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Unformatted text preview: International TradeAppendix 1 Erzo G.J. Luttmer Department of Economics University of Minnesota Spring 2011 1. Introduction This appendix is a crash course on the topics of utility maximization and price indices. In much of international economics, it is useful to assume that consumers have the same preferences everywhere, and that these preferences are homothetic. This simply means that indi f erence curves have the same slope everywhere along a given ray through the origin. Homotheticity implies that aggregate demand curves do not depend on the distri- bution of income among consumers who face the same prices. This is a very useful property. It means that instead of keeping track of millions of consumers with a great variety of incomes, one can consider a single consumer who earns the aggregate income of all these consumers. This aggregation property will be used in many places. It is not always essential, but it certainly tends to sharpen conclusions and simplify proofs. A related implication of homotheticity is that one can use a single price index that applies to everyone. More speci f cally, suppose we hold incomes f xed and change prices from to . Typically, such price changes will make consumers better or worse o f . One can then ask: by how much do we need to scale up or down a particular consumers income to ensure that this consumers utility does not change as a result of the change in prices from to ? Even if everyone has the same preferences, the answer to this question typically depends on the income level of the consumer. But this is not the case if preferences are homothetic. Because relative prices di f er across countries, price indices are needed if we want to make welfare comparisons across countries. Chinese GDP for 2010 is estimated to be about 42 trillion yuan. The dollar-yuan exchange rate is about 7 yuan per dollar, and so this translates into 6 trillion dollars. The Chinese population is about 1.3 billion, and thus per-capita GDP is about 6,000 1 3 4,615 dollars. US GDP for 2010 is estimated to be about 14.6 trillion, or about 14,600 3 48,667 dollars per capita. How should we compare these numbers? One is tempted to conclude that the average Chinese consumer is equally well o f as a 1 US consumer who earns only about a tenth of the average US consumer. But the average Chinese consumer faces di f erent prices than the average US consumer. For example, if everything in China costs only 10% of what it costs in the US, then it would be the case that a Chinese consumer earning 4,615 dollars can buy the exact same set of goods as a US consumer earning 46,150 dollars. Now, it is certainly not true that everything in China costs only 10% of what it costs in the US. But it is true that there are many goods that are cheaper in China than they are in the US. There are also many goods that cost about the same as they do in the US, and goods that are more expensive. This means that Chinese consumers face diand goods that are more expensive....
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