2003%5Csummary4_03

2003%5Csummary4_03 - ECON 371 2003 SUMMARY#4 COMPARATIVE...

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ECON 371 2003 SUMMARY #4 COMPARATIVE STATICS: PROPERTIES OF CONSUMER DEMAND We are now ready to investigate what sort of implications the model we have discussed has on demand behaviour. We have already seen that the (Marshallian) demand functions are homogeneous of degree zero (so that only relative prices and real income matter), and that all income is spent. We want to see if we can obtain further predictions about the way demand might respond to changes in income and prices. As we have seen, the demand for any good, in general, depends on the prices of all the goods and income of the consumer; which we express by writing the demand functions as functions of all prices and income . There are three questions we might typically ask: (a) How does the demand for a good change when its price changes, holding fixed all the other prices and income? (b) How does the demand for a good change with changes in the price of some other good, holding fixed all the other prices and income? (c) How does the demand for a good change with changes in income, hold- ing the prices fixed? That is, what are the own-price, cross-price, and income effects? Can we determine what they are? The examination of a change in outcome in response to a change in under- lying economic parameters is known as comparative statics analysis. “Com- parative” means that we want to compare two situations: before and after the change in the economic environment. “Statics” means that we are not concerned with any adjustment process that may be involved in moving from one choice to another; rather we will only compare the outcomes (choices). 1 The Effects of Changes in Income The effects of a change in income can easily be investigated by simple graphs involving two commodities. Consider the locus of consumption bundles ob- tained as income is varied. (Income expansion path.) Even in this simple world it is easy to show that demand for a good might increase or decrease as income increases. We can, therefore, conclude with no further mathematical 1
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analysis that the consumption of a commodity may increase or decrease when income increases. We say that a commodity is a normal good if demand and income move in the same direction (so that an increase (decrease) in income causes an increase (decrease) in demand). If demand and income move in opposite directions, the commodity is called an inferior good . 1 For differentiable demand functions, the partial derivative of the demand function with respect to income represents the rate of change in the consump- tion of that good with respect to a change in income. Thus, our conclusion is that ∂x i ( p , I ) ∂I = > 0 , if i is a normal good; < 0 , if i is an inferior good. 2 The Effects of Changes in Prices You should be familiar with the intuition about how a price change affects demand from your discussions in ECON 201. For example, when the price of a good declines, there are at least two conceptually separate reasons why we expect some change in quantity demanded. First, that good becomes rela- tively cheaper compared to the other goods. We would expect the consumer
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