Slutsky Equation

Slutsky Equation - Economics 21 Intermediate Microeconomics...

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Economics 21: Intermediate Microeconomics Topic 2: Consumer Theory - The Slutsky Equation Economics 21: Intermediate Microeconomics Topic 2: Consumer Theory The Slutsky Equation Reference: Varian, Chapter 8 Outline: I. Introduction II. Slutsky Equation III. The Total Change in Demand IV. Example – Calculating Income and Substitution Effects V. Rates of Change VI. Deriving the Slutsky Equation by Calculus I. Introduction We have seen that a change in price exerts both an income effect and a substitution effect and that these may work with each other, as in the case of Normal goods, or against each other, as in the case of Inferior and Giffen goods. We now examine these effects more formally via the Slutsky Equation II. Slutsky Equation Consider Figure 1 following: Figure 1: Sltutsky Compensating Variation (Price Fall)
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Economics 21: Intermediate Microeconomics Topic 2: Consumer Theory - The Slutsky Equation Thus in Figure 1 we have a fall in the price of good 1 from p 1 to ! p 1 < p 1 , a pivot outwards of the budget line and a change in the consumer’s optimal bundle from A to B. The fall in the price of good 1 has impacted on the consumer in two ways: First, there is the substitution effect whereby the fall in the economic rate of substitution (ERS) between the two goods means that the consumer does not have to sacrifice as many units of good 2 for additional units of good 1. Second, there is an income effect whereby the fall in the price of good 1 changes leads to an increase in the purchasing power (i.e. real income) of the consumer. In terms of Figure 1, we measure the substitution effect from A-B and the income effect from B-C. Under the Slutsky decomposton, the substitution effect is found by adjusting the consumer’s income following the price change such that the consumer’s original consumption n bundle is affordable. Thus, if the price of a good falls we have to reduce money income and vice versa. By how much do we need to adjust money income? Let ! m denote the amount of money income that will make the original consumption bundle affordable at the new price of good 1 vis : ! p 1 x 1 + p 2 x 2 = ! m (1) Since x = x 1 , x 2 ( ) is affordable at both p 1 , p 2 , m ( ) and ! p 1 , p 2 , ! m ( ) , then we also have: p 1 x 1 + p 2 x 2 = m (2) Subtracting (2) from (1) implies: ! m " m ( ) = x 1 ! p 1 " p 1 ( ) # $ m = x 1 $ p 1 (3) where ! m = " m # m and ! p 1 = " p 1 # p 1 . Note that the change in income and the change in price will always move in the same direction. For example, if the consumer is originally consuming 5 units of good 1, and the price of good 1 rises by $2 per unit, then money income must be increases by 5*£2 = $10 for the consumer to be able to continue consuming his original bundle (i.e. the price of good 2 has not changed). The Substitution Effect
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This note was uploaded on 07/16/2010 for the course ECON 21 taught by Professor Johng.sessions during the Summer '09 term at Dartmouth.

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Slutsky Equation - Economics 21 Intermediate Microeconomics...

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