choose Alternative 1. Her expected utility is 9.80.

d.She should choose Alternative 2. Her expected utility is 9.90.

Answer 1

For Alternative 1

The decision maker now has $10,000 and two possible decisions. For Alternative 1, she loses $1000 for certain

So he will have $9000 since she invest $10000 and loses $1000

Utility U(x) = ln (2x)

Here x = 9000

Utility U(x) = ln (18000)

= 9.7981

= 9.80 riunded to 2 decimals

For Alternative 2

The decision maker now has $10,000

she gains $500 with probability 0.8 and loses $2,000 with probability 0.2

Expected gain or loss = 500 * 0.8 - 2000 * 0.2

= 400 - 400

= 0

So she will be having the initial $10000 with her

Utility U(x) = ln (2x)

Here x = 10000

Utility U(x) = ln (20000)

= 9.9035

= 9.90 riunded to 2 decimals

Her expected utility in Alternative 2 is 9.90 which is more than that of the expected utility of Alternative 1 which is 9.80

So Answer is Option D

She should choose Alternative 2. Her expected utility is 9.90.