1. Price Elasticity of Supply and Applications of the Elasticity Concepts
Module 10
Price Elasticity of Supply and Applications of the Elasticity Concepts

2. Objectives:
Define the price elasticity of supply, understand why it is useful, and how to calculate it. 
Understand how to use the elasticity concepts to analyze economic issues.
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3. Objective 1: Define the price elasticity of supply, understand why it is useful….
The price elasticity of supply measures the responsiveness of the quantity supplied to changes
in price.
For example, consider the supply
curve S1. If price rises from $8 to $10, quantity supplied rises from Qa to Q1.
If the supply curve is S2, then when price rises, quantity supplied rises by a larger amount from Qa to Q2.
The price elasticity of supply focuses on this responsiveness.

4. Objective 1: ….how to calculate the price elasticity of supply
The price elasticity of supply is given by the formula:
Because of the law of supply, the price elasticity of supply will have a positive numerical value.

5. Objective 1: calculating the price elasticity of supply
Example 1: Suppose quantity supplied increases by 12% when price rises by 6%. What is the price elasticity of supply?
Solving the Problem
Apply the elasticity formula:

6. %∆ in Quantity Supplied = Price Elasticity of Supply x %∆Price
Objective 1: understanding the price elasticity of supply
The price elasticity of supply = 2. What does the number 2 mean?
Let’s go back to the elasticity formula and rearrange the
equation by cross multiplying.
%∆ in Quantity Supplied = Price Elasticity of Supply x %∆Price
= 2 x %∆Price
For every 1% increase in price, quantity supplied increases by 2% or for every 1% decrease in price, quantity supplied decreases by 2%. 6

7. Objective 1: calculating the price elasticity of supply
Example 2: When the price of milk rose from $2.00 to $2.20, quantity supplied increased from 100 million gallons to 120 million gallons. Calculate the price elasticity of supply using the midpoint formula.
Solving the Problem
Essentially, we are given two price-
quantity combinations:
Pa = $2.00; Qa = 100 million gallons
Pb = $2.20; Qb = 120 million gallons
We need to apply these values to the midpoint formula.

8. Objective 1: Calculating the price elasticity of supply
using the midpoint formula

9. Objective 1:….using the midpoint formula
Now plug in the given two price-quantity combinations:
Pa = $2.00; Qa = 100 million gallons
Pb = $2.20; Qb = 120 million gallons
The average price elasticity of supply in this segment of the supply curve is 1.91

10. Objective 1…describing the price elasticity of supply
Elastic Supply occurs when percentage change in the quantity supplied is greater than the percentage change in price.
Inelastic Supply occurs when percentage change in the quantity supplied is less than the percentage change in price. 10

11. Objective 1…describing the price elasticity of supply
Along the usual upward sloping supply curve that does not pass through the origin, meaning there is a positive vertical intercept, the elasticity of supply declines as quantity supplied increases.
The elasticity of supply declines as we move up the supply curve.

12. Objective 1…describing the price elasticity of supply
A supply curve that is a ray from the origin is a unit elastic supply curve. The price elasticity of supply is 1
at any point on the supply curve.
Price elasticity is 1at any point on
The supply curve

13. Objective 1…describing the price elasticity of supply
Perfectly inelastic supply occurs when a change in price results in no change in quantity supplied.
s = 0  Supply is perfectly inelastic.
Quantity supplied is fixed and therefore the supply curve is vertical. Examples include the number of original Picasso Paintings, the number of seats in an Opera Hall, and the number of ocean front lots at a given point in time.

14. Objective 1…describing the price elasticity of supply
Perfectly elastic supply occurs when a change in price results in an infinite change in quantity supplied.
s = ∞  Supply is perfectly elastic.
Whenever additional units of a good can be produced by using the same input combination, purchased at the same input prices as the current input prices, the supply curve will be perfectly elastic. For example, a telemarketer producing “telemarketing sales calls”.

15. Objective 2
Understand how to use the elasticity concepts to analyze economic issues
Application 1
The U.S. government's focus on supply reduction efforts in its much publicized “war on drugs” has been relatively unsuccessful at addressing illegal drug use. Some economists believe that a successful anti-drug program must concentrate on reducing demand, for example, through drug education and voluntary treatment programs for addicts.

