Problem_Set_10_Answers

Problem_Set_10_Answers - 280 CHAPTER 10 APPLICATIONS OF...

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280 CHAPTER 10. APPLICATIONS OF CONSUMER DEMAND Answers to Problems on Applications of Consumer Demand. Answer to Problem 10.1. It is well-known that bottles of wine that cost about $30 or more each are almost always purchased by relatively rich people. Poor people almost never purchase expensive wine. Think of two people with the same preferences. One person is rich. The other person is poor. Use the theory of rational choice to explain why the rich person demands a positive quantity of expensive wine while the poor person demands no expensive wine. You should think also of another commodity that you can call “Other Stuff”, representing things like food, electricity, clothing and so on. Answer. The rich person purchases both other stuff and wine, and is rational so the extra utility that the rich person obtains from the last dollar he spends on expensive wine must be the same as the extra utility that he obtains from the last dollar he spends on other stuff. That is, MU Rich OS p OS = MU Rich Wine p Wine where p OS and p Wine denote the per unit prices of other stuff and expensive wine. The poor person is also rational but does not allocate even one dollar to buying expensive wine. What does this imply? It must mean that the poor person’s extra utility from his last dollar spent on other stuff is strictly greater than the extra utility that he would obtain from spending even one dollar on expensive wine. If this were not so, then a rational person would buy some wine (right?). So MU Poor OS p OS > MU Poor Wine p Wine . Comparing these two equations shows us that MU Rich OS < MU Poor OS . That is, the reason that the rich person choose to buy some expensive wine is that he can afford so much other stuff that the marginal utility per extra dollar spent on other stuff has declined to the point where it is no longer strictly greater than the marginal utility per extra dollar spent on expensive wine. Expensive wine is purchased only because the rich person has enough money to buy a quantity of other stuff that is large enough to make the additional utility from another unit of other stuff small. The poor person cannot afford so much other stuff and consequently the marginal utility of another unit of other stuff remains high enough to make it rational to buy only other stuff. Answer to Problem 10.2. In the Second World War there was rationing of gasoline.
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