Elasticity
Today: Thinking like an economist requires us to know how quantities change in response to price

Today

Elasticity

Calculated by the percentage change in quantity divided by the percentage change in price

Denominator could be something else, but for now think price
Elasticity

%

Q
%

P

Elasticity




Elasticity is most commonly associated with demand
Percentage changes are typically small when calculating elasticity
Note elasticity is negative, since price and quantity move in opposite directions
We will typically ignore negative sign

Elasticity

Demand elasticity falls into three broad categories



Elastic, if elasticity is greater than 1
Unit elastic, if elasticity is equal to 1
Inelastic, if elasticity is less than 1

Economist questions of the day


How can you maximize the total ticket expenditures on the Santa Barbara
Foresters?
What happens to total expenditures spent on strawberries (or total revenue received by firms) when growing conditions are good?

Inelastic demand


When demand is inelastic, quantity demanded changes less than price does
(in percentage terms)
What goods are unresponsive to price?



Salt
Illegal Drugs?
Coffee

Salt, illegal drugs, and coffee


Why are these goods price inelastic?
Some determinants of price elasticity of demand



Availability of good substitutes
Fraction of budget necessary to buy the item
Age of currently-owned item when considering replacement, if a durable good

Salt, illegal drugs, and coffee

These items do not have good substitutes

Salt  Potassium chloride


Illegal drugs  Legal drugs?
Coffee  Tea, “energy” drinks

Caution




Some economists use the reference point in calculating percentage changes to be the initial price
Other economists use the average of the two prices involved (see Appendix,
Chapter 4)
In this class, you can use either method
I will use the initial price

Example



Suppose the price of apples falls from
$1.00/lb. to $0.90/lb.
This causes the number of apples consumed in Santa Barbara to increase from 2 tons/day to 2.1 tons/day
What is the price elasticity of apples at this point?

Example

%Δ Q


%Δ P


We will ignore the negative on %Δ P

Example


The demand elasticity of apples in
Santa Barbara is thus 0.05/0.1 = 0.5
The demand of apples is inelastic

Algebra lesson for straight-line demand curves
 

Q / Q

P / P

P
Q


Q

P

P
Q

1 slope


Slope on straight line is Δ P /Δ Q
Along a straight line, elasticity is also equal to
P / Q times inverse of the slope (see above)

Why is studying elasticity important?



Suppose that you work for the Santa
Barbara Foresters, the local amateur baseball team
Suppose that in a previous season, a
UCSB student studied demand and elasticity of demand for tickets
You are asked to use this information to maximize ticket expenditures

Some information lost


The student from the previous season only provided the following information


Demand for tickets is nearly linear
A table of estimated elasticity at various prices
You are asked to price tickets to maximize expenditure

How do we solve this?


We need two additional pieces of information

When demand is linear, total expenditure is maximized at the midpoint of the demand curve

We can prove that price elasticity is 1 at the midpoint of the demand curve
Solution: Find the point with price elasticity is 1

Solution: Find price elasticity of 1



Answer: Price each ticket at $5
Is this table consistent with a linear demand curve?
Yes  Try
P = 10 Q
Price
($/ticket)
9
8
5
2
1
Price elasticity
9
4
1
0.25
0.11

Some other important elasticity facts


On a linear demand curve


Elasticity is greater than 1 on the upper half of the curve
Elasticity is less than 1 on the lower half of the curve
Exceptions


Horizontal demand: Elasticity is always ∞
Vertical demand: Elasticity is always 0

Back to increasing expenditure


This is an example of being able to control price (more on this while studying monopoly)
When you can control price and you want to increase expenditure, go in the direction of the highest change

When demand is elastic, %Δ
 Decrease
Q is higher than %Δ P
P to increase expenditures

Inelastic demand, the opposite occurs  Increase
P to increase expenditures

Back to our bumper crop of strawberries



Under normal growing conditions, suppose that S
1 the supply curve is
In the bumper crop season, supply shifts out to S
2
What happens to total expenditure?

Back to our bumper crop of strawberries


Normal growing conditions: Total expenditure is $56 million
However, look at elasticity (note slope is 1):

ε = P/(Q  slope)

ε = 0.29  inelastic



ε = 0.29  inelastic
Expenditure goes
DOWN moving from
S
1 to S
2
The bumper crop of strawberries actually hurts farmers collectively

What is happening here?



The price drops by 50%, while the % increase in strawberries is small
Price change dominates
Assuming costs are the same in both years, farmers will make less profit in the bumper crop year

Elasticity of supply


Supply has elasticity, too
Most of the math is the same or similar to what we have talked about with demand

Summary



Elasticity tells us what happens to total expenditure along the demand curve
On a straight line demand curve, total expenditure is maximized halfway between the vertical intercept and horizontal intercept
Supply shift to the right does not necessarily increase total expenditure