In: Economics
1. In order to attract customers, Lau's Books Co. is considering offering a lottery to anyone who visits the bookstore. The 2 lotteries under consideration are:
Lottery A) one with a cash prize of $300 and a 10% probability of winning
Lottery B) one with a cash prize of $400 and a 5% probability of winning.
Which lottery is more attractive to a risk-averse individual? Explain in detail with the aid of a diagram. Which lottery is more attractive to a risk-lover? Explain in detail with the aid of a diagram.
1) A risk averse individual will prefer a certain income to a risky income with the same expected value. A risk averse individual's marginal utility diminishes as income increases.
*So,a risk averse individual will prefer a cash prize of 300 $ with a 10 percent probability of winning.
This can be further explained with the help of the following diagram.
As income increases from Y1 to Y1 utility increases from U1 to U2. When income increases from Y2 to Y3 utility increases from U2 to U3. But the increase in utility is less
BC<AC.
Therefor, utility he derives from lottery with 5 percent probability of winning and 400$ prize will be less than the utility he derives from the lottery with 300$ prize with 10 percent probability of winning.
Since he takes decisions based on utility, he chooses lottery with 300$ cash prize.
2) A risk loving individual will prefer a risky income to a certain income. His marginal utility increases with increase in income.
*A risk loving individual will choose lottery with a cash prize of 400$ dollar and 5 percent probability of winning.
This can be further explained with the help of the following diagram
As income increases from Y1 to Y2. Utility increases from U1 to U2. The addition to utility is represented by AC. When income increases from Y2 to Y3 utility increases from U2 to U3. Addition to utility is represented by BC. Its clear that, additional utility received by the individual increases with increase in income as BC> AC
Therefore, utility he derives from the lottery with a cash prize of 400 $ with 5 percent probability of winning is higher than the utility he derives from the lottery with 300$ cash prize and 10 percent probability of winning.