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CAS EC 201. Intermediate Microeconomic Analysis. Problem set 6 (due on Thursday March 19, 2020) 1. This problem set explores the connection between preferences and utility. Suppose a person has the utility function over two goods given by U(x1, x2) = min{2x1 + x2, x1 + 2x2}. Show that this person’s preferences are complete, transitive, continuous, monotonic and convex (a graph will do for the latter). 2. We now use the idea of revealed preference to consider some of the issues that arise in evaluating the effects of inflation. To keep things simple, we first work with the case of two goods, and hence a person who maximizes the function U(x1, x2) subject to the budget constraint p1x1 + p2x2 = M . Our measure of “better off” and “worse off” will be “higher utility” and “lower utility”. 2.1 First, suppose that p1 and p2 both decrease, while M stays constant. Explain why this makes the person better off. Our setting is so simple that this is obvious. The trick is to use ideas from the theory of revealed preference to make your explanation precise. This may seem redundant here, but can be useful in more complicated settings. 2.2 Suppose instead that both prices increase and, as is typically the case, the person’s income increases as well. The person’s original consumption bundle was (15, 4) and the new consumption bundle is (10, 10). Under what circumstances does revealed-preference theory assure us that the person is now worse off? How about better off? In light of this, suppose we encounter a person who tells us that “each year I find that I can no longer afford the things I used to buy last year.” Does this tell us the person is becoming progressively worse off? Why or why not? 2.3 Now consider two years, the “base year” and the “target year.” Suppose that in the base year we have prices (pb1, p b 2). Then the price of good one increases, or pt1 > p b 1 and the price of good two decreases, or p t 2 < p b 2. we would like to find an index that allows us to say either “prices are higher” (i.e., there has been inflation) or “prices are lower” (i.e., the has been deflation). an analyst proposes looking at the price index p1 + p2. give an example of base-year and target year prices such that the price index has decreased if good two is measured in pounds, and increased if good two is measured in tons. in response to the difficulty described in 2.3, it is common to compare weighted price averages, where the weights are the quantities of the various goods consumed. measur- ing inflation is important because many aspects of our economy, such as social security payments, retirement plans, wage contracts, and financial instruments are linked to inflations indices. 1 3. over a three-year period, an individual exhibits the following consumption behavior p1 p2 x1 x2 year 1 3 3 7 4 year 2 4 2 6 6 year 3 5 1 7 3 is this behavior consistent with the weak axiom of revealed preference? 2 p="" b="" 2.="" we="" would="" like="" to="" find="" an="" index="" that="" allows="" us="" to="" say="" either="" “prices="" are="" higher”="" (i.e.,="" there="" has="" been="" inflation)="" or="" “prices="" are="" lower”="" (i.e.,="" the="" has="" been="" deflation).="" an="" analyst="" proposes="" looking="" at="" the="" price="" index="" p1="" +="" p2.="" give="" an="" example="" of="" base-year="" and="" target="" year="" prices="" such="" that="" the="" price="" index="" has="" decreased="" if="" good="" two="" is="" measured="" in="" pounds,="" and="" increased="" if="" good="" two="" is="" measured="" in="" tons.="" in="" response="" to="" the="" difficulty="" described="" in="" 2.3,="" it="" is="" common="" to="" compare="" weighted="" price="" averages,="" where="" the="" weights="" are="" the="" quantities="" of="" the="" various="" goods="" consumed.="" measur-="" ing="" inflation="" is="" important="" because="" many="" aspects="" of="" our="" economy,="" such="" as="" social="" security="" payments,="" retirement="" plans,="" wage="" contracts,="" and="" financial="" instruments="" are="" linked="" to="" inflations="" indices.="" 1="" 3.="" over="" a="" three-year="" period,="" an="" individual="" exhibits="" the="" following="" consumption="" behavior="" p1="" p2="" x1="" x2="" year="" 1="" 3="" 3="" 7="" 4="" year="" 2="" 4="" 2="" 6="" 6="" year="" 3="" 5="" 1="" 7="" 3="" is="" this="" behavior="" consistent="" with="" the="" weak="" axiom="" of="" revealed="" preference?="">