# Utility Index and Selecting Choices based on Utility

Part 1

Entrepreneur Jones has a utility index of 5 for a loss of $1,000, and 12 for a profit of $3,000. He says that he is indifferent between $10 for certain and the following lottery: a 0.4 chance at a $1,000 loss and a 0.6 chance at a $3,000 profit. What is his utility index for $10?

Part 2

Suppose that Smith has a utility function U(x) = x^(2/3) where x is in dollars (0 < x < 100). Smith is offered the following choices:

A: $8 for sure.

B: A lottery with a one-half chance for zero dollars and a one-half chance for $64.

Which choice would you predict Smith will choose?

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#### Solution Preview

Part 1: Entrepreneur Jones has a utility index of 5 for a loss of $1,000, and 12 for a profit of $3,000. He says that he is indifferent between $10 for certain and the following lottery: a 0.4 chance at a $1,000 loss and a 0.6 chance at a ...

#### Solution Summary

This solution helps with various business math problems. It calculates the utility index and analyzes the impact of the utility function on decision making. Step by step calculations and explanations are given.