Question

the florida lottery has done extensive research on the individuals who purchase their products. they have determined that their customers have a square root utility function and an initial wealth of $100. it costs $19 to purchase a lottery ticket and each ticket has a 50/50 chance of being worth $39. true or false, customers will purchase these lottery tickets.

Answer 1

With a square root utility function and an initial wealth of $100, the utility of buying a lottery ticket for $19 with a 50/50 chance of winning $39 results in an expected utility lower than the utility of not buying the ticket. Therefore, customers will not purchase these tickets.

Step-by-step explanation:

The scenario presented involves a decision from customers on whether to purchase a lottery ticket based on their utility function and initial wealth. Let's consider the utility of buying a ticket and not buying a ticket for a customer with the square root utility function and an initial wealth of $100.

When the customer does not buy a ticket, their total wealth remains $100, so their utility is √100 = 10.

If the customer buys a ticket, they spend $19, so their wealth becomes $81. With a 50/50 chance of winning $39 (resulting in wealth of $120), their expected utility from buying a ticket is (0.5 * √81) + (0.5 * √120). This simplified is (0.5 * 9) + (0.5 * √120) = 4.5 + approx. 5.477.

Expected utility from buying a ticket is lower than the utility of not buying the ticket (10 > 9.977), so based on this utility function, the customers will not purchase the lottery tickets.

Answer 2

Risk is the potential of gaining or losing something of value. Values (such as physical health, social status, emotional well-being or financial wealth) can be gained or lost when taking risk resulting from a given action or inaction, foreseen or unforeseen. Risk can also be defined as the intentional interaction with uncertainty.Uncertainty is a potential, unpredictable, and uncontrollable outcome; risk is a consequence of action taken in spite of uncertainty.

Risk perception is the subjective judgment people make about the severity and probability of a risk, and may vary person to person. Any human endeavor carries some risk, but some are much riskier than others.