2. The effect of impatience on consumer choices

Suppose the Super Bowl is this week, and Rosa is in need of a television to watch the big game. As a college student, Rosa knows that she can either buy her flat-screen television at the local electronics store, or she can shop online for a better deal but have to wait three days for the television to arrive. The following problem uses the economic concept of rate of time preference to help determine which decision is better for Rosa. Throughout the question, assume that Rosa pays for the good the day she buys it, so her wealth is affected in the initial time period no matter where she buys the good. Also, assume the shipping cost and cost to travel to the store are incorporated into their respective given prices. Finally, assume the goods are identical, and theres no cost to gaining information about pricesin other words, she knows the best price online and in the store without having to search.

Suppose Rosa receives a utility of 29.46 utils once she actually receives her television. Let indicate Rosas patience level; that is, represents the discount rate between consuming something today versus tomorrow.

For each value of in the following table, compute the present value of Rosas utility from receiving the television when she purchases her television in the store (and receives it today) and when she purchases it online (and receives it three days from now).

Where Purchased	Present Value When . . .
	=0.9=0.9	=0.5=0.5	=0.3=0.3
Store (received today)
Online (received in three days)

If Rosa buys her television in the store, it costs $500; whereas if she buys it online, it costs only $400. Suppose the utility Rosa receives as a function of her wealth can be expressed in the following way: U(W)=W0.7U(W)=W0.7. If Rosas level of wealth is $1,200 before purchasing a television, her utility from wealth will be utils if she purchases her television in the store, or utils if she purchases it online.

Assume Rosas total utility from purchasing a television is the sum of the present value of her utility from consumption and the utility from her remaining wealth.

For each level of , complete the following table with Rosas total utility.

Where Purchased	Total Utility When . . .
	=0.9=0.9	=0.5=0.5	=0.3=0.3
Store
Online

From the previous analysis, you can conclude that as increases, consumers become patient. This indicates that as approaches one, consumers are more likely to purchase the good .