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5 Revealed preferences and price indices We consider some issues relating to the evaluation of price changes. Recall that, in a twogood setting, a consumer is modeled to maximize the utiity function U(:z:1,:1:2) subject to the budget constraint [015151 + [02:152. ln the following, the notion, \"better off\" is the same as \"higher utility\" and \"worse off\" is the same as \"lower utility\". 5.1 Suppose that both prices increase and the consumer's income increases as well. The consumper's original consumption bundle was, say, (20,20) and the new consumption bundle is (32, 8). Under what cases does revealedpreference the ory tell us that the consumer is now worse off? How about being better off? Suppose we have a consumer who tells us that \"each year I nd that I can no longer afford the things I used to buy last year.\" Does this tell us the consumer is becoming worse off? Explain. 5.2 Now consider two years, the \"base year\" and the \"target year.\" Suppose that in the base year we have prices (papa). Then the price of good 1 increases to 193 > pi, and the price of good 2 decreases to 3932