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Economics

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Study of how to allocate scare resources to satisfy unlimited human wants.

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Questions Microeconomics seeks to answer by studying the behavior of individual economic units (3)

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What goods and services will be produced and by how much?

Who will produce them and how?

Who will get them?

Who will produce them and how?

Who will get them?

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Model

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Simplified version of reality that economists study the relationship between them and variables.

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Exogenous Variable

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A variable whose value is taken as given in a model. Determined outside of the system.

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Endogenous Variable

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A variable whose value is determined within the model. We solve for the endogenous variable.

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Constrained Optimization

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Tool to analyze markets. Tool for making the best (optimal) choice, taking into account any possible limitations or restrictions on the choice. Contains two parts.

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Objective Function

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Part of the Constrained Optimization, the relationship the decision maker seeks to maximize or minimize. Maximize profit, minimize costs.

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Constraints

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Part of the Constrained Optimization, the restrictions or limitations imposed on a decision maker in a constraint optimization problem (C.O.P), reflection of scarce resources- income, etc.

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Constrained Optimization Problem Format

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(max) or (Min): Objective Function (in terms of X,Y)

Subject to: (Constraints)

- The solution to any C.O.P. depends on the marginal impact of the decision variables on the value of the objective function (The satisfaction begins to decrease with additional units purchased)

Subject to: (Constraints)

- The solution to any C.O.P. depends on the marginal impact of the decision variables on the value of the objective function (The satisfaction begins to decrease with additional units purchased)

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Marginal

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Tells how a dependent variable changes as a result of adding one more unit of an independent variable.

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Marginal Cost

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Measures incremental impact of the last unit of the independent variable on the dependent variable, thought of as the "Rate of Change"

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Equilibrium

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A state or condition that will continue indefinitely as long as the factors exogenous to the system remain unchanged.

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Market Equilibrium

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Markets move toward equilibrium to sell/buy goods for the correct amount. Market Equilibrium is achieved at a price where the market "Clears", where Qs=Qd. When out of equilibrium, either the price is too high or too low and there is either a surplus or a shortage.

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Comparative Statics

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Analysis used to examine how a change in an exogenous variable will affect the level of an endogenous variable in an economic model. -Shows before and after of a change in Exogenous Variable. - Helps determine Elasticity.

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Positive Analysis

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Explains how an economic system works to predict how it will change over time. Asks "what has happened"

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Normative Analysis

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Analysis that typically focuses on issues of social welfare, examining what will enhance or detract from the common good. Asks "What should be done?"

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Perfect Competitive Markets

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Large number of buyers and sellers, individual transactions are so small that both buyers and sellers are price takers. No barriers to entry, selling identical goods.

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Market Demand Curve

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A curve that shows us the quantity of goods that consumers are willing to buy at different prices. Consists of Derived Demand and Direct Demand. Shows the highest price that the "market will bear" for a given quantity or supply of output.

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Derived Demand

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Demand for a good that is derived from the production and sale of other goods.

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Direct Demand

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Demand for a good that comes from the desire of buyers to directly consume the good itself.

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Movement along demand curve

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A change in price causes movement along the demand curve.

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Demand Shifters

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PINTE:

P:rices of related goods

I:ncome of consumers

N:umber of buyers

T:astes

E:xpectations

P:rices of related goods

I:ncome of consumers

N:umber of buyers

T:astes

E:xpectations

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Law of Demand

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The inverse relationship between the price of a good and the quantity demanded, holding all other factors that influence demand constant (Ceteris Paribus)

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Market Supply Curve

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A curve that shows us the total quantity of good that their suppliers are willing to sell at different prices. Slopes upward because as prices rises, more suppliers are willing to offer more of the good.

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Movement along supply curve

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Movement along supply curve is caused by a change in price.

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Supply Shifters

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PINTE

P:rice of substitutes in production- shitting to other goods b/c of a change in market price.

I:nput prices- factors of production

N:umber of Sellers

T:echnological enhancements

E:xpectations

P:rice of substitutes in production- shitting to other goods b/c of a change in market price.

