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Theory of Consumer Behavior

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given a budget constraint and preferences, which bundle will the consumer chose to maximize utility?

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We use the TCB to...

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derive a Demand Curve

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Endogenous

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independent variables

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Exogenous

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dependent variables

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Comparative Statics

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shocking an exo variable, ceteris paribus, and observing the effects.

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analytical method

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pen and paper way to find optimal solution

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numerical method

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using excel's solver to find optimal solution

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Consumption Possibilities Frontier (CPF)

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the budget constraint; a fence where things on/under the curve are attainable while things over the curve are not

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How to derive a demand curve

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change price, ceteris paribus

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What pivots the budget line?

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change in price

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What shifts the budget line?

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change in income

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Funky Budget Lines

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taxes, subsidies, rationing and food stamps

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Increase in Price of x1 (p1)

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rotate left (from x1 to x1')

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Decrease in Price of x1 (p1)

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rotate right (from x1 to x1')

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Increase in price of x2 (p2)

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rotate left (from x2 to x2')

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Decrease in price of x2 (p2)

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rotate right (from x2 to x2')

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Increase in Income (m)

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shift BC right

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Decrease in income (m)

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shift BC left

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Preferences

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a set of the consumer's likes, desire, and tastes

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Comparing Preferences (3 ways)

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Strictly preferred, indifferent, weakly preferred

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Indifference Curve

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Set of combinations that give equal satisfaction

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Marginal Rate of Substitution (MRS)

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slope of the indifference curve; "how much is someone willing to give up x2 to get x1"

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Funky Preferences and Indifference Curves

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Perfect Substitutes, perfect complements, bads, neutral goods

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Perfect Substitutes

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constant slope. EX: 1 five dollar bill; 5 one dollar bills

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Perfect Complements (L-Shaped)

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Things that can only be used in fixed proportions. EX: 1 car, 4 tires. 2 cars, 8 tires

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Income Consumption Curve

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given a change in income, ceteris paribus, this is the line through the optimal solutions

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Price Consumption Curve

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given a change in income, ceteris paribus, this is the line through the optimal solutions

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Theory of Revealed Preference

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in every consumer's head there is the ability to compare and decide about items

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Cardinal

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1,2,3,4 (can add, subtract, multiply, and divide)

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Ordinal

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1st, 2nd, 3rd, 4th (cannot add, subtract, multiply, divide)

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Monotonic Transformation

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squared rankings mean the same as their non squared counterparts. MRS remains the same under any transformation

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Computing the MRS for a Utility Function (2 options)

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from a point and @ a point

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MRS from a point

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change in x2 over change in x1

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MRS @ a point

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(negative) partial derivative of x1 over partial derivative of x2. x-axis is numerator. y-axis is denominator.

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If MRS=12

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Im willing to give up 12 x2 in order to get one more x1.

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Canonical Graph

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graph of budget constraint, and indifference map. y-axis is x2, x-axis is x1

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Indifference Map

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shows consumer's preferences; convex, downward sloping, and insatiable

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Initial Solution

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finding max Utility through analytical or numerical methods

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Steps to find optimal solution

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1) rewrite constraint

2) Write the Legrangean

3) Take Partial Derivatives with respect to endogenous variables

4) Set equations=0 (first order condition)

5) divide equation one by equation 2 (cancel lambdas

6) Sub value into the budget constraint (third order condition)

2) Write the Legrangean

3) Take Partial Derivatives with respect to endogenous variables

4) Set equations=0 (first order condition)

5) divide equation one by equation 2 (cancel lambdas

6) Sub value into the budget constraint (third order condition)

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How to find lambda*

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use sensitivity report in solver

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Quasilinear Utility function

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"sorta-linear", cannot get a giffen good

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Miserable Result

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when solver tries to put a negative # in the function

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Disastrous Result

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when solver found a wrong answer, but the graph did not move; you cant tell the answer is wrong

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Corner Solution

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food stamps, MRS does not = price ratio but it is still the optimal solution given the possible bundles.

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Distorted Consumers

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willing to give up very little x2 to get x1. prefers x2.

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Carte Blanche Principle

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cash is always as good or better than in-kind

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If MRS > p1/p2

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need to move up budget line. until MRS < price ratio

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Own Unit Elasticity

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change in endo divided by change in exo

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Elasticity

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responsiveness of the agent to a shock

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Engel Curve

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graph of endogenous variable as a function of exogenous variable. (Income is the shock variable)

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Unit Elastic

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=1; percent change is same for both variables. move at the same rate

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Inelastic

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between 0 and 1. the shock did not cause the endogenous variable to change as much

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Perfectly Inelastic

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A shock will have no change in the endogenous variable

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Demand Curve Axis

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Y-endogenous variable

X-price

X-price

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Inverse Demand Curve Axis

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Y-Price

X-Endogenous Variable

X-Endogenous Variable

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Giffen Goods

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violates the law of demand. If price were to increase we would consumer more of these products. Demand Curve is upward sloping

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Price Elasticity of demand

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% change in x1 over % change in income

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Total Effect

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Substitution Effect+Income Effect. B+C

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Substitution Effect

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From A to B. When price changes, what bundle will we prefer

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Income Effect

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From B to C. Amount I want to buy given the 'perceived' change in income

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When IE & SE work together

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Normal good, downward sloping demand curve

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When IE & SE work against each other

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Inferior good, downward sloping demand curve

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When IE swamps SE

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Giffen good, upward sloping demand curve.

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SE is always negative because....

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relationship between price and quantity is always negative

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Endowment Model

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consumer has a specific allotted amount for x1 and x2. The consumer starts at a point on the graph. Can move to anywhere on the budget constraint.

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Move northwest of the initial endowment means....

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sell x1 for more x2.

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Move southeast of the initial endowment means...

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selling x2 for more x1

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Increase in p1 (EM)

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bundles of x2 become more desirable. Budget line shifts right while still going through IE

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Decrease in p1 (EM)

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bundles of x1 become more desirable. Budget line shifts left while still going through IE

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Increase in p2

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bundles of x1 become more desirable. Budget line shifts right while still going through IE.

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Decrease in p2

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bundles of x2 become more desirable. Budget line shifts left while still going through IE