1. Motivating the idea of elasticity.

Direction of change:   We know that an increase in the price of a good
                                 will decrease the Qd of that good.

Magnitude of change:  We don’t know if a the change in Qd is large or small
                                   though.  The concept of elasticity allows us to measure the magnitude of changes in one variable caused
                                   by changes in another variable.

For example:  The price elasticity of demand tells us how responsive Qd is to changes in price – if it is very responsive then the change
                      in Qd is said to be large for a given change in price, and if it is very unresponsive then the change in Qd is said to be small
                      for a given change in price.

The elasticity concept is used in economics to measure the responsiveness of one variable to changes in another variable in a number of different contexts.

We will look at, for example:

The price elasticity of demand.
The income elasticity of demand.
The cross-price elasticity of demand.
The price elasticity of supply.
 

2. Price elasticity of demand (N)

Consider the effect of an increase in supply on equilibrium price and quantity of a good.
The Law of supply tells us: An increase in S will lead to a decrease in Pe and an increase in Qe.

The question is:   By how much will price and quantity change?
The answer is: It depends on the price elasticity of demand.

If demand is ELASTIC – Qd is very responsive to changes in P

If demand is INELASTIC – Qd is very unresponsive to changes in P

Graph of two demand curves (insert here):
D2 is flatter than D1.

Q. Which curve is more elastic?
 
 

Q.  How can you show how the effects of an increase in supply on Pe, Qe depend on the price elasticity of demand?
 
 

Definition of price elasticity of demand:
The price elasticity of demand measures the responsiveness of Qd to changes in the price of a good.

a. Measuring price elasticity of demand:

N = % change in quantity demanded / % change in price

Note: comparing changes in price with changes in quantity when they are measured in different units makes it impossible to say anything about magnitudes so we standardize the comparison by looking at % changes in the two variables.

The formula that is used to compute price elasticity of demand when price changes from P1 to P2 and quantity demanded changes from Q1 to Q2 is:

N = (Q2-Q1)/ (Q2+Q1)
      ______________

     (P2-P1)/ (P2+P1)
 

Note: The sign  of  N will be negative because price and quantity demanded move in opposite directions but there is a convention in economics where we ignore the negative sign and focus solely on the magnitude of the elasticity.  So we treat N as a positive number.

N can vary from 0 to infinity.

Graphs of:
a. perfectly elastic demand (N = infinity)
b. perfectly inelastic demand (N = 0)
c. unitary elastic demand (N = 1)
d. elastic demand (N > 1)
e. inelastic demand (N <1)
 

b. Price elasticity of demand along a linear demand curve

Although the slope of the demand curve gives an approximation of elasticity – slope and elasticity are not the same thing.

One way of illustrating that is to show how the price elasticity of demand varies along a linear demand curve.

Note: Slope is constant along a straight line.

Q. Why does the price elasticity of demand fall along a straight line demand curve?

Slope =  change in P /  change in Qd

Elasticity =  change in Qd/ Qd
                  _______
                  change in P/ P

Numerical example from Figure 5-2 in the text:

c. Determinants of price elasticity of demand

The main determinant of the price elasticity of demand is the availability of substitutes for a good.

- a product with close substitutes will tend to have an elastic demand curve
- a product with no close substitutes will tend to have an inelastic demand curve

d. Price elasticity of demand in the short run and in the long run

It generally takes some time to find substitutes for a good.  Thus, the price elasticity of demand will generally vary between the short run and the long run.

Demand for a good will tend to be more price inelastic in the SR than in the LR.
-- the SR demand curve will be more inelastic than the LR demand curve.

Q. Which demand curve for gasoline (D1 or D2) will be the SR demand curve and which will be the LR demand curve?

e. Price elasticity of demand and total expenditure

We know that an increase in the price of a good decreases the quantity that consumers want to buy of that good – but what happens to total expenditures on the good?

The answer is – it depends on the price elasticity of demand.

Total expenditure = P * Q

Change in TE = P * change in Q + Q * change in P

Predicting the change in TE is difficult because the signs of change in Q and change in P are opposite – the question becomes: which effect dominates?

If N > 1  then % change in Qd > % change in P
  The Q effect dominates.

