Question

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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 U21,22) subject to the budget constraint pıtı + P202 = M. Our measure of "better off" and "worse off" will be "higher utility" and "lower utility". 2.1 First, suppose that Pı 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 ( pp). Then the price of good one increases, or p > pl and the price of good two decreases, or p < P. 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 pı + 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.

Answer 1

2.1 Under the Revealed Preference theorem there are many assumptions -one being that the more quantity the consumer consumes of both goods x and y the better off he will be.And as mentioned that if the prices P₁ and P₂ both decrease as income(M) remains constant or unchanged, meaning now the consumer can purchase more quantities of both good x and y and get a higher level of satisfaction(Utility) hence making the consumer better off.

2.2 The consumer is worse off because even though the price of the 2 goods has decreased and the income has increased, he doesn't purchase in the same proportion, he reduces his consumption of good x₁ and increases his consumption of good x_2, which goes against the revealed preference theory.If the person cannot afford those goods which he could afford last year,means that the real value of money has decreased dude to inflation, with the same income level he cannot afford what he could the previous year.