380 L10-Slutsky

# 380 L10-Slutsky - The Slutsky-Equation and Various...

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The Slutsky-Equation and Various Elasticity Calculations R. Pope In Figure 5.3 of the text, a price change is decomposed into income and substitution effects. This turns out to be a very important exercise so stay with it. In the Figure the price of x falls. The original equilibrium is at x* and y*. As p x falls, the equilibrium consumption changes to x** and y**. Thus, x isn’t a Giffen good. As p x falls more of the good is consumed.

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The movement from x* to x** are two points on an ordinary demand curve. Now, decompose the movement from x* to x** into an income effect and a substitution effect. The substitution effect lets price change but keeps a person’s real income constant. Here real income constant means that one is on the same indifference curve. It can be thought of as the following: if p x falls, real income has gone up. Let the new price of x prevail but take away enough income so that the individual is on the same indifference curve. That level of income is shown as a dotted line in Figure 5.3. What would the person consume in such an experiment: B in Figure 5.3 were the new budget (price ) line is tangent to the original indifference curve. x B is a point on the compensated demand curve x c (p x ,p y ,U) that we have seen before. It is not yet shown on the graph but we can p x x(p x ,p y ,I) p x 2 p x 1 x* x B x**
locate x B (really 2 ( , , ) c x y x p p U ) in between x* and x**. Thus, as the substitution effect is always non-positive as one slides along an indifference curve (what case is it zero?). It reflects a person’s desire to substitute towards (away from) the good whose price has fallen (risen). The movement from x B to x** is the income effect because prices don’t change as one moves from B to the tangency on the outer budget line. You can think of this income effect as: what would the person do with the increase in income at the new price? Consumption would move from x B to x**. The income effect is positive (reinforcing moving in the same direction as income) if the good is normal. If the good is inferior, a rise in income will reduce consumption. Thus the total or ordinary or Marshallian effect of a price change can be decomposed as follows: Substitution Effect-x* to x B Negative-moving opposite the price change. + Income Effect- x B to x** Can be negative (inferior) or positive (normal) ___________________ =Total Effect Result 1: Substitution Effect + Income Effect= Total Effect - + or - + or – (+ consistent with Law of Demand) This result can be developed with calculus as follows. Consider the relationship between the compensated that the ordinary demand curve. At x*, they are equal: , *( , , ) *( , ) x y x y x p p U x p p I = but as soon as p

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## This note was uploaded on 04/07/2011 for the course ECON 380 taught by Professor Showalter,m during the Winter '08 term at BYU.

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380 L10-Slutsky - The Slutsky-Equation and Various...

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