Price Elasticity of Demand Overheads

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How much would your roommate pay to watch a live fight? How does Showtime decide how much to charge for a live fight?

What about Hank and Son’s Concrete? How much should they charge per square foot? Can ISU raise parking revenue by raising parking fees? Or will the increase in price drive demand down so far that revenue falls?

All of these pricing issues revolve around the issue of how responsive the quantity demanded is to price. Elasticity is a measure of how responsive one variable is to changes in another variable?

The Law of Demand The law of demand states that when the price of a good rises, and everything else remains the same, the quantity of the good demanded will fall. The real issue is how far it will fall.

The demand function is given by Q D = quantity demanded P = price of the good Z D = other factors that affect demand

The inverse demand function is given by To obtain the inverse demand function we just solve the demand function for P as a function of Q

Examples Q D = P 2P + Q D = 20 2P = 20 - Q D P = /2 Q D Slope = - 1/2

Examples Q D = P 3P + Q D = 60 3P = 60 - Q D P = /3 Q D Slope = - 1/3

The slope of a demand curve is given by the change in Q divided by the change in P One measure of responsiveness is slope For demand

The slope of an inverse demand curve is given by the change in P divided by the change in Q For inverse demand

Q D = P Examples Slope = - 1/3 Slope = - 3 P = /3 Q D

Q D = P Examples Slope = - 1/2 Slope = - 2 P = /2 Q D

We can also find slope from tabular data QP QQ PP 

QP Demand for Handballs

QP Demand for Handballs Quantity Price P

QP Demand for Handballs Quantity Price  QQ  PP  Q = = -2  P = = 1

Problems with slope as a measure of responsiveness Slope depends on the units of measurement The same slope can be associated with very different percentage changes

Examples Q D = P 2P + Q D = 200 2P = Q D P = /2 Q D

QP Consider data on racquets Let P change from 95 to 96  P = = 1  Q = = -2  QQ PP  A $1.00 price change when P = $95.00 is tiny

Graphically for racquets Demand for Racquets Quantity Price Large % change in Q Small % change in P Slope = - 1/2

Graphically for hand balls Large % change in QLarge % change in P Slope = - 1/2 Demand for Handballs Quantity Price P  P = = 1  Q = = -2

So slope is not such a good measure of responsiveness Instead of slope we use percentage changes The ratio of the percentage change in one variable to the percentage change in another variable elasticity is called elasticity

Own Price Elasticity of Demand The Own Price Elasticity of Demand is given by There are a number of ways to compute percentage changes

Initial Initial point method for computing Own Price Elasticity of Demand The Own Price Elasticity of Demand

Price Elasticity of Demand (Initial Point Method) P Q QQ   PP

Final Final point method for computing Own Price Elasticity of Demand The Own Price Elasticity of Demand

Price Elasticity of Demand (Final Point Method) P Q QQ   PP

The answer is very different depending on the choice of the base point So we usually use The midpoint The midpoint method for computing Own Price Elasticity of Demand The Own Price Elasticity of Demand

Elasticity of Demand Using the Mid-Point For Q D we use the midpoint of the Q’s

Similarly for prices For P we use the midpoint of the P’s

Price Elasticity of Demand (Mid-Point Method) QP

Classification of the elasticity of demand Inelastic demand When the numerical value of the elasticity of demand inelastic is between 0 and -1.0, we say that demand is inelastic.

Classification of the elasticity of demand Elastic demand When the numerical value of the elasticity of demand elastic is less than -1.0, we say that demand is elastic.

Classification of the elasticity of demand Unitary elastic demand When the numerical value of the elasticity of demand unitary elastic is equal to -1.0, we say that demand is unitary elastic.

