Econ 520: Chapter 3

perfectly elastic demand

Demand is perfectly elastic if the own price elasticity is infinite in absolute value. In this case the demand curve is horizontal.

perfectly inelastic demand

Demand is perfectly inelastic if the own price elasticity is zero. In this case the demand curve is vertical.

unitary elastic demand

Demand is unitary elastic if the absolute value of the own price elasticity is equal to 1.

cross-price elasticity formula

EQdxPy = %change Qdx / %change Py

Calculation Analysis: Given Qd and Px columns - How do you find Elasticity?

EQx,Px = %change in Qd / % change in Px = (Q2-Q1/Q2) / (P2-P1/P2)

arc elasticity of demand

Finds the elasticity of demand by dividing by the averages of each component. The change in Q demanded x average P / the change in P x average Q. In the formula, the average Q is (Q1 + Q2)/2 and the average P is (P1 + P2)/2.

Cross-price Elasticity Analysis: Elasticity < 0 (negative)

Goods X and Y are complements, an increase in the price of Y leads to a decrease in the demand for X.

Cross-price Elasticity Analysis: Elasticity > 0 (positive)

Goods X and Y are substitutes, an increase in the price of Y leads to an increase in the demand for X

iid normal assumption

independently and identically distributed normal random variables

statistical inference

we infer information about the population by looking at the sample in front of us

parameter estimates

â and b hat, represent the values of a and b that result in the smallest sum of squared errors between a line and the actual data.

2 important aspects of elasticity

1. whether its positive or negative 2. whether its greater than 1 or less than one in absolute value

log-linear demand

Demand is log-linear if the loga-rithm of demand is a linear function of the logarithms of prices, income, and other variables.

elasticity

A measure of the responsiveness of one variable to changes in another variable; the per-centage change in one variable that arises due to a given percentage change in another variable. - specifically, we measure "responsiveness of consumers"

income elasticity

A measure of the responsiveness of the demand for a good to changes in consumer income; the percentage change in quantity demanded divided by the percentage change in income.

cross-price elasticity

A measure of the responsiveness of the demand for a good to changes in the price of a related good; the percentage change in the quantity demanded of one good divided by the percentage change in the price of a related good.

own price elasticity of demand

A measure of the responsiveness of the quantity demanded of a good to a change in the price of that good; the percentage change in quantity demanded divided by the percentage change in the price of the good.

regression analysis

A technique that produces an equation that "fits" the data better than any other

F-statistic

An F statistic is a value you get when you run an ANOVA test or a regression analysis to find out if the means between two populations are significantly different.

elastic demand

Demand is elastic if the absolute value of the own price elasticity is greater than 1.

inelastic demand

Demand is inelastic if the absolute value of the own price elasticity is less than 1.

regression line

Linear Regression. ... A linear regression line has an equation of the form Y = a + bX, where X is the explanatory variable and Y is the dependent variable. The slope of the line is b, and a is the intercept (the value of y when x = 0).

Calculation Analysis: Given Qd and Px columns - How do you find Marginal Revenue?

MR = Change in TR/ Change in Q

multiple regression

Multiple regression is an extension of simple linear regression. It is used when we want to predict the value of a variable based on the value of two or more other variables. The variable we want to predict is called the dependent variable (or sometimes, the outcome, target or criterion variable).

own advertising elasticity

Own advertising elasticity of demand for good X is the ratio of the percentage change in the consumption of X to the percentage change in advertising spent on X.

Calculation Analysis: Given Qd and Px columns - How do you find Total Revenue?

TR = Price x Quantity

adjusted R-square

The adjusted R-squared is a modified version of R-squared that has been adjusted for the number of predictors in the model.

Marginal Revenue

The change in revenue attributable to the last unit of output; for a competitive firm, MR is the market price.

coefficient of determination

The coefficient of determination (denoted by R2) is a key output of regression analysis. It is interpreted as the proportion of the variance in the dependent variable that is predictable from the independent variable. ... An R2 between 0 and 1 indicates the extent to which the dependent variable is predictable.

least squares regression line

The line that minimizes the sum of squared deviations between the line and the actual data points. --> Y = a + bx + e ----> Y = ^a+^bX

Demand is perfectly inelastic if the own price elasticity is zero. In this case the demand curve is vertical.

The ratio of the value of a parameter estimate to the standard error of the parameter estimate.

T-statistic

The ratio of the value of a parameter estimate to the standard error of the parameter estimate.

standard error

The standard error of each estimated coefficient is a measure of how much each estimated coefficient would vary in regressions based on the same underlying true demand relation, but with different observations. The smaller the standard error of an estimated coefficient, the smaller the variation in the estimate given data from different outlets (different samples of data).

econometrics

The statistical analysis of economic phenomena.

cross-advertising elasticity

This elasticity between goods X and Y would measure the % change in consumption of X that results from a 1 % increase in advertising towards Y

total revenue test

This relationship among the changes in price, elasticity, and total revenue. If demand is elastic, an increase (decrease) in price will lead to a decrease (increase) in total revenue. If demand is inelastic, an increase (decrease) in price will lead to an increase (decrease) in total revenue. Finally, total revenue is maximized at the point where demand is unitary elastic.

Income Elasticity Analysis: Elasticity < 0 (negative)

X is a normal good, an increase in income leads to an increase in the consumption of X.

Income Elasticity Analysis: Elasticity < 0 (negative)

X is an inferior good, an increase in income leads to a decrease in the consumption of X.

confidence interval

a range of values so defined that there is a specified probability that the value of a parameter lies within it.

R-square

also called the coefficient of determination) tells the fraction of the total variation in the dependent variable that is explained by the regression. It is computed as the ratio of the sum of squared errors from the regression (SSRegression) to the total sum of squared errors (SSTotal):

Determinants affecting own price elasticity

available substitutes, time, and expenditure share (% of consumers income spent on good) substitutes - more subs = more elastic time - more time = more elastic greater % of budget = more elastic