I:nput prices- factors of production

N:umber of Sellers

T:echnological enhancements

E:xpectations

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Law of Supply

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The positive relationship between price and quantity supplied when all other factors that influence supply are held fixed.

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Market Equilibrium

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a point at which there is no tendency for the market price to change as long as the exogenous variables remain unchanged. At any other point other than the equilibrium, there is pressure to move towards equilibrium.

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Basics Laws of Supply and Demand (4)

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1) Increase in demand+Unchanged Supply= higher equilibrium price, larger equilibrium quantity.

2) Decrease in Supply+ Unchanged Demand= Higher equilibrium price and smaller equilibrium quantity.

3) Decrease in Demand + Unchanged Supply= lower equilibrium price and smaller equilibrium quantity.

4) Increase in supply+ unchanged demand= lower equilibrium price and larger equilibrium quantity.

2) Decrease in Supply+ Unchanged Demand= Higher equilibrium price and smaller equilibrium quantity.

3) Decrease in Demand + Unchanged Supply= lower equilibrium price and smaller equilibrium quantity.

4) Increase in supply+ unchanged demand= lower equilibrium price and larger equilibrium quantity.

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Shifts in both supply and demand

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Increase in demand + decrease in Supply= increase in equilibrium price and ambiguous change in quantity.

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Price Elasticity of Demand

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A measure of the rate of percentage change of quantity demanded with respect to price, ceteris paribus. Measures sensitivity of the quantity demanded to price.

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Formula for Price Elasticity of Demand

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E(q,p)=% change in quantity/ % change in price equivalent:

E(q,p)= (dQ/dP) * (P/Q)

-d denotes the derivative (rate of change)

E(q,p)= (dQ/dP) * (P/Q)

-d denotes the derivative (rate of change)

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Equation for Linear Demand Curve

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Q=a-bP

a= all factors that will shift the demand curve

b= how price affects Qd

a= all factors that will shift the demand curve

b= how price affects Qd

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Inverse Demand Curve

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1-(Q/P)

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Total Revenue

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TR=P*Q. Elasticity of the good determines the price effect and quantity effect. Have to find out which is stronger to determine the change in TR. If the good is inelastic, an increase in price raises the TR. Elastic with an increase in price decreases TR.

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Perfectly Inelastic Demand

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E(q,p)= 0. TR changes with price. completely vertical demand curve. QD is totally insensitive to P. * the flatter of the two curves that cross at a particular point is the more ELASTIC good.

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Inelastic Demand

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-1<E(q,p)<0. TR changes with price. Price effect. Qd is relatively insensitive to price.

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Unit Elastic Demand

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E(q,p)=-1. Neither effect changes TR, a % increase in Qd= a % decrease in P. Completely horizontal demand curve.

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Elastic Demand

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-infinity<E(q,p)<-1. TR changes with quantity effect. Qd is sensitive to P.

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Perfectly Elastic Demand

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Any increase in price results in Qd decreasing to zero and any decrease in price results in quantity demanded increasing to infinity. P Increase= TR= 0. P decrease= TR= Infinity.

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Determinants of Price Elasticity of Demand (4)

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1) Number of available substitutes: more substitutes available means the demand is more elastic. (more narrowly defined markets have more substitutes- market for minute maid vs juice in general)

2) Percentage of income spent: demand for highly priced items which take up larger shares of income is more elastic. Usually durable goods: Cars, furniture, kitchen appliances.

3) The good is a Necessity or a Luxury: Necessities tend to have inelastic demand- food. Luxuries tend to have more elastic demand- diamonds.

4) Time horizon: for some good, the demand is more elastic in the long run. For gas, it is a necessity in the short run but you can substitute away from driving in the long run.

* Remember, consider the different elasticities for general goods (cigarettes) vs brands (parliaments)

2) Percentage of income spent: demand for highly priced items which take up larger shares of income is more elastic. Usually durable goods: Cars, furniture, kitchen appliances.

3) The good is a Necessity or a Luxury: Necessities tend to have inelastic demand- food. Luxuries tend to have more elastic demand- diamonds.