Classification of the elasticity of demand Perfectly elastic -  D = -  Perfectly inelastic -  D = 0 horizontal vertical

Elasticity of demand with linear demand Consider a linear inverse demand function The slope is (-B) for all values of P and Q For example, The slope is -0.5 = - 1/2

PQ Demand for Diskettes Quantity Price  PP QQ   PP QQ 

The slope is constant but the elasticity of demand will vary PQ  PP QQ 

The slope is constant but the elasticity of demand will vary PQ  PP QQ 

The slope is constant but the elasticity of demand will vary A linear demand curve becomes more inelastic as we lower price and increase quantity P smaller Q larger The elasticity gets closer to zero

QPElasticityExpenditure The slope is constant but the elasticity of demand will vary

QPElasticityExpenditure The slope is constant but the elasticity of demand will vary

Note We do not say that demand is elastic or inelastic ….. We say that demand is elastic or inelastic at a given point

Example Constant with linear demand

Own Price Elasticity of Demand The Own Price Elasticity of Demand Total Expenditure on an Item and Total Expenditure on an Item How do changes in an items price affect expenditure on the item? If I lower the price of a product, will the increased sales make up for the lower price per unit?

Expenditure for the consumer is equal to revenue for the firm Revenue = R = price x quantity = PQ Expenditure = E = price x quantity = PQ

 P = change in price Modeling changes in price and quantity  Q = change in quantity The Law of Demand says that as P increases Q will decrease P  Q 

P = initial price  P = change in price So P +  P = final price Q = initial quantity  Q = change in quantity Q +  Q = final quantity

Initial Revenue = PQ So P +  P = final price = P Q +  P Q + P  Q +  P  Q Q +  Q = final quantity Final Revenue = (P +  P) (Q +  Q)

Now find the change in revenue  R = final revenue - initial revenue = P Q +  P Q + P  Q +  P  Q - P Q =  P Q + P  Q +  P  Q %  R =  R / R =  R / P Q

We can rewrite this expression as follows

Classification of the elasticity of demand Inelastic demand %  Q and %  P are of opposite sign so %  R has the same sign as %  P + -

Classification of the elasticity of demand Inelastic demand %  Q and %  P are of opposite sign so %  R has the same sign as %  P - + Lower price  lower revenue Higher price  higher revenue

Classification of the elasticity of demand Elastic demand %  Q and %  P are of opposite sign so %  R has the opposite sign as %  P Higher price  lower revenue Lower price  higher revenue + -

Classification of the elasticity of demand Unitary elastic demand %  Q and %  P are of opposite sign so their effects will cancel out and %  R =

QPElasticityRevenue Tabular data Elastic Revenue rises Inelastic Revenue falls Price falls

Graphical analysis QPElasticityRevenue Demand for Diskettes Quantity Price Demand A B C P0, Q0 P1, Q1 Lose B, gain A, revenue rises

Graphical analysis QPElasticityRevenue Demand for Diskettes Quantity Price Demand P1, Q1 Lose A, gain B, revenue falls P0, Q0 A B

Factors affecting the elasticity of demand Availability of substitutes Importance of item in the buyer’s budget

Availability of substitutes The easier it is to substitute for a good, the more elastic the demand With many substitutes, individuals will move away from a good whose price increases

Examples of goods with “easy “substitution Gasoline at different stores Soft drinks Detergent Airline tickets Local telephone service

Narrow definition of product The more narrowly we define an item, the more elastic the demand With a narrow definition, there will lots of substitutes

Examples of narrowly defined goods Lemon-lime drinks Corn at a specific farmer’s market Vanilla ice cream Food Transportation

“Necessities” tend to have inelastic demand Necessities tend to have few substitutes

Examples of necessities Salt Insulin Food Trips to Hawaii Sailboats

Demand is more elastic in the long-run There is more time to adjust in the long run

Examples of short and long run elasticity Postal rates Gasoline Sweeteners

Factors affecting the elasticity of demand Importance of item in the buyer’s budget The more of their total budget consumers spend on an item, the more elastic the demand for the good The elasticity is larger because the item has a large budget impact

“Big ticket” items and elasticity Housing Big summer vacations Table salt College tuition

The End