16. a. Suppose the price elasticity of demand for cocaine is -0. 5
a. Suppose the price elasticity of demand for cocaine is What will happen to the equilibrium price, quantity and total expenditures on cocaine if the government succeeds in its efforts to reduce demand? What is likely to happen to the incentive to traffic cocaine?
The price elasticity of demand for cocaine is -0.5  demand is relatively inelastic
Suppose government succeeds in reducing demand  equilibrium price ↓ and equilibrium quantity ↓.
What happens to total expenditure on cocaine? If price↓, total expenditure ↓ because demand is price inelastic.
What happens to incentive to traffic cocaine? ↓ Reduced revenues is likely to deter drug trafficking. 16

17. b. Suppose the government continues to concentrate its efforts on supply reduction and is able to reduce the supply of cocaine. As a result of the reduction in supply the price of cocaine soars by 25 percent. If the price elasticity of demand is -0.5, what is likely to happen to the incentive to traffic cocaine?
Suppose government succeeds in reducing supply  equilibrium price ↑ and equilibrium quantity ↓.
What happens to total expenditure on cocaine? If price↑, total expenditure ↑ because demand is price inelastic.
What happens to incentive to traffic cocaine? ↑ Increased revenues raises the incentive to traffic cocaine.

18. Objective 2: Using the elasticity concepts to analyze economic issues
Example 1, continued
c. Based on your answers, explain why one approach might be preferred over the other.
If people respond to incentives, the government will be more successful at achieving the goal of reducing cocaine consumption if it uses anti-drug programs that concentrate on reducing demand rather than programs that concentrate on reducing supply

19. Objective 2: Using the elasticity concepts to analyze economic issues
Application 2
A study of the effects of the minimum wage on employment of low-skilled workers estimated the price elasticity of demand for low-skilled workers is Suppose that the government is considering raising the minimum wage from the current $6.00 per hour to $6.50 per hour. Based on this information, calculate the percentage change in the employment of low skilled workers. Use the midpoint formula.

20. Objective 2: …..analyze economic issues
Consider the given information:
the price elasticity of demand for low-skilled workers is
the government is considering raising the minimum wage from the current $6.00 per hour to $6.50 per hour.
calculate the percentage change in the employment of low skilled workers using the midpoint formula. 20

21. Objective 2: …..analyze economic issues
Solving the problem
Step 1: Use the midpoint formula to calculate the %∆Wage
%Wage = {[( ) ÷ [½ ( )]} x 100 = 8%
Step 2: Solve for % in labor using the elasticity formula.
Price Elasticity of demand = %∆Quantity of labor demanded ÷ %∆Wage
% in Quantity of labor demanded = Price Elasticity of demand x %Wage
= −0.75 x 8%
= −6%
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22. Objective 2: …..analyze economic issues
Application 3: Determining How the Burden of Tax is Shared
If the price elasticity of demand (in absolute terms) is higher than the price elasticity of supply, then buyers are more willing to do without the product and will avoid most of the tax. Thus, the consumers’ burden of the tax is less than the producers’ burden.
If the price elasticity of supply is higher than the price elasticity of demand elasticity (in absolute terms), then, sellers are more responsive to price changes and can avoid most of the tax. Thus, the consumers’ burden is greater than the producers’ burden.
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23. Application 3, Example 1: Determining How the Burden of Tax is Shared
Consider the cigarette market. Suppose at “e”, the absolute value of the price elasticity of demand is 0.7 and the price elasticity of supply is 1.1. Now a per-unit tax is imposed on every unit sold. How is the tax burden shared?
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24. Application 3, Example 1
Since the price elasticity of supply > price elasticity of demand
(in absolute value), the consumer’s burden is greater than the producer’s burden. You can verify this by shifting the supply curve upwards by the full amount of the tax. The vertical distance jk represents the amount of the tax. Observe how the tax burden is shared.
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25. Application 3, Example 2: Determining How the Burden of Tax is Shared
Consider a market in which supply is perfectly elastic and the demand curve is the usual downward-sloping curve. If a $0.20 unit tax is imposed in this market, how is the tax burden shared?

26. Application 3, Example 2
At point f the price elasticity of supply is infinity and the absolute value of the price elasticity of demand is less than infinity. In this case, consumers bear the entire burden of the tax.
You can verify this by noting that after the imposition of the $0.20 unit tax, consumers pay $2.20. Suppliers receive $2.20 but must give $0.20 to the tax authorities, leaving them with a net price of $2.00 – exactly the same as the amount received before the imposition of the tax. 26