Elasticity

1
Elasticity

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

2
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

3
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

4
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

5
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?

6
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

7
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

8
Salt, illegal drugs, and coffee

• These items do not have good substitutes
• Salt ? Potassium chloride
• Illegal drugs ? Legal drugs?
• Coffee ? Tea, energy drinks

9
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

10
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?

11
Example

• ?Q
• ?P
• We will ignore the negative on ?P

12
Example

• The demand elasticity of apples in Santa Barbara
  is thus 0.05/0.1 0.5
  
• The demand of apples is inelastic

13
Algebra lesson for straight-line demand curves

• Slope on straight line is ?P/?Q
• Along a straight line, elasticity is also equal
  to P/Q times inverse of the slope (see above)

14
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

15
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

16
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

17
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

18
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 8
• Vertical demand Elasticity is always 0

19
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, ?Q is higher than ?P ?
  Decrease P to increase expenditures
  
• Inelastic demand, the opposite occurs ? Increase
  P to increase expenditures

20
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?

21
Back to our bumper crop of strawberries

• e 0.29 ? inelastic
• Expenditure goes DOWN moving from S1 to S2
• The bumper crop of strawberries actually hurts
  farmers collectively

• Normal growing conditions Total expenditure is
  56 million
  
• However, look at elasticity (note slope is 1)
• e P/(Q ? slope)
• e 0.29 ? inelastic

22
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

23
Elasticity of supply

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

24
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