# Part Three

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﻿Section Three Preferences

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Rationality in Economics Behavioral Postulate : A decisionmaker dependably picks its most favored option from its arrangement of accessible options. So to model decision we should model decisionmakers' inclinations.

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Preference Relations Comparing two diverse utilization groups, x and y: strict inclination : x is more favored than is y. frail inclination : x is as in any event as favored as is y. detachment : x is precisely as favored as is y.

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Preference Relations Strict inclination, feeble inclination and lack of concern are all inclination relations. Especially, they are ordinal relations; i.e. they state just the request in which packs are favored.

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Preference Relations p indicates strict inclination; x y implies that package x is favored entirely to package y. p

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Preference Relations p indicates strict inclination; x y implies package x is favored entirely to package y. ~ signifies lack of interest; x ~ y implies x and y are similarly favored. p

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f ~ Preference Relations p indicates strict inclination so x y implies that package x is favored entirely to package y. ~ indicates lack of interest; x ~ y implies x and y are similarly favored. signifies frail inclination; x y implies x is favored at any rate as much as is y. p

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f ~ Preference Relations x y and y x infer x ~ y.

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f ~ Preference Relations x y and y x suggest x ~ y. x y and (not y x) suggest x y. p

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f ~ Assumptions about Preference Relations Completeness : For any two groups x and y it is constantly conceivable to put forth the expression that either x y or y x.

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f ~ Assumptions about Preference Relations Reflexivity : Any package x is dependably at any rate as favored as itself; i.e. x.

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f ~ Assumptions about Preference Relations Transitivity : If x is at any rate as favored as y, and y is at any rate as favored as z, then x is in any event as favored as z; i.e. x y and y z x z.

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Indifference Curves Take a reference package x'. The arrangement of all packs similarly wanted to x' is the lack of concern bend containing x' ; the arrangement of all groups y ~ x'. Since a lack of interest "bend" is not generally a bend a superior name may be a detachment "set".

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Indifference Curves x 2 x' ~ x" ~ x"' x' x" x"' x 1

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Indifference Curves x 2 z x y p x z y x 1

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Indifference Curves I 1 All groups in I 1 are entirely wanted to all in I 2 . x 2 x z I 2 All packs in I 2 are entirely wanted to all in I 3 . y I 3 x 1

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Indifference Curves x 2 WP(x), the arrangement of groups pitifully liked to x. x I(x') I(x) x 1

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Indifference Curves x 2 WP(x), the arrangement of groups pitifully wanted to x. x WP(x) incorporates I(x). I(x) x 1

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Indifference Curves x 2 SP(x), the arrangement of packs entirely wanted to x, does exclude I(x). x I(x) x 1

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Indifference Curves Cannot Intersect From I 1 , x ~ y. From I 2 , x ~ z. Thusly y ~ z. I 2 x 2 I 1 x y z x 1

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Indifference Curves Cannot Intersect From I 1 , x ~ y. From I 2 , x ~ z. Accordingly y ~ z. However, from I 1 and I 2 we see y z, a disagreement. I 2 x 2 I 1 p x y z x 1

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Slopes of Indifference Curves When all the more a product is constantly favored, the ware is a decent . On the off chance that each item is a decent then apathy bends are contrarily inclined.

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Slopes of Indifference Curves Good 2 Two products a contrarily inclined detachment bend. Better Worse Good 1

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Slopes of Indifference Curves If to a lesser extent a ware is constantly favored then the item is a terrible .

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Slopes of Indifference Curves Good 2 One great and one terrible an emphatically inclined detachment bend. Better Worse Bad 1

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Extreme Cases of Indifference Curves; Perfect Substitutes If a purchaser dependably respects units of items 1 and 2 as equal, then the products are flawless substitutes and just the aggregate sum of the two wares in packs decides their inclination rank-arrange.

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Extreme Cases of Indifference Curves; Perfect Substitutes x 2 Slopes are steady at - 1. 15 I 2 Bundles in I 2 all have an aggregate of 15 units and are entirely liked to all packs in I 1 , which have a sum of just 8 units in them. 8 I 1 x 1 8 15

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Extreme Cases of Indifference Curves; Perfect Complements If a shopper dependably devours products 1 and 2 in settled extent (e.g. coordinated), then the items are impeccable supplements and just the quantity of sets of units of the two products decides the inclination rank-request of packs.

