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: \(Utility = \ln(Y) = \ln(18000)\)

Key concepts

Expected Utility

Expected utility is a way to anticipate the satisfaction or benefit from different possible outcomes under uncertainty. For Molly, expected utility helps her make a decision when faced with uncertain prices for the television. It takes into consideration both the utility derived from buying the television at certain prices and the likelihood of each scenario happening.

In this case, Molly faces two potential outcomes regarding the purchase of her TV. Either Crazy Eddie offers it at \(1,700, or he doesn't, and prices it at \)2,000. To factor in the uncertainty and cost of discovering the truth, expected utility combines these scenarios:

• The utility if Molly buys the TV at \(2,000 is \ln(18,000)\.
• If she travels to Crazy Eddie's and the TV is available for \)1,700, her leftover income is \(18,200. Thus, \ln(18,200)\ is the utility.
• The journey cost of \)100 must be considered, as it reduces her available income to explore this cheaper option.
• With a 50% chance of either outcome, expected utility is calculated by weighing the utility of each with their respective probabilities.

This analysis will show Molly whether driving to Crazy Eddie's, despite the uncertainty and travel costs, will maximize her utility.

Consumer Choice

Consumer choice examines the decision-making process of individuals when they face various products at different prices, given a certain income. Molly's situation highlights this as she decides between definite and potentially beneficial choices with financial limitations.

Let's review Molly's decision points:

• If she idefinitely knew the TV would cost $2,000, she could instantly choose to buy it and know her income after the purchase would be $18,000.
• Alternatively, the possible $1,700 option depends on the uncertain offer from Crazy Eddie's.
• The choice involves evaluating known costs versus potential savings, balanced against her total budget and the additional expense or inconvenience of confirming the price at Crazy Eddie's.

Understanding consumer choice requires a balance between certainty and risk. Molly needs to evaluate the tangible benefits against hypothetical ones, while also considering her comfort level with uncertainty.

Price Uncertainty

Price uncertainty occurs when there's variability or lack of information about the future price of a good or service. In Molly's dilemma, price uncertainty is a major factor as she evaluates her purchase options.

Handling price uncertainty involves several steps Molly can take:

• Considering how the inability to confirm Crazy Eddie's lower price in advance affects her buying decision.
• Weighing the risk of spending extra money and time traveling to find out the truth.
• Recognizing that price uncertainty could result in either realizing a lower cost or just higher upfront costs without any savings.

Price uncertainty can challenge typical consumer decisions. In Molly's case, the lack of clear and confirmed pricing information forces her to rely on expected utility calculations and her risk tolerance, which ultimately guide her purchasing decision.