4) Time horizon: for some good, the demand is more elastic in the long run. For gas, it is a necessity in the short run but you can substitute away from driving in the long run.

* Remember, consider the different elasticities for general goods (cigarettes) vs brands (parliaments)

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Income Elasticity of Demand

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The ratio of the percent change in QD to the percent change in income, determinants held constant.

Normal goods have Positive income Elasticity.

Inferior goods have Negative income elasticity.

Necessities has small income elasticities.

Luxuries have large income elasticities.

Normal goods have Positive income Elasticity.

Inferior goods have Negative income elasticity.

Necessities has small income elasticities.

Luxuries have large income elasticities.

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Income Elasticity of Demand Equation

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E(q,i)= dQ/dI * (I/Q)

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Cross-Price Elasticity of Demand

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The ratio of the percent change of the Quantity of one good demanded with respect to the percent change in the price of another good.

Substitutes have positive cross-price elasticity.

Complements have negative cross-price elasticity.

Substitutes have positive cross-price elasticity.

Complements have negative cross-price elasticity.

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Cross-Price Elasticity of Demand Equation

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E(Qi,Pj)= dQi/QPj * (Pj/Qi)

j= good 2

i= good 1.

j= good 2

i= good 1.

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Price Elasticity of Supply

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The percent change in quantity supplied for each percent change in price. Determinants held constant.

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Price Elasticity of Supply Equation

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E(qs,p)= dQs/dp * (p/qs)

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Basket

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A combination of goods and services that an individual might consume. Also known as a "Consumption Bundle"

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Consumer Preferences

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Indications of how a consumer would rank any two possible baskets, assuming the baskets were available to the consumer at NO COST.

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Assumptions about Consumer Preferences (3)

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1) Preferences are complete: the consumer is able to rank any two baskets; A & B.

- Completeness:

If a consumer prefers A: A>B (not a greater sign)

Etc. Indifference looks like a = sign but with two of these: ~

2) Preferences are transitive: The consumer makes consistent choices.

-If a consumer likes basket A more than B and B more than C, the consumer should like basket A more than basket B.

3) More is Better- More is ALWAYS better.

- Completeness:

If a consumer prefers A: A>B (not a greater sign)

Etc. Indifference looks like a = sign but with two of these: ~

2) Preferences are transitive: The consumer makes consistent choices.

-If a consumer likes basket A more than B and B more than C, the consumer should like basket A more than basket B.

3) More is Better- More is ALWAYS better.

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Ordinal Ranking

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Rankings that indicate whether a consumer prefers one basket to another but does not contain quantitative information about the intensity of that preference. does NOT TELL DEGREE.

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Cardinal Ranking

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A quantitative measure of the intensity of a preference for one basket over another. Shows INTENSITY OF PREFERENCE. gives more information than an Ordinal Ranking.

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Utility Function

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A function that measures the level of satisfaction a consumer receives from any basket of goods and services. Must satisfy the 3 assumptions of preference: Completeness, transitive, and more is better.

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Marginal Utility

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Denoted MU. The rate at which total utility changes as the level of consumption rises. It is the derivative of the Utility function.

1)MU is always positive, so U is increasing in T.

2) MU is decreasing, so U is increasing at a decreasing rate.

1)MU is always positive, so U is increasing in T.

2) MU is decreasing, so U is increasing at a decreasing rate.

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Marginal Utility Equation

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MUt= Du/Dt (derivative of T in the Utility function)- slope of U at different levels of T.

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Principle of Diminishing Marginal Utility

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The principle that after some point, as consumption of a good increases, the MU of that good will begin to fall.

-UT and MU cannot be plotted on the same graph, vertical axis represent U for the respective functions.

-MU is slope of UT.

1) The slope of MU is Negative.

2) 1st order derivatives decides if U is increasing or not.

3) 2nd order derivative decides the rate at which U is changing.

4) TR increases when MU is positive.

5) TR decreases when MU is negative.

- on a graph, the portion of the graph above the X axis shows where U is increasing, below is where U is decreasing.

-UT and MU cannot be plotted on the same graph, vertical axis represent U for the respective functions.

