03 - Elasticities and Regression Flashcards
Elasticity
Measure of the responsiveness of a percentage change in one variable resulting from a percentage change in another variable.
NOTE: elasticity is expressed as percent change in Quantity Demanded (run on x axis) over percent change in price (rise on y axis.) So ratio is a statement of run over rise and the inverse of a typical rise over run construct. Because Q is on horizontal axis.
Own Price Elasticity of Demand
The responsiveness of a parentage change in the quantity demanded of good X to a percentage change in its price.
Sign is negative by law of demand.
If absolute value is > 1 then demand is elastic
If absolute value is < 1 then inelastic demand
If absolute value =1 then demand is Unitary
Elastic Demand
Absolute value > 1
From 1 to infinity
Expl
A 10% Increase in price leads to a greater Han 10% decrease in revenue and vise versa.
Inelastic Demand
Absolute value < 1
From zero to 1
Expl
A 10% Increase in price leads to an less than 10% decrease in revenue and vise versa.
Unitary Elastic Demand
Absolute value = 1
Revenue is largest at Unitary Elastic level of demand.
Expl
A 10% increase in price leads to exactly a 10% decrease in demand.
Total Revenue Test
When demand is elastic (E>1),
total revenue increases when price decreases.
When demand is inelastic (E<1),
total revenue increases when price increases.
Revenue is largest at unit elastic.
Perfect Elastic
Elasticity is equal to Infinity on a horizontal line.
This is the demand curve for the condition of Perfect Competition
Perfectly Inelastic
Elasticity of demand is zero on a perfectly vertical line at some qty. The exact same quantity will be bought no matter the price.
Own price elasticity magnifiers.
More available substitutes
Definition of good
Broad definition good class like “food” is not as elastic as narrow definition goods like “apples”
Elastic - apples, fruit, food - inelastic
A high budget percent
More time
To shop
Longer time horizons
Factors affecting Own Price Elasticity of a good
Available Substitutes - more substitutes = more elastic demand
Time - less urgent will spend more time shopping
Expenditure of Share - higher percentage of budget expense will cause greater consideration
Elasticity and Marginal Revenue
Marginal Revenue is the additional revenue due to a change in output.
When demand is elastic, MR>0
When demand is inelastic, MR<0
When demand is unitary, MR=0
Cross-Price Elasticity
Responsiveness of a percent change in demand for good X due to a percent change the price for good Y.
If cross-price elasticity > 0, then X and Y are substitutes.
If cross-price elasticity < 0, then X and Y are complements.
Substitutes
Goods that demonstrate an inverse demand relationship.
When price goes up on good Y the demand for good X goes up.
The sign is positive for the Py coefficient. Thus, as the price for Y goes up it contributes to the increase in demand for X.
Complements
Goods that demonstrate a positive demand relationship.
When price goes up on good Y the demand for good X goes down.
The sign is negative for the Py coefficient. Thus, as the price for Y goes up it contributes to the decrease in demand for X.
Income Elasticity
Responsiveness of a percent change in demand for good X due to a percent change in income.
If income elasticity > 0 then X is a normal good.
If income elasticity < 0 then X is an inferior good.
Normal Good
A good that demonstrates an increase in demand when income goes up.
The sign is positive for the M coefficient. Thus, as M goes up it contributes to the increase in demand for X.
Inferior Good
A good that demonstrates a decrease in demand when income goes up.
The sign is negative for the M coefficient. Thus, as the absolute value for M goes up it contributes to the decrease in demand for X.
Linear Demand Function
Introduced in Ch - 2
Formula for demand of (X) in light of common demand shifters.
Qx =
ao + axPx + ayPy + amM + ahH
Qx = # units X demanded a.. = coefficients for demand shift factors. Px = $ of X - see law of demand Py = $ of Y - see substitute/complement M = income - see normal/inferior H = other variable affecting demand
Non-linear Demand Function
Log- linear formula for demand of (X) in light of common demand shifters.
lnQxd =
Bo + BxlnPx + BylnPy + BmlnM + BhlnH
Same principal as Linear Demand Function except coefficients for each factor are derived from regression analysis of multiple data points. Use logarithmic conversion to convert non-linear demand function into log-linear demand function above.
B.. = coefficients for demand shift factors
Ordinary Least Squares Regression on population data
Values for each parameter coefficient derived from regression analysis on entire population.
Y = a + bX + e
a = population intercept parameter b = population slope parameter e = standard error of the regression
Ordinary Least Squares regression on sample data.
Values for each parameter coefficient derived from regression analysis on sample set.
Y = a(hat) + b(hat)X
a = population intercept estimate parameter
b = population slope estimate parameter
*** do not adjust (add in) standard error.
Standard Error of the Coefficient
A measure of how much the coefficient varies in the sample regression based on the same true demand model using complete population data.
Confidence intervals:
a(hat) +- 2standard deviation
R Square
The fraction of the total variation in the dependent variable that is explained by the regression.
Ranges between 0 and 1. Closer to 1 means the data fits the least squares function better.
It is also called the coefficient of determination.
R^ = explained variation/total variation Also = SSR/SST
Adjusted R Square
A version of R Square that adjusts the value down (less tight) to account for having too few degrees of freedom relative to the number of coefficients.
If you are estimating more than 3 coefficients in a multi regression, the Adjusted R-square is usually a better estimate of fit than R-square.
The Adjusted R-square can be negative.
T Statistic
If the absolute value of the coefficient’s t Stat is greater than 2, we are 95% confident that the true parameter in the regression is NOT zero.
t-stat = coefficient / standard error
P-value
A measure of the F-stat
Lower P-value are associated with better overall regression fit.
An absolute value below .05 is considered an indication of coefficient significance
F-statistic
A measure of the total variation explained by the regression relative to the total unexplained variation.
F-stat = Explained Variation/unexplained Variation. = SSR/SSE
The higher the F-stat, the better the fit.
The Significance F value indicates the percent chance the model fit the data by accident.
Significance F
Indicates the percent chance that the estimated regression model fit the data by accident.
Like the P-values for coefficients, values at .05 and lower for Significance are an indication of significance.
Upper and Lower Control Limits
Confidence Factors
At 95%
95% of the data fall within the upper and lower control limit.
The upper limit =
coefficient + (2 * standard deviation)
The lower limit =
coefficient - (2 * standard deviation)
The rage is 4 * standard deviation with the value of the coefficient in the middle.
Calculate the own price elasticity of demand.
The variable (own, cross or income) elasticity of demand is the variable coefficient multiplied by the ratio of the price of the variable over the quantity consumed of the whole function.
So for income elasticity:
- Fill in demand function to derive qty demanded.
- Multiply the income coefficient times ratio of income factor over total demanded.
