# The slutsky decomposition is an analytical tool that

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The Slutsky decomposition is an analytical tool that allows us to understandhow demand changes when a price changes. It does this by breaking the totalchange in demand up into smaller pieces. The sign of the overall effect dependson the sign of the pieces, but the sign of the pieces is easier to determine.I have used the Slutsky definition of substitution effect in this chapter. This isbecause it is much easier to compute examples using this definition. The Hicksiandefinition is theoretically more elegant, but students can’t compute with it untilthey have more advanced mathematical tools.A large part of getting this material across is just convincing the students toread the book. The change in income necessary to compensate for a change inprice is neither a difficult concept nor a difficult calculation, but it has to berepeated a few times before the students grasp it.One way to describe income and substitution effects is to give an examplebased on their own consumption patterns. Talk about a student who spends all of
21her allowance on food and books. Suppose that the price of books drops in half,but her parents find out about it and cut her allowance. How much do they cuther allowance if they want her to keep her old consumption level affordable?Once they grasp the idea of the substitution and income effect, it isn’t hard toput them together in Section 8.4. The next real hurdle is expressing the Slutskyequation in terms of rates of change, as is done in Section 8.5. This is the way thatwe usually refer to the Slutsky equation in later chapters, so it is worthwhilegoing through the algebra so they can see where it comes from. However, if youdon’t want to go through the algebraic computations, just make sure that they getthe basic point: the change in demand can be decomposed into a substitutioneffect (always negative, i.e., opposite the direction of price change) and an incomeeffect (positive or negative depending on whether we have a normal or inferiorgood).I usually skip the Optional sections in this chapter, but they are there forreference if needed. I like the tax rebate section, but it is a little sophisticated.Emphasize the idea that even if you give the money from the tax back to theconsumers, the demand for the good will go down and consumers will be leftworse off.Slutsky EquationA.We want a way to decompose the effect of a price change into “simpler”pieces.1.that’s whatanalysisis all about2.break up into simple pieces to determine behavior of wholeB.Break up price change into apivotand ashift— see Figure 8.2.1.these are hypothetical changes2.we can examine each change in isolation and look at sum of two changesC.Change in demand due to pivot is thesubstitution effect.

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