Answered: An individual is oered a choice of…

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.8P

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Question

An individual is oered a choice of either $50 or a lottery which may result in $0
and $100, each with equal probability 1/2 . If the individual has a utility function u(w) = 5 + 2w, which one would they choose? If the individual has a utility function u(w) =w^1/2 + 1?

Expert Solution

Step 1

Given Utility function, u(w) = 5 + 2w

Probability = $\frac{1}{2}$

$\begin{array}{rcl} Now find the Utility in the case of $ 50 . & = & 5 + 2 w \\ = & 5 + 2 (50) \\ = & 105 \\ Now find utility incase of lottery & = & \frac{1}{2} (5 + 2 w) + \frac{1}{2} (5 + 2 \times w) \\ = & \frac{1}{2} (5 + 2 \times 0) + \frac{1}{2} (5 + 2 \times 100) \\ = & 105 \end{array}$

Since the utility is the same so the consumer will be indifferent.

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