lecture05_slides

lecture05_slides - Econ 121. Intermediate Microeconomics....

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Unformatted text preview: Econ 121. Intermediate Microeconomics. Eduardo Faingold Yale University Lecture 5 Outline of the course I. Introduction II. Individual choice III. Competitive markets IV. Market failure Outline of the course I. Introduction II. Individual choice       Budget constraint (Ch. 2) Preferences (Ch. 3) Utility (Ch. 4) Consumer problem (Ch. 5) Revealed Preference (Ch. 7) Slutsky Equation (Ch. 8) III. Competitive markets IV. Market failure Slutsky Equation  We want a way to decompose the effect of a price change into “simpler” pieces  Break up price change into a rotation and a shift  These are hypothetical changes  We can examine each change in isolation and look at the sum of two changes Substitution Effect  Change in demand due to rotation is the substitution effect  This measures how demand changes when we change prices, keeping the original optimal bundle affordable  this isolates the pure effect of change in relative prices  substitution effect must be negative, by revealed preference  the other effect is called income effect  the total effect is the sum of these two effects Income Effect  Change in demand due to shift is the income effect  Increase income, keep prices fixed  Income effect can increase or decrease demand depending on whether we have a normal or inferior good   Let x1 .p1; p2; m/ be the optimal consumption of good 1 at prices .p1; p2/ and income m    Normal good: @x1 =@m > 0; Inferior good: @x1 =@m < 0. Total Effect  Total change in demand is substitution effect plus the income effect  if good is a normal good, the substitution effect and the income effect reinforce each other  if good is an inferior good, the substitution effect and the income effect go in opposite directions; total effect is ambiguous  when total effect is positive, good is called a Giffen good x2 EFFECT OF A PRICE INCREASE Initial budget line Final budget line x1 x2 EFFECT OF A PRICE INCREASE Initial Final x1 x2 EFFECT OF A PRICE INCREASE Initial Final x1 x2 EFFECT OF A PRICE INCREASE Initial Final Income-adjusted (hypothetical) x1 x2 WHERE MUST BE LOCATED? Initial Final Income-adjusted (hypothetical) x1 x2 WHERE MUST BE LOCATED? Initial Final Income-adjusted (hypothetical) IS THIS COMPATIBLE WITH REVEALED PREFERENCE? x1 x2 WHERE MUST BE LOCATED? Initial Final Income-adjusted (hypothetical) IS THIS COMPATIBLE WITH REVEALED PREFERENCE? NO!!! x1 x2 WHERE MUST BE LOCATED? Initial Final Income-adjusted SOMEWHERE OVER HERE (hypothetical) x1 x2 INFERIOR GOOD: IE < 0 TWO POSSIBLE CASES Initial Final Income-adjusted NORMAL GOOD: IE > 0 (hypothetical) x1 x2 CONSIDER INDIFFERENCE CURVES NOW INCOMPATIBLE WITH R.P. Initial Final OK Income-adjusted (hypothetical) x1 x2 EFFECT OF A PRICE INCREASE (NORMAL GOOD) Initial Final Income-adjusted (hypothetical) I.E. S.E. x1 x2 EFFECT OF A PRICE INCREASE (INFERIOR GOOD) Initial Final Income-adjusted (hypothetical) I.E. S.E. x1 Law of Demand For a normal good, a price increase always results in a decreased demand. That is, normal goods have a downward sloping demand. Examples  perfect complements: no substitution effect  perfect substitutes: no income effect  quasilinear: no income effect Rates of change  can also express Slutsky effect in terms of rates of change  takes the form: s   @x1 @x1 @x1   .p1; p2; m/ D .p1; p2; x1 .p1; p2; m// .p1; p2; m/x1 .p1; p2; m/ @p1 @p1 @m where the function x s .p1; p2; x/ is such that for each vector of prices .p1; p2/ and each bundle x ,  s x1 .p1; p2; x/ D x1 .p1; p2; p1x1 C p2x2/; s i.e. x1 .p1; p2; x/ is the optimal consumption bundle given the budget line that has slope p1=p2 and passes through bundle x .  can interpret each part as before x2 SLUTSKY EQUATION: NORMAL GOOD Initial Price increase Final x1 x2 SLUTSKY EQUATION: NORMAL GOOD Initial Final x1 x2 SLUTSKY EQUATION: NORMAL GOOD Initial Final Income-adjusted (hypothetical) x1 SLUTSKY EQUATION: x2 NORMAL GOOD Initial Final Income-adjusted (hypothetical) x1 S.E . I.E. ...
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