Question

You have $500,000 that can be invested for one time period and your utility function is U = √ W You must choose between the following two options:

Invest $500,000 all of the money in a safe money market fund paying 5.0%.

Invest $400,000 of the money into a new invention that is much riskier. If the invention is a success, you will get back $800,000. If it is not a success, you will get $100,000 back. The probability that the invention will be a success is 0.6

Which option should you choose? Explain.

Answer 1

a. In question total wealth given to invest is $ 500000 and  U = √ W . so, in first option by investing $500000 in market fund get 5% . Total money get is {500000+25000}$ is $525000. Putting in utility function[ U = √ W , =724.56]. Now in second option we find expected utility (the expected value of an action to an agent ,calculated by multiply the value to an agent of each possible outcomes of the action by probability of that outcomes occuring .)

=> EU =0.6+0.4+ = 0.6* 894.4+0.4*316.2+316.2 =536.64+126.48+316.2 =[979.32].

Since, utility from second option is more , I willl choose second option.