2. The effect of impatience on consumer choices Suppose the Super Bowl is this week, and Van is in need of a television to watch the big game. As a college student, Van knows that he can either buy his Flat-screen television at the local electronics store, or he 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 Van. Throughout the question, assume that Van pays for the good the day he buys it, so his wealth is affected in the initial time period no matter where he 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 there's no cost to gaining information about pricesin other words, he knows the best price online and in the store without having to search. Suppose Van receives a utility of 19.45 utils once he actually receives his television. Let 3 indicate Van's patience level; that is, ,8 represents the discount rate between consuming something today versus tomorrow. For each value of 3 in the following table, compute the present value of Van's utility from receiving the television when he purchases his television in the store (and receives it today) and when he purchases it online (and receives it three days from now). Present Value When . . . Where Purchased ,6 : 0.8 ,3 : 0-6 )9 Z 0'4 Store (received today) 19.45 utils V 19.45 utils V 19.45 utils 7 Online (received in three days) V v v If Van buys his television in the store, it costs $500; whereas if he buys it online, it costs only $370. Suppose the utility Van receives a5 a function of his wealth can be expressed in the following way: UM) : W\". If Van's level of wealth is $1,200 before purchasing a television, his utility from wealth will be V utils if he purchases his television in the store, or V utils if he purchases it online. Assume Van's total utility from purchasing a television is the sum of the present value of his utility from consumption and the utility from his remaining wealth. For each level of B, complete the following table with Van's total utility. Total Utility When . . . Where Purchased B = 0.8 B = 0.6 B = 0.4 Store Online From the previous analysis, you can conclude that as / increases, consumers become patient. This indicates that as B approaches one, consumers are more likely to purchase the good