1Elasticity and Surplus

Chapter 3

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You Are Here

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Elasticity

• One of the most important concepts in economics is elasticity• The elasticity of demand and elasticity of supply are

basically the slope of the supply and demand curve• They are very important for determining the

magnitudes of interventions• Formally

Elasticity=

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• One kind of annoying thing about this is the P and the Q

• If it were just: it would just be the slope of the curve

• For all intensive purposes this is what it is• Ignoring (or conditioning on Q and P) the larger is

the slope the larger is the elasticity.• Lets focus on the elasticity of demand.• I am going to use straight lines because it is the

easiest to think about• With a linear demand curve elasticity is technically

greater at higher prices but lets not worry about that

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Elasticity Labels

• Elastic : the condition of demand when the percentage change in quantity is larger than the percentage change in price• Inelastic: the condition of demand when the percentage change in quantity is smaller than the percentage change in price• Unitary Elastic: the condition of demand when the percentage change in quantity is equal to the percentage change in price

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P

Q

Medium (Unitary) Elasticity of Demand

High Elasticity

Perfectly Elastic

Inelastic

Perfectly Inelastic

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Why Do we Care

• Economic behavior depends a lot on the elasticity of the demand curve (and of the supply curve)

• As an example lets think about what happens when the supply curve shifts

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Medium Elasticity

0 10 20 30 40 50

P

Q/t

$2.50

$2.00

$1.50

$1.00

$0.50

0Demand

Supply

Old Equilibrium

New Equilibrium

New Supply

Pricerises

Quantityfalls

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Perfectly elastic Demand

0 10 20 30 40 50

P

Q/t

$2.50

$2.00

$1.50

$1.00

$0.50

0Demand

Supply

Old Equilibrium

New Equilibrium

New Supply

Price doesn’tchange

Quantitydecreases a lot

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Perfectly Inelastic Demand

0 10 20 30 40 50

P

Q/t

$2.50

$2.00

$1.50

$1.00

$0.50

0Demand

Supply

Old Equilibrium

New Equilibrium

New Supply

Price changesa lot

Quantitydoesn’t change

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Comparing Elasticities

0 10 20 30 40 50

P

Q/t

$2.50

$2.00

$1.50

$1.00

$0.50

0Large Elasticity

Low Elasticity

When Demand is more elastic price change is smaller and quantity change is larger

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Alternative Ways to Understand Elasticity

• A good for which there are no good substitutes is likely to be one for which you must pay whatever price is charged. It is also likely to be one for which a lower price will not induce substantially greater consumption. Thus, as price changes there is very little change in consumption, i.e. demand is inelastic and the demand curve is steep.• Inexpensive goods that take up little of your

income can change in price and your consumption will not change dramatically. Thus, at low prices, demand is inelastic.

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Seeing Elasticity Through Total Expenditures

•Total Expenditure Rule: if the price and the amount you spend both go in the same direction then demand is inelastic while if they go in opposite directions demand is elastic.

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Determinants of Elasticity

• Number of and Closeness of Substitutes• The more alternatives you have the less likely you

are to pay high prices for a good and the more likely you are to settle for something that will do.

• Time• The longer you have to come up with alternatives

to paying high prices the more likely it is you will shift to those alternatives.

• Portion of the Budget• The greater the portion of the budget an item

takes up, the greater the elasticity is likely to be.

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Elasticity ExamplesInelastic Goods Price Elasticity

Eggs 0.06

Food 0.21

Health Care Services 0.18

Gasoline (short-run) 0.08

Gasoline (long-run) 0.24

Highway and Bridge Tolls 0.10

Unit Elastic Good (or close to it)

Shellfish 0.89

Cars 1.14

Elastic Goods

Luxury Car 3.70

Foreign Air Travel 1.77

Restaurant Meals 2.27

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Price Elasticity Supply

• Identical in concept to elasticity of demand.• Formula is the Same• It is also related to the slope of the supply curve but

is not simply the slope of the supply curve.• Terminology is the same

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P

Q

Medium (Unitary) Elasticity of Supply

High Elasticity

Perfectly Elastic

Inelastic

Perfectly Inelastic

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Perfectly elastic Supply

0 10 20 30 40 50

P

Q/t

$2.50

$2.00

$1.50

$1.00

$0.50

0

Old Equilibrium

New Equilibrium

Price doesn’tchange

QuantityIncreasesa lot

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Perfectly Inelastic Supply

0 10 20 30 40 50

P

Q/t

$2.50

$2.00

$1.50

$1.00

$0.50

0

Old Equilibrium

New Equilibrium

Price Increasesa lot

Quantitydoesn’tchange

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Comparing Elasticities

0 10 20 30 40 50

P

Q/t

$2.50

$2.00

$1.50

$1.00

$0.50

0

Low Elasticity

High Elasticity

When supply is more elastic price change is smaller and quantity change is larger

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Consumer Surplus

I think this is easiest to see in our extensive margin example that we started with

Name Willingness to Pay

Jim $200

Jackie $400

Bill $600

Sally $800

Lisa $1000

So for Bill the value of the Ipad is $600.

If he could get an Ipad for free this would be worth $600

This gave the demand curve

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In this case Bill, Sally and Lisa all get their Ipads, Jackie and Jim do not

Lisa

Sally

Bill

Jackie

Jim

The Value to Lisa is $1000.

