Chapter 3

What is the two important aspects of elasticities?

(1) whether it is positive or negative (2) whether it is greater than 1 or less than 1 in absolute value.

Own price elasticity

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.

Three factors affecting the magnitude of the own price elasticity

Available substitutes, time and expenditure share.

Elastic demand

Demand is elastic if the absolute value of the own price elasticity is greater than 1. (price sensitive + not that steep curve)

Inelastic demand

Demand is inelastic if the absolute value of the own price elasticity is less than 1. (not that price sensitive - steeper curve)

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.

Expenditure Share - own elasticity

Goods that comprise a relatively small share of consumers' budgets tend to be more inelastic than goods for which consumers spend a sizable portion of their incomes.

cross price elasticity - E<0

Indicates complementing goods - an increase in the price of Y leads to a decrease in the demand for X.

What does the absolut value of the elasticity indicate?

It determines how responsive one variable is to changes in the other one

least squares regression (OLS)

The line that minimizes the sum of squared deviations between the line and the actual data points.

MR in relations to own elasticity

The more inelastic the demand for a product, the greater the decline in revenue that results from the increased quantity demanded that results from a price cut.

Many substitutes - own elasticity

The more substitutes available for the good, the more elastic the demand for it (the more price sensitive people are)

Income elasticities and inferior goods

When X is an inferior good, an increase in income leads to a decrease in the consumption of X - E<0 when X is an inferior good

Income elasticities and normal goods

When good X is a normal good, an increase in income leads to an increase in the consumption of X - E>0 when X is a normal good

cross price elasticity - E>0

indicates substituting goods - an increase in the price of Y leads to an increase in the demand for X

The cross-advertising elasticity between goods X and Y

measures the percentage change in the consumption of X that results from a given percentage change in advertising directed toward Y.

Elasticities formula for Linear Demand

pp. 91

Log-linear demand Demand is log- linear if the logarithm of demand is a linear function of the logarithms of prices, income, and other variables. When you have a multiplicative model (gange)

s. 93 if its a log transformed demand function, then det coefficients (beta) is the elasticities.

Perfectly inelastic demand

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

What characterizes the relationship between the two variables if the elasticity is negative?

An increase in one leads to a decrease in the other one.

What characterizes the relationship between the two variables if the elasticity is positive?

An increase in one leads to an increase in the other one.

Log-linear demand - interpretation

As in the case of linear demand, the sign of the coefficient of ln Py deter- mines whether goods X and Y are substitutes or complements, whereas the sign of the coefficient of ln M determines whether X is a normal or an inferior good. For example, if b is a positive number, an increase in the price of good Y will y lead to an increase in the consumption of good X; in this instance, X and Y are substitutes. If by is a negative number, an increase in the price of good Y will lead to a decrease in the consumption of good X; in this instance, goods X and Y are complements. Similarly, if bM is a positive number, an increase in income leads to an increase in the consumption of good X, and X is a normal good. If bM is a negative number, an increase in income leads to a decrease in the consumption of good X, and X is an inferior good.

If the absolute value of the elasticity is greater than 1

Small percentage change in S will lead to a relatively large percentage change in G.

Arc elasticity

(P1+P2)/2 (Q1/Q2)/2 Average

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.

Total Revenue Test

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.

Unitary elastic demand

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

Time - own elasticity

Demand tends to be more inelastic in the short term than in the long term - time allows the customers to seek out available substitutes. Notice that all the short-term elasticities are less (in absolute value) than the corresponding long-term elasticities

Firms with elastic demand lowering prices.

If demand is elastic, a price cut results in a greater than proportional increase in sales and thus increases the firm's total revenues

What do an elasticity measure?

The responsiveness of one variable to changes in another variable: the percentage change in one variable that arises due to a given percentage change in another variable.

If the absolute value of the elasticity is less than 1

a given percentage change in S will lead to a relatively small percentage change in G

Few substitutes - own elasticity

When there are few close substitutes for a good, demand tends to be relatively inelastic (the less price sensitive people are)