# HW5_sol - Intermediate Microeconomics 2008 Problem Set No 5...

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Intermediate Microeconomics, 2008 Problem Set No 5: Solutions Problems (4.7) During his first year at school, Ximing buys eight new college textbooks at a cost of \$ 50 each. Used books cost \$ 30 each. When the bookstore announces a 20% price increase in new texts and a 10% increase in used texts for the next year, Ximing’s father offers him \$ 80 extra. Is Ximing better off, the same, or worse off after the price change? Why? See the figure below. He will either be better off or could be the same as before. The combination of the new prices and increased income moves Ximing to a larger budget set. He can still purchase his old bundle of 8 new books, but could purchase other bundles that were unaffordable before. (4.11) Illustrate that the Paasche cost-of-living index (see application “Fixing the CPI Substitution Bias”) underestimates the rate of inflation when compared to the true cost-of-living index. See the figure below. A change in the true cost-of-living index measures the change in total price levels, incorporating the substitution effect. An equivalent way to think about this is as a change in income. In other words, having all prices go up by 1% has the same effect as having your income shrink by 1%. So suppose that the price of good 2 increases. We can think of the change in the true cost-of-living-index as the equivalent decrease in wealth that is if wealth dropped instead of p 2 increasing, how much wealth would have to drop in order to make us indifferent between the two events. In the figure, because the price increase moves the consumer from e 0 to e 1 , the equivalent wealth drop would be from the original budget line to the one parallel to it going through point e 2 . This drop is the change in the true cost-of-living index. Now the Paasche index says that the equivalent wealth drop is the one that would allow us to still buy the new bundle e 1 at the old prices . This wealth drop is strictly smaller than the wealth drop in the true cost-of-living index. 1

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(4.15) The local swimming pool charges nonmembers \$ 10 per visit. If you join the pool, you can swim for \$ 5 per visit, but you have to pay an annual fee of F . Use an indifference curve diagram to find the value of F such that you are indifferent between joining and not joining. Suppose that the pool charged you exactly F . Would you go to the pool more or fewer times than if you did not join? For simplicity, assume that the price of all other goods is \$ 1. See the figure below. Assume the budget is \$100. Compare e 1 and e 2 . We know that you would go to the pool fewer times if you did not purchase the membership. 2
(4.16) In Solved Problem 4.5, suppose that French meals are relatively more expensive than Amer- ican meals in Paris, so the L F budget line cuts the L A budget line from below rather than from above as in the solved problem’s figure. Show that the conclusion that Alexx is better off after his move still holds. Explain the logic behind the following statement: “The analysis holds as long as the relative prices differ in the two cities. Whether both prices, one price, or neither price in Paris

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