Lecture 10 handout - Substitutes Complements and Slutsky Equation

# Lecture 10 handout - Substitutes Complements and Slutsky Equation

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1 Substitutes and Complements Two goods are substitutes if each separately ful fi lls the same desired purpose. The more substitutable are two goods, the closer to linear are the indi ff erence curves. That is, the MRS does not change much as you move along the indif- ference curve. (The extreme case is perfect substitutes.) Two goods are complements if they jointly ful fi ll a single desired purpose. The more complementary are two goods, the curvier the indi ff erence curves; intuitively, since the two goods jointly serve the same goal, mixing them is very advantageous. That is, the MRS diminishes rapidly as you move along the indi ff erence curve. (The extreme case is perfect complements.) The above de fi nitions are somewhat vague because di ff erent (precise) de fi n- itions are useful in di ff erent contexts. Here is one set of precise de fi nitions that is useful in the context of consumer demand: Good 1 is a gross substitute for Good 2 if 1  2 0 . Good 1 is a gross complement for Good 2 if 1  2 0 . 2 The Slutsky Equation Suppose a consumer with income and facing prices 1 and 2 has the (optimal) consumption bundle ( 1 2 ) . Now suppose the price of Good 1 increases from 1 to 0 1 . We can see graphically that such a price increase of Good 1 can either increase or decrease quantity demanded for Good 1. Slutsky’s insight is that we

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