Download Overview I. The Elasticity Concept II. Demand Functions II

Overview
I.
The Elasticity Concept
- Own Price Elasticity
- Elasticity and Total Revenue
- Cross-Price Elasticity
- Income Elasticity
II. Demand Functions
- Linear
- Log-Linear
II.
Regression Analysis
The Elasticity Concept
I How responsive is variable G to a change in variable S
Elasticity is dimensionless measure, i.e. it does not depend on
the units in which we measure G and S.
Two aspects of an elasticity are important: (1) whether it positive
or negative and (2) whether it is greater than 1 or less than 1 in
absolute value
Sign:
If EG;S > 0, then S and G are directly related.
If EG;S < 0, then S and G are inversely related.
If EG;S = 0, then S and G are unrelated.
Formal Definition of Elasticity
An alternative way to measure the elasticity of a function
G = f (S) is
I Sign:
If EG;S > 0, then S and G are directly related.
If EG;S < 0, then S and G are inversely related.
If EG;S = 0, then S and G are unrelated.
Own Price Elasticity of Demand
Measures responsiveness of quantity demanded to a change in
price:
Should be negative according to the “law of demand.”
Absolute value:
Demand is elastic if:
Demand is inelastic if:
Demand is unitary elastic if:
If demand is perfectly elastic, raising price even slightly will result
in situation where none of the good is purchased.
If demand is perfectly inelastic, consumers do not respond at all
to changes in price.
Own-price Elasticity and Revenue
Profits = Revenue - Cost = Price x Quantity – Cost
Suppose that you have invented a product which can be
produced costlessly: Cost = 0.
Revenue function: R (p) = p. Q (p)
You have commissioned a study of market demand, and they
report that if you price the product at p you will sell Q units.
Further, the own-price elasticity of demand is .
How many units Q_ should you sell to maximize revenue (profits)?
Changes in Price, Own-Price Elasticity, and Total Revenue
Relationship among changes in price, own-price elasticity, and
total revenue is called the total revenue test:
Elastic demand
– Increase (a decrease) in price leads to a decrease (an increase) in
total revenue.
Inelastic demand
– Increase (a decrease) in price leads to an increase (a decrease) in
total revenue.
Unitary elastic demand
– Total revenue is maximized at the point where demand is unitary
elastic.
Demand, Marginal Revenue (MR) and Elasticity
How is marginal revenue linked to own-price elasticity of
demand?
Factors Affecting the Own-Price Elasticity
Available Substitutes
– The more substitutes available for the good, the more elastic the
demand.
– Broadly defined commodities tend to be more inelastic than the
demand for specific commodities.
Time
– Demand tends to be more inelastic in the short term than in the long
term.
– Time allows consumers to seek out available substitutes.
Expenditure Share
– Goods that comprise a small share of consumer’s budgets tend to be
more inelastic than goods for which consumers spend a large portion of
their incomes.
Cross-Price Elasticity of Demand
A measure of the responsiveness if the demand for a good to
changes in the price of a related good:
When the demand function is
the crossprice elasticity of demand between goods X and Y may be found
using calculus:
Predicting Revenue Changes from Two Products
Cross-price elasticities important in pricing decisions of firms that
sells multiple products. Suppose that a firm sells two related
goods, X and Y.
Income Elasticity
A measure of the responsiveness of demand for a good to
changes in consumer income; the percentage change in quantity
demanded by the percentage change in income.
Uses of Elasticities
Pricing.
Managing cash flows.
impact of changes in competitors’ prices.
Impact of economic booms and recessions.
Impact of advertising campaigns.
Example 1: Pricing and Cash Flows
I According to an FTC Report by Michael Ward, AT&T’s own price
elasticity of demand for long distance services is -8.64.
I AT&T needs to boost revenues in order to meet it’s marketing
goals.
I To accomplish this goal, should AT&T raise or lower it’s price?
Answer: Lower price!
I Since demand is elastic, a reduction in price will increase
quantity demanded by a greater percentage than the price
decline, resulting in more revenues for AT&T.
Example 2: Quantifying the Change
I If AT&T lowered price by 3 percent, what would happen to the
volume of long distance telephone calls routed through AT&T?
Answer: Calls Increase!
Calls would increase by 26 percent!
Example 3: Impact of a Change in a Competitor’s Price
According to an FTC Report by Michael Ward, AT&T’s cross
price elasticity of demand for long distance services is 9.06.
If competitors reduced their prices by 4 percent, what would
happen to the demand for AT&T services?
Answer: AT&T’s Demand Falls!
AT&T’s demand would fall by 36 percent!
Interpreting Demand Functions
Mathematical representations of demand curves. Example:
Law of demand holds (coefficient of Px is negative).
X and Y are substitutes (coefficient of Py is positive).
X is an inferior good (coefficient of M is negative).
Elasticities for Linear Demand Functions
If the demand function is linear and given by:
Note that for a linear demand curve, value of elasticity depends
on the particular price-quantity point at which it is calculated.
Example of Linear Demand