Elasticity Today: Thinking like an economist requires us to know how quantities change in response to price
Feb 25, 2016
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
PQElasticity
%%
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 %ΔQ
%ΔP
We will ignore the negative on %ΔP
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
Slope on straight line is ΔP/ΔQ Along a straight line, elasticity is also equal
to P/Q times inverse of the slope (see above)
slopeQP
PQ
QP
PPQQ 1//
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)
Price elasticity
9 9
8 4
5 1
2 0.25
1 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, %ΔQ is higher than
%ΔP Decrease 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 S1 is the supply curve
In the bumper crop season, supply shifts out to S2
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 S1 to S2
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