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Lagrangian

answer

Function to be maximized or minimized, plus a

variable (the Lagrange multiplier) multiplied by the constraint.

variable (the Lagrange multiplier) multiplied by the constraint.

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Lagrangian constraint

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If you relax the constraint and increase production, cost, whatever the constraint may be, then original objective unit will change by ABSOLUTE VALUE of amount "x"

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Demand

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The various quantities of a specific good consumers are willing and able to purchase at various prices;

ceteris parebus = those variables held constant (i.e., price of related goods, income, weather, etc.), does not include P

ceteris parebus = those variables held constant (i.e., price of related goods, income, weather, etc.), does not include P

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Increase in quantity demanded vs. increase in demand

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Increase in quantity = movement along demand curve, increase in demand = movement of curve (caused by a change in ceteris paribus conditions)

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Supply

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Quantities of a specific good producers are willing and able to sell at various prices (same with ceteris paribus)

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Elasticities

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Measure the % change in one thing from a given % change in something related / something that affects it

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Own price elasticity of demand

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Shows the % change in quantity demanded of one good from a given % change in the price of that good

dQ/dP * P0/Q0

dQ/dP * P0/Q0

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| elasticity | is _ 1

answer

> = Elastic

< = Inelastic

= 1 = Unit Elastic

< = Inelastic

= 1 = Unit Elastic

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What determines the magnitude of elasticity

answer

1) Availability of substitutes

2) Fraction of the budget spent on the good (more spent = higher elasticity)

3) Length of time to respond (more time = higher elasticity)

2) Fraction of the budget spent on the good (more spent = higher elasticity)

3) Length of time to respond (more time = higher elasticity)

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Income elasticity of demand

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Measures the % change in D for a good from a given % change in consumer income

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Normal good vs. inferior good

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normal = income elasticity > 0

inferior = income elasticity < 0

inferior = income elasticity < 0

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Cross-price elasticity of demand

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Measures the % change in the demand for one good in response to % change in price of a different good

(dQx/dPz * Pz/Qx)

(dQx/dPz * Pz/Qx)

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Substitute goods vs. compliment goods

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Substitute = Cross-price elasticity > 0

Compliment = Cross-price elasticity < 0

Compliment = Cross-price elasticity < 0

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Advertising elasticity of demand

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Measures the % change n D for a good from a given % change in advertising expenditures

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Regression Analysis

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Used to estimate demand functions; estimates the relation that exists among statistically related variables

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R^2

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Coefficient of determination; shows how much of the variation in the dependent variable can be explained by variation in the independent variable(s)

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Standard Error of the Estimates

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Measures variability of the true values (of the dependent variable) around the predicted values

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F-Statistic

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Statistically measurable test of the explained variation in the dependent variable; Testing whether Ho = Alpha1 = Alpha2 = ...

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t-Statistic

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Provides statistical test of significance of the estimated parameters; compare the | calculated t | to a t-value at a certain level of significance (if calculated>chart, reject H0)

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T by hand (without regression output)

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| Equation coefficient / SE of parameter estimate | --> if > than t-stat, reject H0

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Magnitudes of coefficients

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i.e., a $1 increase in income will lead to a 5 unit increase in consumption (normal good)

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Degrees of freedom

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n-k

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Dummy Variable

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A variable used to model the effect of categorical independent variables in a regression model; generally takes only the value zero or one

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Marginal Rate of Technical Substitution

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Shows how much of one input that needs to be substituted to use one additional unit of another input, keeping output fixed

graphically - slope of the isoquant

mathematically - Q = f(k,l), MRTS = dk/dl or MPl/MPk)

graphically - slope of the isoquant

mathematically - Q = f(k,l), MRTS = dk/dl or MPl/MPk)

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Present value

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the current value of future cash flows discounted at the appropriate discount rate

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Marginal Revenue Product

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The change in total revenue when an additional unit of a resource is employed, other things constant

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Advertising Elasticity of Demand

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Percentage change in quantity demanded resulting from a 1-percent increase in advertising expenditures

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Short-run production theory

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At least one input is fixed and cannot be altered

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Long-run production theory

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All inputs can be altered and are variable

