Econ 201Spring 2009Lecture 4.1

Elasticity

Taxes & Subsidies

4-28-09

Demand Elasticity Calculation• Economist use the price elasticity of demand

to summarize how responsive quantity demanded is to price

• Demand curves are not always linear; and responsiveness can change with price

%

%dchangein Q

elasticitychangein price

Overview of Elasticity

• Own-price demand elasticity

• Measures movement (Qd) along the demand curve in response to a change in the (own) price of the good

• Cross-price demand elasticity– Measures change in Qd

due to a shift in demand

( / ) /( / )d dxx x x x xQ Q P P

( / ) /( / )d dxx x x x xQ Q P P

( / ) /( )d dxy x x y yQ Q P P

Demand Elasticityfor the linear demand curve

price per unitQd Num (Q) Den (P) Ed$10 1$9 2 -1 0.10 -10$8 3 -0.5 0.11 -4.5$7 4 -0.33333 0.13 -2.66667$6 5 -0.25 0.14 -1.75$5 6 -0.2 0.17 -1.2$4 7 -0.16667 0.20 -0.83333$3 8 -0.14286 0.25 -0.57143$2 9 -0.125 0.33 -0.375$1 10 -0.11111 0.50 -0.22222

Demand Elasticity

-12

-10

-8

-6

-4

-2

0

$10 $9 $8 $7 $6 $5 $4 $3 $2

ElasticityP

rice Ed

Calculating Elasticity• Elasticity is calculated at a point on the demand curve

– Several choices:• Initial point, final point, average (arc) elasticity

– At $5 -> Qd = 6; At $6 ->Qd = 7– Elasticity of demand (intital point):

1 2 1

1 2 1

( ) / (6 7) / 6 ( 1/ 6) 5

( ) / ($5 $4) / $5 (1/ 5) 6d Q Q Q

P P P

Why Bother?

• Own-price elasticity tells us how responsive quantity demanded is to price changes– Affect’s a firm’s

revenues & profitability– Affect’s pricing

strategy

Demand for Eggs

0

10

20

30

40

50

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32

# Eggs per month

$ P

er D

oze

n

Individual A

Individual B

What Affects (Own) Price Elasticity

• Availability and closeness of substitutes– Fewer close substitutes -> inability to shift

consumption to other goods -> can only decrease current consumption

• Demand will be more inelastic

• Proportion of Income– Lower % of income -> lower price sensitivity -

> lower price responsiveness (inelastic)• Affordability study

What Does Cross-price Elasticity Tell Us?

• Sign of cross-price elasticity is important– (+) sign -> increases in price (Py) of other

good results in an increase in consumption of this good (Qx)

• Shifts demand for X to the right -> substitute

– (-) sign -> increase in Py results in decrease in Qx

• Shifts demand for X to the left -> complement

More on Cross-Price

• Magnitude of the shift (or elasticity) tells us:– If a substitute

• How close/good a substitute– Closer substitute -> bigger shift in demand for X

» Larger cross-price elasticity

– If a complement• How important it is to “joint” consumption

– E.g. if “fixed proportions” -> bigger shift in demand for X» Large (absolute) cross-price elasticity

Why Else It Might Be Useful

• Firm’s perspective– Strategic:

• Substitutes: allows us to anticipate changes in demand to competitors prices

• Complements: allows us to anticipate the impact of changes in prices of suppliers on the demand for our product

• Policy Evaluation– Evaluate impact of taxes used to subsidize

other goods/services

Evaluating the Impact of Government Intervention

• Policy Instruments Available– Taxes

• Typically: per-unit tax on output• Others: lump-sum, value added (VAT)

– Subsidies• Rebate on per-unit produced

– Price Floors• Minimum price that can be charged (e.g., minimum wage)

– Price Ceilings• Limit on the maximum price that can be charged (WIN)

– Quotas• Limits on amounts produced/imported • Infant industry/protectionism

Key Assumptions

• No Market Failure– No externalities

• i.e., benefits or costs that are not accounted for in the marketplace (e.g., no free riders, no pollution costs that aren’t captured in the product’s price)

– Perfectly competitive markets• Large # of suppliers and buyers

• Evaluate Market Efficiency– Look at losses/gains in consumer/producer

surplus

Effect of a Tax on the Supply Curve

• To the supplier: increases per-unit costs– Shifts supply curve to the left

• Reduces amount supplied and raises the market clearing price

• How do we measure the effects of the tax?– Efficiency or deadweight losses are losses in

consumer and producer surplus relative to the “ideal” market

How Do We Analyze the Effects of Taxes and Subsidies

• The efficient ideal market– “perfectly competitive” market

• Consumers and suppliers are price-takers, i.e. have no market power

Effect of a Tax on the Supply Curve

Deadweight Loss

How Do We Evaluate the Impact of a Tax?

• Framework for analysis is comparing benefits and costs– Costs of the tax

• Reduction in equilibrium quantity • Increase in price paid

– Costs can be calculated as the deadweight loss in $ if demand and supply curves are known

What Are the Benefits?

• Depends on what we do with the taxes– Suppose we use it to subsidize another good

• Subsidy appears as a reduction in per-unit costs to the firm getting the subsidy

Figure A-1. The Deadweight Loss from a Price Subsidy

SOURCE: Congressional Budget Office.

Evaluating The Impact

• Costs:– Deadweight loss: sum of reduction in consumer and

producer surplus for the taxed good• Reflects reduction in Qd and higher price paid

• Benefits– Gain in CS and PS from subsidized cost

• Will Benefits > Tax– Depends on the relative demand elasticities for the 2

goods

Evaluating the Impact

• “A Positive Analysis” (Distributional Consequences)– Who gains/loses from the tax and subsidy?– Both producers and consumers of the taxed

good lose (in terms of lost surpluses)– Relative demand/elasticities determine who loses most

» More inelastic demand -> greater is CS loss

– Producers and Consumers of subsidized good win (lower price and more Q)

– Relative demand supply elasticities determine who benefits most

Total Social Welfare

• Ideally the impact of a program should be evaluated as: {Pareto efficient}

– 1) can any one (or more) person’s welfare be improved

– 2) without any one else’s welfare being reduced– http://en.wikipedia.org/wiki/Pareto_efficiency

• More realistically: Could the winners compensate the losers? {Pigouvian}

– Is the deadweight loss of the taxed good less than the surplus gain from the subsidized good?

– http://en.wikipedia.org/wiki/Pigovian_tax

So Do They Do This in the Real World?

• The Senate has approved a bill that would require gasoline producers to blend 36 billion gallons of ethanol into gasoline by 2022, an increase from the current standard of 7.5 billion gallons by 2012. The House did not include such a provision in the version it passed, and it is uncertain whether any final legislation will emerge this year and what it will say about ethanol if it does.

• What would be the impact of such legislation on the demand for ethanol? For corn-based food prices?