Question

Suppose Molly Jock wishes to purchase a high-definition television to watch the Olympic Greco-Roman wrestling competition. Her current income is \(\$ 20,000,\) and she knows where she can buy the television she wants for \(\$ 2,000\). She has heard the rumor that the same set can be bought at Crazy Eddie's (recently out of bankruptcy) for \(\$ 1,700,\) but is unsure if the rumor is true. Suppose this individual's utility is given by \\[\text { utility }=\ln (Y),\\] where \(Y\) is her income after buying the television. a. What is Molly's utility if she buys from the location she knows? b. What is Molly's utility if Crazy Eddie's really does offer the lower price? c. Suppose Molly believes there is a \(50-50\) chance that Crazy Eddie does offer the lowerpriced television, but it will cost her \(\$ 100\) to drive to the discount store to find out for sure (the store is far away and has had its phone disconnected). Is it worth it to her to invest the money in the trip?

Short answer

Answer: If Molly buys the television from the known location, her utility will be the natural logarithm of her remaining income, which is \(Utility = \ln(18,000)\).

Step-by-step solution

a. Utility if buying from the known location

To calculate the utility from buying the television from the known location, first, we need to find Molly's income after purchasing the television: \(Y = 20000 - 2000\) Now, plug this value into the utility function: \(Utility = \ln(Y) = \ln(18000)\)