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Notes-08_Slutsky Equation-2

Notes-08_Slutsky Equation-2 - Econ 3130 Spring 2012 R...

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Econ 3130, Spring 2012, R. Masson Chapter 8: p. 1 Chapter 8: Slutsky Equation I. Again my biases A. It is crucial to know the income and substitution effects, which are captured in this relationship 1. The important material in my opinion is conceptual and can be conveyed via graphical analysis 2. It is not important for my 3130 to know the math: The Equation itself is not required a. What the equation adds to intuition is simply that it pertains to n-space and in the limit, as ± p < 0 two concepts (Hicksian and Slutsky) converge. B. This material, especially in Varian with more math, is in my opinion one of the harder chapters in the course, especially if one emphasizes the Equation, which I will not do. II. Conceptual Basis of Income and Substitution Effects and the Interpretation A. Think of M=y+px and utility maximization (choice and indifference curves). 1. The conceptual issues here are complex and will need quite a bit of explanation before illustrating with indifference curves B. Suppose the price of x is p 0 and now lower it to p 1 1. Note, I will be talking about signs of changes from lowering a price, I will not always remember to remind you that I am modeling a lowering of the price of x 2. We can decompose the effects of this price decrease into what we will call an income effect and a substitution effect a. We say that the “ Total Effect ” is the sum of two hypothetical effects, an income effect and a substitution effect (1) Subtle English here, to be dropped shortly. An income effect because there are two definition of an income effect, one by Slutsky and the other by Hicks.
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Econ 3130, Spring 2012, R. Masson Chapter 8: p. 2 Ditto a substitution effect because of two definitions. (2) That subtle English being said I will follow most texts and refer to the income effect and the substitution effect. One simply must be careful to let one know, for example, when you mean the Slutsky income effect or the Hickian income effect (ditto for substitution effects) b. An income effect is related to what happens to both x and y as income, M, is changed (1) The income effect, however, generally stands for an effect on x (2) E.g., looking at two points on an Income Consumption Curve, ICC and projecting the change to the horizontal axis (3) In the context of this chapter it is a hypothetical income change, as will become obvious later c. The substitution effect is a pure price effect, holding either the initial commodity bundle constant (Slutsky) or the initial utility level constant (Hicks) (1) Math majors may wish to note that in the limit as ± p ± 0, these effect on {x,y} converge (2) The Slutsky substitution effect, holding the initial commodity bundle constant (a) Pivot the budget line through the pre price change commodity bundle and find out the change in x (and y) as if the consumer were just able to afford his/her initial commodity bundle but at the new price (or prices) (b) This relates to the Chapter 7 material on revealed preference, when thinking about revealed preference, the Slutsky substitution effect is more
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