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Extreme Cases of Indifference Curves; Perfect Complements x 2 Each of (5,5) , (5,9) and (9,5) contains 5 sets so each is similarly favored. 45 o 9 5 I 1 x 1 5 9

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Extreme Cases of Indifference Curves; Perfect Complements x 2 Since each of (5,5) , (5,9) and (9,5) contains 5 sets, each is less favored than the package (9,9) which contains 9 sets. 45 o 9 I 2 5 I 1 x 1 5 9

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Preferences Exhibiting Satiation A package entirely wanted to some other is a satiation point or a joy point . What do lack of concern bends look like for inclinations showing satiation?

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Indifference Curves Exhibiting Satiation x 2 Satiation (rapture) point x 1

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Indifference Curves Exhibiting Satiation x 2 Better Satiation (euphoria) point Better x 1

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Indifference Curves Exhibiting Satiation x 2 Better Satiation (joy) point Better x 1

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Indifference Curves for Discrete Commodities An item is interminably distinguishable on the off chance that it can be procured in any amount; e.g. water or cheddar. A product is discrete in the event that it comes in unit chunks of 1, 2, 3, … et cetera; e.g. flying machine, boats and fridges.

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Indifference Curves for Discrete Commodities Suppose ware 2 is an endlessly separable great (fuel) while item 1 is a discrete decent (airplane). What do apathy "bends" resemble?

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Indifference Curves With a Discrete Good Gas-oline Indifference "bends" are accumulations of discrete focuses. Air ship 0 1 2 3 4

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Well-Behaved Preferences An inclination connection is " all around acted " in the event that it is monotonic and arched . Monotonicity : More of any product is constantly favored ( i.e. no satiation and each item is a decent).

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Well-Behaved Preferences Convexity : Mixtures of packs are (in any event feebly) liked to the groups themselves. E.g., the 50-50 blend of the packs x and y is z = (0.5)x + (0.5)y. z is at any rate as favored as x or y.

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Well-Behaved Preferences - Convexity. x 2 x+y is entirely liked to both x and y. x 2 +y 2 z = 2 y 2 x 1 +y 1 x 1 y 1 2

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Well-Behaved Preferences - Convexity. x 2 z =(tx 1 +(1-t)y 1 , tx 2 +(1-t)y 2 ) is liked to x and y for each of the 0 < t < 1. y 2 x 1 y 1

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Well-Behaved Preferences - Convexity. Inclinations are entirely raised when all blends z are entirely wanted to their part packages x and y. x 2 z y 2 x 1 y 1

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Well-Behaved Preferences - Weak Convexity. Inclinations are feebly curved if no less than one blend z is similarly wanted to a segment package. x' z' x z y'

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Non-Convex Preferences x 2 Better The blend z is less favored than x or y. z y 2 x 1 y 1

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More Non-Convex Preferences x 2 Better The blend z is less favored than x or y. z y 2 x 1 y 1

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Slopes of Indifference Curves The slant of a lack of interest bend is its minimal rate-of-substitution (MRS). In what manner can a MRS be ascertained?

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Marginal Rate of Substitution x 2 MRS at x' is the slant of the lack of interest bend at x' x' x 1

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Marginal Rate of Substitution x 2 MRS at x' is lim { D x 2/D x 1 } D x 1 0 = dx 2/dx 1 at x' x' D x 2 D x 1 x 1

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Marginal Rate of Substitution dx 2 = MRS " dx 1 along these lines, at x', MRS is the rate at which the purchaser is just barely eager to trade item 2 for a little measure of ware 1. x 2 x' dx 2 dx 1 x 1

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MRS & Ind. Bend Properties Good 2 Two merchandise a contrarily slanted lack of concern bend Better MRS < 0. More awful Good 1

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MRS & Ind. Bend Properties Good 2 One great and one awful a decidedly slanted lack of interest bend Better MRS > 0. More awful Bad 1

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MRS & Ind. Bend Properties Good 2 MRS = - 5 MRS dependably increments with x 1 (turns out to be less negative) if and just if inclinations are entirely arched. MRS = - 0.5 Good 1

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MRS & Ind. Bend Properties x 2 MRS diminishes (turns out to be more negative) as x 1 increments nonconvex inclinations MRS = - 0.5 MRS = - 5 x 1

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MRS & Ind. Bend Properties MRS is not continually expanding as x 1 increments nonconvex inclinations. x 2 MRS = - 1 MRS = - 0.5 MRS = - 2 x 1