She pays $600, so her surplus is $400

Sally’s Value is $800 so her surplus is $200

Bill’s value is $600 so he gets no surplus

Total Consumer Surplus: $600

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Now lets think about this in a more more standard (and general) context

0 10 20 30 40 50

P

Q/t

$2.50

$2.00

$1.50

$1.00

$0.50

0Demand

Total Consumer Value

Consumer Surplus

Total that consumers pay

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Now the firm

0 10 20 30 40 50

P

Q/t

$2.50

$2.00

$1.50

$1.00

$0.50

0Demand

Total firms receive in revenue

Variable costs to producer

Producer Surplus

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0 10 20 30 40 50

P

Q/t

$2.50

$2.00

$1.50

$1.00

$0.50

0Demand

Total Combined Surplus

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Market Efficiency

One can see from this why people think markets are efficient

Suppose rather than having the market choose Q we decided to do it ourselves.

Could we do any better in terms of total surplus.

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Now lets think about this in a more more standard (and general) context

0 10 20 30 40 50

P

Q/t

$2.50

$2.00

$1.50

$1.00

$0.50

0

What if we chose a lower Q?

Surplus Now

Total surplus is lower

DeadweightLoss

I did not say anything about how surplus isdistributed-could be moreequitable

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0 10 20 30 40 50

P

Q/t

$2.50

$2.00

$1.50

$1.00

$0.50

0

What if we chose a higher Q?

Thus Total surplus is lower

This bit is actually negative,Costs are higher than users valuation

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Do Markets Always Work Well?

• No, for many reasons markets may fail• Market Failure: the circumstance where the market

outcome is not the economically efficient outcome• Possible Sources:• Consumption or production can harm an innocent

third party.• A good may not be one for which a company can

profit from selling it though society profits from its existence. • The buyer may not be able to make a well-

informed choice. • A buyer or seller may have too much power over

the price.

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Categorizing Goods:Exclusivity and Rivalry

• Exclusivity: the degree to which the consumption of the good can be restricted by a seller to only those who pay for it • Rivalry: the degree to which one person’s consumption reduces the value of the good for the next consumer

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Private and Public Goods

• Purely private good: a good with the characteristics of both exclusivity and rivalry• Purely public good: a good with the neither of the characteristics exclusivity and rivalry• Excludable public good: a good with the characteristic of exclusivity but not of rivalry• Congestible public good: a good with the characteristic of rivalry but not of exclusivity

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Taxes

• I am mostly following Guell quite closely• However here I will not, I think this is a good time in the

course to talk about taxes• The book talks about specific aspects in many places in

the book• I want to make some general points• Think about a $1.00 tax on the good (like gas tax)• Very similar to standard sales tax (just a percentage

rather than a level)

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0 10 20 30 40 50

P

Q/t

$2.50

$2.00

$1.50

$1.00

$0.50

0

Tax Example

Before I would have bought 25 units ifprice was $1.25. Now if price is $0.25 it costs me $1.50 so I buy 25 units

Price firmgets

Effective priceconsumer pays

Consumersurplus

Producersurplus

Governmentrevenue

Deadweightloss

Actual Demand

Demand from consumers perspective

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Incidence

It doesn’t matter here at all whether the tax was imposed on the producer or consumer

You get exactly the same result either way

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0 10 20 30 40 50

P

Q/t

$2.50

$2.00

$1.50

$1.00

$0.50

0

Producer pays taxNew supply curvefirms act like price is P-$1.00

Before I would have sold 20 units ifprice was $1.50. Now if price is $2.50, I get $1.50 so I sell 20 units

Effective price firmgets

Price consumer paysConsumersurplus

Producersurplus

Governmentrevenue

Dead Weightloss

It is exactly the same as before

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Taxes and elasticity

• A really really important issue here is that the deadweight loss depends upon the elasticity• Suppose elasticity of supply or demand were zero

• There are a bunch of different ways to do this, but suppose elasticity of demand is zero and tax is on producer• Then consider the case in which elasticity of supply is

zero and tax is on consumer

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0 10 20 30 40 50

P

Q/t

$2.50

$2.00

$1.50

$1.00

$0.50

0

Perfectly Inelastic DemandNew supply curvefirms act like price is P-$1.00

Price consumer pays

Governmentrevenue

I would sell 20 units whether there are taxes or not

This means there is no deadweight lossEffective price

that firm gets

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0 10 20 30 40 50

P

Q/t

$2.50

$2.00

$1.50

$1.00

$0.50

0

Perfectly Elastic Supply

New demand curveWorkers act like price is P+$1.00

Price firmgets

Effective priceconsumer pays

Producersurplus

Governmentrevenue

No deadweightloss

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•More generally the size of the deadweight loss depends on the elasticity

•The larger the elasticity the larger the deadweight loss

•For similar reason the larger the elasticity the smaller the government revenue

•For that reason Governments should tax things with low elasticity

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0 10 20 30 40 50

P

Q/t

$2.50

$2.00

$1.50

$1.00

$0.50

0

New demand curveWorkers act like price is P+$1.00

Think about what happens as elasticity increases?Deadweight Loss Rises and Government Revenue Falls

Both are bad so we don’t want to tax things that are high elasticity

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Stop Coddling the Super-RichWarren Buffett, New York Times, Aug. 11 2011

“According to a theory I sometimes hear, I should have thrown a fit and refused to invest because of the elevated tax rates on capital gains and dividends.

I didn’t refuse, nor did others. I have worked with investors for 60 years and I have yet to see anyone — not even when capital gains rates were 39.9 percent in 1976-77 — shy away from a sensible investment because of the tax rate on the potential gain.”