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Monopoly theory of profits

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Barriers to entry create profits for existing firms

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Innovation theory of profits

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Someone comes up with a good idea and it results in profit

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Frictional theory of profits

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Adjustments or shocks in the long-run equilibrium

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Risk bearing theory of profits

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Riskier activities require higher profits

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Managerial efficiency

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Manager is more efficient and leads to profits (and increased wage demands as a result)

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Perfect competition

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Homogenous products, free entry and exit, price takers, many buyers and sellers

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Optimal Pricing

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Set MR = MC to maximize profits

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Marginal Revenue in relation to elasticity

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MR = MC = P((1/elasticity) + 1)

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Obtaining elasticities from functions

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Linear - elasticity is coefficient in front of variable

Nonlinear - elasticity is exponent of variable

Nonlinear - elasticity is exponent of variable

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Demand estimation with difficulty teasing out information about variables

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Marketing professionals, interviews with the public, experiments (lab, actual markets, online)

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Short-run input decsions

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Continue to hire until the benefit of hiring additional = the cost of hiring additional

MPl*P = w

OR if we have an imperfectly competitive market, MPl*MR = w

MPl*P = w

OR if we have an imperfectly competitive market, MPl*MR = w

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Long-run input decisions

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Firm's optimal mix occurs when the MP per dollar spent is equalized across all inputs; actual amount of inputs is dictated by:

1) Cost of producing a desired level of output OR

2) Level of output that results from a chosen TC

1) Cost of producing a desired level of output OR

2) Level of output that results from a chosen TC

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Producing using multiple plants (same output)

answer

Optimal allocation results from equating Marginal Products across both plants' production functions

(start allocating to facility with highest marginal, productivity, then switch when MP of first declines below MP of second)

(start allocating to facility with highest marginal, productivity, then switch when MP of first declines below MP of second)

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Producing with multiple products that require the same inputs

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Optimal allocation results from equating marginal profitability across the two products

Marginal profitability = profit per unit * MP

Marginal profitability = profit per unit * MP

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Constant Returns to Scale

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a given % change in all inputs results in a proportional % change in output (firm's output can be replicated)

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Increasing Returns to Scale

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a given % change in all inputs results in a greater % change in output (firm is able to use a more efficient production technology at a higher level of output)

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Decreasing Returns to Scale

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a given % change in all inputs results in a less than equal % change in output (occurs due to organizational difficulties arising at larger production scale)

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Measuring returns to scale

Q = f(x, y, z)

Q = f(x, y, z)

answer

Multiply inputs by a small value k, and measure the effect of that increase by an effect on Q

hQ = f(kx, ky, kz) and if h>k, increasing returns to scale

hQ = f(kx, ky, kz) and if h>k, increasing returns to scale

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Measuring returns to scale

Elasticity

Elasticity

answer

Elasticity = (%change Q / %change all inputs)

if elasticity >1, increasing returns to scale

if elasticity >1, increasing returns to scale

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Marginal Rate of Technical Substitution

answer

-MPl/MPk

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Linear vs. Cobb Douglas vs. Leontief Production functions

answer

Linear - Output can be produced from only one good

Cobb Douglas - both k and l are required to produce output

Leontief - substitution of k and l occurs in fixed proportions

Cobb Douglas - both k and l are required to produce output

Leontief - substitution of k and l occurs in fixed proportions

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Multicollinearity

answer

Occurs when two or more independent variables are strongly correlated (SE is too high and get a low t-stat); can be avoided by:

- increasing sample size

- using a priori information

- dropping one of the correlated variables

- increasing sample size

- using a priori information

- dropping one of the correlated variables

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Heteroscedasticity

answer

Occurs when the uniform / constant variation among variables is violated (leads to biased SEs); can be avoided by:

- using log of independent variable

- use weighted least squares

- using log of independent variable

- use weighted least squares

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Autocorrelation

answer

Occurs when consecutive errors are correlated, usually in time series data; can be avoided by

- inserting a variable for time on indep var

- adding additional explanatory variables

- use a non-linear function

- inserting a variable for time on indep var

- adding additional explanatory variables

- use a non-linear function