-MU is slope of UT.

1) The slope of MU is Negative.

2) 1st order derivatives decides if U is increasing or not.

3) 2nd order derivative decides the rate at which U is changing.

4) TR increases when MU is positive.

5) TR decreases when MU is negative.

- on a graph, the portion of the graph above the X axis shows where U is increasing, below is where U is decreasing.

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Preferences with Multiple goods

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When measuring the MU of the utility of two goods, we hold constant the levels of consumption of all other goods. You take partial derivatives of both goods.

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Indifference Curves

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A curve connecting a set of consumption baskets that yield the same level of satisfaction to the consumer.

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Properties of Indifference curves (4)

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1) When the consumer likes both goods (MUx & MUy > 0) all the indifferences curves have negative slope.

2) Indifference curves cannot intersect, the baskets need to be transitive to satisfy them being a consumer preference so if the curves intersect, that means it depends on what side of the curve you're looking at, they will change which one is more NE.

3) Every consumption basket likes on one and only one indifference curve. (They can't cross)

4) Indifference curves aren't thick. For two baskets that are right next to each other, you would assume the more NE one is the preferred basket, but since they lie on the same curve, that can't be true and that isn't true.

2) Indifference curves cannot intersect, the baskets need to be transitive to satisfy them being a consumer preference so if the curves intersect, that means it depends on what side of the curve you're looking at, they will change which one is more NE.

3) Every consumption basket likes on one and only one indifference curve. (They can't cross)

4) Indifference curves aren't thick. For two baskets that are right next to each other, you would assume the more NE one is the preferred basket, but since they lie on the same curve, that can't be true and that isn't true.

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Marginal Rate of Substitution

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A feature of consumer preferences for which the MRS of one good for another good diminishes as the consumption of the first good increases along an indifference curve. MRS is the negative of the slope of the indifference curve. Y=vert X=Horiz. Holding Utility constant. If MUx & MUy are positive. IC curves are negatively sloped. MRSxy diminishes as increase X along an indifference curve. Diminishing MRSxy MUST have indifference curves bowed towards the origin.

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Marginal Rate of Substitution Equation

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MRSxy= MUx/MUy= Change Y/ Change X

*as you increase consumption of one good, you are willing to give up less of the other good.

*as you increase consumption of one good, you are willing to give up less of the other good.

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Perfect Substitutes

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Two goods such that the MRS of 1 good for the other is CONSTANT. Therefore, the indifference curves are straight lines. MRS=1. Slope of IC=1.

COKE AND PEPSI. MRS is constant along ICs. Same shape as the DEMAND CURVE.

COKE AND PEPSI. MRS is constant along ICs. Same shape as the DEMAND CURVE.

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Perfect Complements

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Two good that the consumer ALWAYS wants to consume in fixed proportion to one and other. Left and Right Shoes. IC are RIGHT ANGLES. The indifference curves are parallel to the ORIGIN, same exact shape.

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Cobb-Douglas Utility Function

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U(x,y)=Ax^&y^%

&= Alpha- (fish shape)

%= Beta-(Chinese Character shape)

A, &, % are positive constants. (usually &+%=1)

1) MU>0 for each good- more is better.

2) MU>0 means downward sloping IC

3) Diminishing MU (when % and & <1)

&= Alpha- (fish shape)

%= Beta-(Chinese Character shape)

A, &, % are positive constants. (usually &+%=1)

1) MU>0 for each good- more is better.

2) MU>0 means downward sloping IC

3) Diminishing MU (when % and & <1)

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Cobb-Douglas Utility Function Proof

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U(x,y)=Ax^&y^%

MUx=&A^(&-1)y^%

MUy=%Ax^&y^(%-1)

MRS(x,y)=&A^(&-1)y^%/%Ax^&y^(%-1)

= &/% * Y/x

MUx=&A^(&-1)y^%

MUy=%Ax^&y^(%-1)

MRS(x,y)=&A^(&-1)y^%/%Ax^&y^(%-1)

= &/% * Y/x

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Quasi-Linear Function

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When a consume buys the same amount of a commodity regardless of her income. Indifference Curves are Parallel to one and other, utility jumps when increase consumption of the good. At any value X, the slope of all the indifference curves will be the same (MRSxy remans the same) MRS depends SOLELY on X.