If N < 1 then % change in Qd < % change in P
  The P effect dominates

If N = 1 then the %change in Qd = % change in P
The Q effect and the P effect cancel each other out

The following table summarizes the effect of price elasticity of demand on TE:

                                             Increase in Price                                     Decrease in Price
Demand is elastic                     TE decreases                                         TE increases
Demand in inelastic                  TE increases                                           TE decreases
Demand is unitary elastic         TE unchanged                                         TE unchanged
 

An example: How a better than average crop can lower farmers’ incomes.

3. Other demand elasticities

a. Income elasticity of demand
Income is one of the most important determinants of demand.

Definition of income elasticity of demand:
It measures the responsiveness of the quantity demanded of a good to changes in average consumer income.

Measuring income elasticity of demand:

NY = % change in quantity demanded/ % change in income

For most goods: Increase in income leads to an increase in Qd
These are called normal goods
     NY > 0

For some goods: Increase in income leads to a decrease in Qd
These are called inferior goods
     NY < 0

Among normal goods the magnitude of NY is:
NY <1  income inelastic demand
% change in Qd < % change in income

NY > 1 income elastic demand
% change in Qd > % change in income

Determining income elasticity of demand:

The more basic a good is in a consumer’s consumption patterns the lower the income elasticity of demand.

For example:
Food bought to be prepared at home – income elastic – necessity
Restaurant meals – income inelastic -- luxury

We can graph the relationship between income and Qd, holding all other things constant.

These graphs are called income-consumption curves (insert here)

(i) Income inelastic demand
(ii) Income elastic demand
(iii) Negative elastic demand

b. Cross-price elasticity of demand

Definition of cross-price elasticity of demand:
Measures the responsiveness of the quantity demanded of good x to changes in the price of good y.

Measuring cross-price elasticity of demand:

Nyx = % change in Qdx / % change in Py

A change in the price of good y will cause the demand curve for good x to shift (unless goods x and y are unrelated).

The sign of the cross-price elasticity of demand tells us something about the relationship between two goods:

If x and y are substitutes:
An increase in Py will lead to an increase in Qdx
Nyx >0

If x and y are complements:
An increase in Py will lead to a decrease in Qdx
Nyx < 0

Note:  goods that are in competition with one another will tend to have a large and positive cross-price elasticity of demand.

4. Price elasticity of supply

a. Definition of price elasticity of supply:
It measures the responsiveness of the quantity supplied of a good to changes in its price.

Measuring price elasticity of supply:

Ns = % change in Qs/ % change in P

Note:  The sign of price elasticity of supply will always be positive since Qs and P change in the same direction so it is only the magnitude of the elasticity that we are interested in.

Ns can vary from 0 to infinity

Graphs of:
a. perfectly elastic demand (Ns = infinity)
b. perfectly inelastic demand (Ns = 0)
c. unitary elastic demand (Ns = 1)
d. elastic demand (Ns > 1)
e. inelastic demand (Ns <1)
 

b. Determinants of price elasticity of supply

The ease of substitution in production is the main determinant of the price elasticity of supply.

The easier it is for producers to substitute resources in the production of one good for another good, the more elastic the supply curve will be.
This can also be explained in terms of how steeply the firm’s costs rise with increases in output.  If costs rise rapidly when output rises then the supply curve will be very steep and supply will be price inelastic.

c. Short run versus long run elasticity of supply:

It usually takes some time for a firm to be able to substitute resources in production.

Since there will generally be fewer opportunities for substitution in the SR than in the LR, the SR supply curve will tend to be more inelastic that the LR supply curve.

Q. What will the supply curve look like in the market for wheat when farmers have planted their fields?
 
 

5. Examples of how elasticity matters

a. The incidence of a sales tax

Per unit of output tax t is imposed on a good.
This has the effect of shifting the supply curve up by t.
Graph (insert here)

Q. Who bears the burden of the tax?
 
 
 

Q. How does tax incidence depend on the price elasticities of demand and supply?
 
 

b. Employer provided health insurance

A similar analysis can be applied to the provision of health insurance by employers.

The per worker cost of providing health insurance shifts the supply curve up by t.
Graph (insert here)

Q. Who bears the cost of the employer providing workers will health insurance?
 

c. Illegal drugs

The government has tried many different policies to reduce illegal drug use.

Q. What are examples of demand-side policies (policies to decrease demand for illegal drugs)?

Q. What are examples of supply-side policies (policies to decrease the supply of illegal drugs)?

Q. What effect does the price elasticity of demand for illegal drugs have on the success of demand-side versus supply-side policies?

Graph (insert here).