Answer to Question #219442 in Microeconomics for Zeki

Question

Suppose Martha earns an of income 400 Birr currently, and her utility function is given by: U(m)
= 4m, where m represents income. She has two options:
Option 1: to buy a share. If she is successful her income will be 700 Birr and if she is not
successful her income will be 100 Birr.
Option 2: to do nothing and keep on earning 400 Birr. Assuming that success and failure are
equally likely,
a) What would be her expected income if she buys the share?
b) What would be her expected utility of buying the share?
c) Would Martha buy the share? Why?
d) Is Martha risk averse, risk lover or risk neutral?

Answer 1

Part a )

Expected income when Martha buys the share :

= Probability of success ( income in case of success ) + probability of failure ( income in case of failure )

$= \frac{1}{2} (4×700) + \frac{1}{2} (4×100)\\ = 1400 + 200 = 1600$

Part b )

Expected utility when Martha buys the share :

= Probability of success ( utility in case of success ) + probability of failure ( utility in case of failure )

$= \frac{1}{2} (700) + \frac{1}{2} (100)\\ = 350 + 50 = 400$

Part c)

Utility ( at 400 income ) = 4m = 1600

Expected utility ( when buying the share ) = 1600 

Martha might or might not buy the share since her utility in both the cases is same.

Martha's utility function is linear therefore she is risk neutral.It refers to a mindset where an individual is indifferent to risk when making an investment decision.