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Quasi-Linear Function Equation

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U(x,y)=X^2+y (quadratic in X, NOT Y)

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Budget Constraint

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The set of baskets that a consumer can purchase with a limited amount of Income. Measure of purchasing power of your nominal money: REAL income. So a change in nominal income is equivalent to a change of the same ratio of the price of both goods.

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Budget Line

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The set of baskets that a consumer can purchase when spending all of his/ her income. The slope of the budget line tells us how many units of the good on the vertical axis a consumer must give up to obtain an additional unit of the good on the horizontal axis. Location depends on Level of Income.

1)Income Shifts B.L.

2) Price changes change intercepts.

1)Income Shifts B.L.

2) Price changes change intercepts.

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Budget Line Equation

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I=Px

I= Income

Px, Py= Price of good.

**X+Py**YI= Income

Px, Py= Price of good.

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Budget Constraint Equation

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I<(OR EQUAL TO) Px

**X+Py**Yquestion

Optimal Choice

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Consumer choice of a basket of goods that

1) Maximizes satisfaction while,

2) allowing him to live within his budget constraint.

-Optimal amount of each good to purchase.

-Located on the Budget Line.

C.O.P: Maximize U(x,y)

{x,y} subject to:

PxX+PyY<(equal to) I

X>(or equal to) 0

Y>(or equal to) 0

Optimal consumption bundle is the tangent point of her budget line and on one of her indifference curves. (Slope of BC=Slope of IC)

1) Maximizes satisfaction while,

2) allowing him to live within his budget constraint.

-Optimal amount of each good to purchase.

-Located on the Budget Line.

C.O.P: Maximize U(x,y)

{x,y} subject to:

PxX+PyY<(equal to) I

X>(or equal to) 0

Y>(or equal to) 0

Optimal consumption bundle is the tangent point of her budget line and on one of her indifference curves. (Slope of BC=Slope of IC)

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Tangency Condition

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MUx/MUy=Px/Py

Shows optimal Basket

"bang for your buck"

Shows optimal Basket

"bang for your buck"

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Interior Optimum

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An optimal basket at which a consumer will be purchasing positive amount of all commodities. Where BL is tangent to IC. MUx/Px=MUy/Py. consumer chooses commodities so that the MU per dollar spent on each commodity is the same.

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Cookbook for finding Interior Solution

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1) Take Partial Derivatives of U(x,y) to get MUx and MUy.

2) Set MRSxy= MUx/MUy=Px/Py

3) Get relationship between X and Y from (2). Solve for Y in terms of X.

4) Plug (3) back into BL, solve for remaining variable X to get X*.

5)Plug solution X

6) Check to make sure I is exhausted (In BL)

7) Optimum is X

2) Set MRSxy= MUx/MUy=Px/Py

3) Get relationship between X and Y from (2). Solve for Y in terms of X.

4) Plug (3) back into BL, solve for remaining variable X to get X*.

5)Plug solution X

**from (4) into solved equation from (3), solve for Y to get Y**.6) Check to make sure I is exhausted (In BL)

7) Optimum is X

**,Y**.question

Corner Point

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A solution to the consumer's optimal choice problem at which some good is not being consumed at all, in which case the optimal basket lies on an axis. Optimal when a consumer is quite willing to substitute one commodity for another.

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Perfect Complements

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AKA Leontief Preferences, Form: U(x,y)= MIN (ax, by)

1) set ax=by and solve for y in terms of x.

2) plug (1) into BL to solve for x*.

3) plug x

The IC curves are right angles to the axis, exact same as the axis.

1) set ax=by and solve for y in terms of x.

2) plug (1) into BL to solve for x*.

3) plug x

**into (1) to get y**.The IC curves are right angles to the axis, exact same as the axis.

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Composite Goods

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A good that represents the collective expenditures on every other good except the commodity being considered.

