Question

please solve question 3 completely.

thank you,

3) We want to decide whether to invest in a restaurant. The payoff if there is high demand for our food is $400 with probability 80% and -$100 with probability 20%. If we don't invest, we have no payoff. a. What is the outcome of the game if we are risk neutral? b. What is the outcome of the game if we are risk averse and our utility function is U(X) = (x + 100)1/2?

Answer 1

a)

A risk neutral person will play game if expected profit is positive.

Expected profit=0.80*400+0.20*(-100)=$300

Since expected profit is positive, a person will go for the game.

b)

First we estimate the utility if person does not go for game.

Utility in case of no game=U(x=0)=(100+0)^0.5=10 utils

Now we calculate the expected utility in case he goes for game,

Utility in case of loss=(100-100)^0.5=0 utils

Utility in case of profit=(100+400)^0.5=22.3607 utils

Expected utility in case of game=0.80*22.3607+0.20*0=17.8886 utils

We find that expected utility is higher in case of game. So, agent will go for game.