Final answer:
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.