v UNDERSTANDING RATE OF TIME PREFERENCE, BY THE APLIA ECONOMICS CONTENT TEAM 8 Amazontcom's success over the last two decades has allowed the online shopping venue to continue to offer low-cost baby products sewing parents around the country As a mother of a one-yearold child, Amy sometimes nds herself in an interesting economic predicament when it comes to buying time-sensitive items, such as diapers. Although she knows that she can purchase them for a lower price online, this doesn't help her when she unexpectedly runs out of diapers and needs some today. In this situation, her only option is buying them locally, where she inevitably pays a premium because of her immediate need for diapers. You've probably experienced having to pay more to get something sooner. This Is related to the nancial fact that a dollar today Isn't worth the same amount as a dollar tomorrow. The Intuition behind this Is simple: 31 could be put In the bank today, where It earns Interest and is worth 31 x (1 + r) tomorrow. in financial context, the term r represents the Interest rate, which determines how much a present value will be worth In the future (the future value), as well as the present value of a future payment (the discounted value), From the previous example, you can calculate the future value (FV) of a present value (PV) earning interest at rate r in n periods in the following way: Future Valuz = Present Value x (l + r)\" Rearranging terms leads to the formula for the present value: Present Value = WIMW'VRM in other words, 11;, represents the discount rate of a future payment in one period (n = 1), telling you how much less a given amount is worth today compared to the future. Notice that because r is usually assumed to he a positive number, the discount rate rfalls between 0 and 1. Therefore, at an annual interest late of 11% (0.11), the discount rate ls equal to 'mf 0.9, meaning that a dollar a year from new is worth 50-90 today. How does this relate to the value of consuming something (such as diapers) today as opposed to tomorrow? Economists assert that consumers value things not only based on the interest rate, but also on their rate of time preference, typically modeled using 5. Like the discount rate, I9 falls in the interval (0, 1), but instead of indicating the monetary opportunity cost of spending a dollar today versus tomorrow, 5 reflects people's impatience. An individual with a I? close to 1 receives nearly the same discounted utility whether he or she consumes the good today or in the future; economists would dene this consumer as very patient, whereas an individual with a 5 close to zero is very impatient. Therefore, you can use [1 to discount the future value of consuming a good in the same way that you could use rm discount a future value of a monetary payment. This notion of consumers' late of time preference allows economists to compare the value of consuming something today versus tomorrow, which plays heavily into consumers' decision making about purchasing online or in the store Everyone knows of the success stories of online stores, such as Amazon.com, over the last two decades. For example, In just one year Amazon's net sales grew 22.6% to $35.7 billion in the rst quarter of 2017, duein large partto its competitive prices and tworday Prime free shipping. (Source: Spencer Soper, \"Amazon Extends Double-Digit Sales-Growth Streak," Seattle 17mes, April 27, 2017.) So given the existence of online shopping, how do brickrand-mortar stores survive when their prices are usually higher? In light of these principles, one possible explanation is that there Is an impatience distribution among consumersmeaning that some consumers are willing to pay a higher price to receive the good now (lower 17), whereas other consumers are patient and willing to wait (higher ). Therefore, despite knowing that diapers are d1eaper on Amazon.com, Amy's local grocery store can get away with charging her a higher price because she cannot wait for them to arrive In the mall. Suppose the annual interest late is r = .07. If you earn $40,000 next year, what is the approximate present value of this future income? $43,011 $42,800 $37,383 $571