1 Price elasticity of demand and revenue implications Often in economics we look at how the value of one variable changes when another variable changes. The concept called elasticity is a summary statement about those changes.

2 Percentage change examples Say you put $1 in the bank and at the end of the year you have $2 (this is a special bank!). The percentage change in the amount of money in your account is found by the basic formula (end value – start value) divided by start value and we have (2 – 1)/1 = 1 (and you could multiply by 100 to say 100 percentage increase.

3 Elasticity The law of demand or the law of supply is a statement about the direction of change of the quantity demanded, or supplied, respectively, when there is a price change. The concept of elasticity adds to these concepts by indicating the magnitude of the change in quantity, given the price change. The magnitude of the change is reported in percentage terms.

4 own price elasticity of demand Ed = (% change in Q)/(% change in P) by definition. As an example, if Ed = -2 we say for every 1 % change in the price of the good the quantity demand changed in the opposite direction by 2 %. The % change can be calculated as(for the change in Q) Q2 - Q1 Q1 Note Q2 is the later value, Q1 is the earlier value.

5 Elasticity example P Q D As the price falls from 10 to 9, the quantity rises from 1 to 2. The elasticity of demand is (2-1)/1 (9-10)/10 = - 10/1 The price elasticity of demand is a negative number because P and Q move in opposite directions.

6 absolute value You may recall a function in math called the absolute value. Basically this function makes negative values positive and leaves positive values positive. In the notes I will write abs( ) to mean take the absolute value. The own price elasticity of demand is a negative number, so we will take the absolute value to describe some concepts about it.

7 Elasticity can have three basic values If abs(Ed) > 1 we say demand is elastic. This means the % change in the Qd is greater than the % change in price. If abs(Ed) = 1 we say demand is unit elastic. This means the % change in the Qd is equal to the % change in price. If abs(Ed) < 1 we say demand is inelastic. This means the % change in the Qd is less than the % change in price.

8 Elasticity again P Q P1 P2 Q1 Q2 In the upper left of the demand curve the % change in the Qd is greater than the % change in the P and thus the Ed > 1. Without a real formal proof of the above statement, we can see the % change in Qd is about 100 % and the % change in P is less than 100 %. Demand is elastic here.

9 Elasticity has several ranges of values P Q P1 Q1 Q2 In the lower right of the demand curve the % change in the Qd is less than the % change in the P and thus the Ed < 1. Without a real formal proof of the above statement, we can see the % change in Qd is less than 100 % and the % change in P is about 100 %. Demand is inelastic here. P2

10 Elasticity has several ranges of values P Q P1 Q1 Q2 In the middle of the demand curve the % change in the Qd is equal to the % change in the P and thus the Ed = 1. Without a real formal proof of the above statement, we can see the % change in Qd is about equal to the % change in P. Demand is unit elastic here. P2

11 Elasticity of supply The elasticity of supply is used to indicate the percentage change in the quantity supplied given a percentage change in price. The elasticity of supply is calculated in a manner similar to the demand elasticity we have seen and has a similar interpretation in terms of the range of values the elasticity might take, i.e. elastic, inelastic and unit elastic.

12 Special Case – vertical curve P Q P1 P2 Q1

13 Special case Let’s say the curve on the previous slide is a supply curve. What we see here is that when the price rises from P1 to P2 the quantity supplied stays at Q1 (or you could say Q1 = Q2). The reason for this is that a capacity limit has been reached so that physically no more can be produced in the time frame of interest in our story. Maybe at lower prices an upward slope may occur, but at some point the supply curve becomes vertical. An example of this would be at a major college sports stadium where there are only so many seats available. For the game this Saturday there are only so many seats available.

14 Special case – perfect inelasticiy The elasticity of supply is calculated (Q2 minus Q1)divided by Q1 and then this all divided by (p2 minus P1) divided by P1. Since Q2 = Q1 in this special case the elasticity of supply is zero. A change in price leads to a zero change in the quantity supplied. In this case the elasticity is said to be perfectly inelastic and the meaning is that there is an inability of the quantity supplied to change here (like a physical limit has been reached).

15 The Paradox resolved P Q P1 P2 Q1 S D Mantle D Aaron

16 The Paradox resolved In the case of baseball cards with Aaron and Mantle we are assuming that the same number of each player card was made. Note, I could have two graphs here with the same supply and the demand in the appropriate graph. Since Mantle played in New York and Aaron played in Atlanta and Milwaukee, Mantle likely had a greater number of fans and with New York likely being wealthier means the demand for Mantle cards is higher than for Aaron cards. The authors also suggest that maybe due to prejudices that some have that taste and preferences for Aaron cards are lower. This last point shows that even unsavory cultural elements can have an economic impact.