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Lecture7 - LECTURE 7 The Slutsky Equation(continued E...

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LECTURE 7 E. Giffen Goods as a (Very) Special Case The Slutsky Equation (continued) If good X is SO inferior that its income effect more than offsets the (opposite) substitution effect then the total effect is positively related to the price change (price and quantity move in the same directions) and demand will be upward sloping This scenario is the very special case of a Giffen Good In empirical . This scenario is the very special case of a Giffen Good. In empirical studies, researchers have found little or no evidence that Giffen Goods exist in reality. They are presented as a theoretical construct in this course for completeness. Let’s see how this decomposition works using our graphing analysis analysis.
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The Slutsky Equation (continued) E. Giffen Goods as a (Very) Special Case When we decompose the partial effect of a fall in P X , we want to account for the change due to the new relative prices (SE). This is the move from A to B (similar to our prior analysis) Y M / P Y (similar to our prior analysis). However, for a Giffen good, the income effect (from B to C) is negative and strong enough to “more than offset” the SE (from A to B). Therefore, the TE (A to C) no M ! / P Y C the SE (from A to B). Therefore, the TE (A to C) no longer displays the negative relationship between P X and X (resulting in an upward sloping demand curve). A B Pivot Shift X BL O IE BL C SE TE BL F
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The Slutsky Equation (continued) P X d In terms of demand curves, since consumption of X d d lt f d i P th TE i E. Giffen Goods as a (Very) Special Case A C - - decreased as a result of a decrease in P X , the TE in this very special example is positively related to a change in price for an inferior good and the corresponding demand curve is upward sloping (Giffen G d) X P X ! " X ! X is inferior and IE is stronger Good). The necessary and sufficient condition for a good to have an upward sloping demand is that the good must b i f i th t th IE th ff t th SE be so inferior that the IE more than offsets the SE. Since Giffen Goods almost never exist in reality, we can safely conclude that the “Law of Demand” holds in most (all?) cases…where the Law of Demand refers to the “law” that demand curves are downward sloping. So…now that we know how all of this works theoretically, let’s calculate a practical example. First, though, we need to set up the logic of the problem and work through it step by step…
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The Slutsky Equation (continued) F Problem Logic and Sample Solution So, in order to determine the substitution effect we need to use the consumer’s demand function to calculate the optimal choices at the new price and compensated income, denoted X(P ! X , I ! ) and the consumer demand at the original F. point, denoted X(P X , I). So the change in X due to the substitution effect is: # X s = X(P $ X , I $ ) - X(P X , I) The change in demand for X may be large or small, depending on the shape of the consumer’s indifference curves. But given the demand function, it is straight forward to plug in the numbers and calculate the substitution effect (holding P Y constant).
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