Elasticity

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