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Unformatted text preview: Econ 121. Intermediate Microeconomics. Eduardo Faingold Yale University Lecture 4 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) III. Competitive markets IV. Market failure Revealed Preference
up until now we've started with preference and then described behavior revealed preference is "working backwards" - start with behavior and describe preferences recovering preferences - how to use observed choices to "estimate" the indifference curves Basic idea
if .x1; x2/ is chosen when .y1; y2/ is affordable, then we know that .x1; x2/ is at least as good as .y1; y2/ in equations: if .x1 ; x2/ is chosen when prices are .p1; p2/ and p1x1 C p2x2 p1y1 C p2y2, then .x1 ; x2/ .y1; y2/ if p1x1 C p2x2 p1y1 C p2y2 we say that x D .x1; x2/ is directly revealed preferred to y D .y1; y2/ if x is directly revealed preferred to y , and y is directly revealed preferred to z , then we say that X is indirectly revealed preferred to z such "chains" of revealed preference can give us a lot of information about preferences the information revealed about tastes by choices can be used in formulating economic policy Weak Axiom of Revealed Preference
recovering preferences makes sense if consumers' behavior is consistent with maximization what if we observed a case like in the following picture? Viola5on of WARP slope = -p1/p2 y = (y1,y2) slope = -q1/q2 x = (x1,x2) Weak Axiom of Revealed Preference
in this case, x is revealed preferred to y and y is also revealed preferred to y ! in symbols, we have .x1; x2/ purchased at prices .p1; p2/, and .y1; y2/ purchased at prices .q1 ; q2 / and p1x1 C p2x2 > p1y1 C p2y2 and q1y1 C q2y2 > q1x1 C q2x2 ! this is not consistent with the optimizing model of consumer choice the WARP rules out this kind of behavior Weak Axiom of Revealed Preference
WARP: if .x1 ; x2 / is directly revealed preferred to .y1; y2/, then .y1; y2/ cannot be directly revealed preferred to .x1; x2/ WARP: if .x1 ; x2 / is chosen under .p1; p2/, .y1; y2/ is chosen under .q1; q2/ and p1x1 C p2x2
then p 1 y1 C p 2 y2 ; q1y1 C q2y2 < q1x1 C q2x2:
this condition can be checked by hand or by computer WARP OK slope = -p1/p2 x = (x1,x2) y = (y1,y2) slope = -q1/q2 WARP also OK slope = -p1/p2 y = (y1,y2) x = (x1,x2) slope = -q1/q2 Strong Axiom of Revealed Preference
WARP is only a necessary condition for behavior to be consistent with utility maximization not sufficient SARP: if .x1 ; x2 / is directly or indirectly revealed preferred to .y1; y2/, then .y1; y2/ cannot be directly or indirectly revealed preferred to .x1 ; x2/ Viola0on of SARP x = (x1,x2) x is chosen under blue budget line; y is chosen under black budget line; z is chosen under red budget line; y = (y1,y2) z = (z1,z2) The power of indirect revealed preference slope = -p1/p2 x = (x1,x2) y = (y1,y2) z = (z1,z2) Note that z is not affordable at the prices at which x was picked ! slope = -q1/q2 Strong Axiom of Revealed Preference
SARP is a necessary and sufficient condition for utility maximization this means that if the consumer is maximizing utility, then his behavior must be consistent with SARP further, if his observed behavior is consistent with SARP, then we can find a utility function that explains the behavior of the consumer as maximizing behavior just like WARP, it can also be checked by hand or computer New topic: 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: we will see it in the next lecture the total effect is the sum of these two effects ...
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