Question

A Suppose a com er has a Bernoulli utility function of money (1) - V. There are two financiales, both et 100 available to the owner, and the consumer going to buy these two facial l pay $103 with certainty, while Asset 2 pays $110 with probability 0.95, and with probability 0.05 Which set will the consumer buy? Next consider another whose Ber t ility function of money is '(x) = Which we will the second commerby Brietly explain what drives the difference in the two consumers' investment plans

thank you

Answer 1

In case of first consumer

u(x)=x^1/2

Utility in case of asset 1 i.e. certain payment of $103

u(103)=103^1/2=10.15

In the second case of asset 2,

Expected payoff=0.95*110+0.05*0=$104.50

Expected utility=0.95*u(110)+0.05*u(0)=0.95*110^1/2+0.05*0^1/2=9.96

Expected utility has decreased in case of asset 2. So, consumer will buy asset with certain payoff of $103.

In case of second consumer

u'(x)=x²

Utility in case of asset 1 i.e. certain payment of $103

u'(103)=103²=10609

In the second case of asset 2,

Expected payoff=0.95*110+0.05*0=$104.50

Expected utility=0.95*u(110)+0.05*u(0)=0.95*110²+0.05*0²=11495

Expected utility has increased in case of asset 2. So, consumer will buy Asset 2.

In the case of first consumer, expected utility has decreased despite there is an increase in  expected payoff i.e. first consumer is risk averse.

In the case of second consumer, expected utility has increased as there is an increase in  expected payoff i.e. second consumer is risk loving.

We can see that asset choice is different for both consumers despite the same return pattern and cost. It is due to utility function i.e. behavior towards risk. Consumer 1 is risk averse while consumer 2 is risk loving.