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Application of Composite Good

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Coupons and Cash Subsidies: Gov't/ deals given to give consumers the option of a better basket. (flat BL line until the coupon runs out)

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Application of Composite Good

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Joining a Club: Consumers can join clubs that let them purchase goods and services at a discount, consumers can be no worse off after joining the club because they can still purchase the basket they choose when he was not in the club.

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Application of Composite Good

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Borrowing or Lending: We assuming lending entails money in the bank. The slope of the B.L= -(1+R) R being interest rate. Horizontal intercept= I1+I2/(1+R). This shows how consumer preferences and interest rates determine why some people are borrowers and some are lenders.

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Application of Composite Good

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Quantity Discounts: Firms offer a better price for the more bought. Quantity discounts expand the set of baskets a consumer can purchase.

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Revealed Preference

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Analysis that enables us to learn about a consumer's ordinal ranking of baskets by observing how his or her choices of basket change as price and income vary. Preferences don't change

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Price Consumption Curve

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The set of optimal baskets as the price of one good varies. Ceteris Paribus. When plotted, shows the demand curve for that good, CHANGE IN PRICE.

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Income consumption curve

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Set of optimal baskets as income varies and prices held constant. CHANGE IN INCOME. It's a connection of all the optimal baskets when income is changing. when the points are plotted on a demand curve, they are separate lines because income is a demand shifter.

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Engel Curve

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A curve that relates the amount of a commodity purchased to the level of income, holding prices of all other goods constant.

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Normal Goods

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A good that consumers purchase more of as income rises. For a normal good, the Engel curve will have POSITIVE SLOPE. *Income elasticity of Demand is POSITIVE.

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Inferior Goods

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A good that consumers purchase less of as income rises. The engel curve for inferior goods will have negative slope. *Income elasticity of demand is NEGATIVE.

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Substitution effect

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The Change in the amount of a good that a consumer would buy as purchasing power changes, holding all prices and level of utility constant.

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Finding Substitution effect

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1) Find initial basket (P is at initial price)

2) Find Final Basket (with price decrease)

3) Find Decomp. Basket, it's on the original BL, reflects the price decrease. SE=Decomp-Intial. Decomp basket is where the budget line is tangent to the initial indifference curve. Remember, the decrease in the price makes the b.l flatter, the point on B.L2 that is tangent to UC1 is the decomp. basket.

2) Find Final Basket (with price decrease)

3) Find Decomp. Basket, it's on the original BL, reflects the price decrease. SE=Decomp-Intial. Decomp basket is where the budget line is tangent to the initial indifference curve. Remember, the decrease in the price makes the b.l flatter, the point on B.L2 that is tangent to UC1 is the decomp. basket.

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Income Effect

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The change in the amount of a good that a consumer would buy as purchasing power changes, holding prices constant. IE=Final-initial.

We cannot have two inferior goods in our basket, EVER. When one is normal and one is inferior, we consume more of the normal good.

We cannot have two inferior goods in our basket, EVER. When one is normal and one is inferior, we consume more of the normal good.

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Giffin Goods

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A good so strongly inferior that the income effect outweighs the substitution effect, resulting in an upward sloping demand curve over some regions of prices. No good examples because it is so unlikely to happen. Income elasticity would have to be negative and the expenditures on the good would need to represent a large portion of the consumers budget. Closest Example: Irish Potato Famine.

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Consumer Surplus

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The difference between max amount a consumer is willing to pay fora good and the amount actually paid. (CS=WTP-P). Area below the demand curve and above the price.

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Compensating Variation

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A measure of how much money a consumer would be willing to give up AFTER a reduction in the price of a good to be just as well of as before the price decrease. Consumer is making decision AFTER the price change and wants to get back to original utility. CV is positive when P is decreasing- giving up money. CV is negative when P is increasing getting paid.

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Equivalent Variation

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A measure of how much additional money a consumer would need BEFORE a price reduction to be as well off as after to price decrease. Consumer is making decision BEFORE the price change and wants to reach the new utility curve. EV is positive when P decreases, getting paid. EV is negative when P is increasing, giving up money.