lecture 4: elasticitylfbrooks/leahweb/teaching/pppa6085/...short-run (< 1 year) price elasticity of...

Admin RFH Corners Curves Elasticities Paper Recap

Lecture 4:Elasticity

September 22, 2015


Overview

Course Administration

Ripped from the Headlines

Corner Solutions

Demand Curves Are Not Linear

Many Types of Elasticity

Paper Assignment

Recap


Course Administration

1. Return problem sets

2. Midterm October 20: three full classes after this one, then themidterm

• Last year’s midterm is posted• Don’t wait till the last office hours• Come see me, or call me!

3. Any questions or outstanding issues?


How What You’re Learning is Policy-RelevantRipped from Headlines presentation(s)

As a reminder, next week

Afternoon

Finder Presenter

Caroline DeCelles Mariah McConnell

Evening

Finder Presenter

Arielle Atherley Nayda LakeliehJulia Robbins Erika Solem


A Usual Maximization of Utility s.t. Budget Constraint


A “Corner Solution”

Three key things to note

• Consumer is still maximizingutility

• He is not consuming bothgoods

• Is the indifference curve istangent to budgetconstraint? No






• Is the indifference curve istangent to budgetconstraint?

No






• Is the indifference curve istangent to budgetconstraint? No


Demand Curves are Not Linear

1. What do we mean by linear?

2. Implications of linear curve

3. Building a non-linear curve

4. Example of why the shape matters


What Do We Mean By Linear?

• A linear function can be written as y = mx + b• If b is zero (y = mx), then a 5-unit change in x → change iny equal to 5*1-unit change in x

• If b is not zero, this isn’t exactly true. However, the slope isalways the same everywhere along the function


Implications of a Linear Demand Curve

• There is a price sufficiently high that no one wants toconsume the good

• At a price of zero, there is a finite quantity demanded• Implies that many small changes in price always have the

same impact as an equivalent large change in price

→ thismay be quite wrong


Implications of a Linear Demand Curve

• There is a price sufficiently high that no one wants toconsume the good

• At a price of zero, there is a finite quantity demanded• Implies that many small changes in price always have the

same impact as an equivalent large change in price → thismay be quite wrong


Where a Demand Curve Comes FromThanks to Hal Varian’s textbook

Let’s assume we’re interested in the market for apartments in amedium-sized college town. Further assume that

• there are two types of apartments: near and far from university• near apartments are better• if you don’t get an apartment near, you can get one far at a

known fixed price

• all apartments are identical• each person wants only one apartment

We are interested in the price of the near apartments.


Putting Together a Demand Curve

• Reservation price is the “maximum willingness to pay forsomething”

• What is the highest reservation price of anyone in thismarket? → this is the top of the demand curve

• As we lower the price one dollar, how many additional peoplewant an apartment? This is Q

• Another dollar? This is the next (Q,P) on the curve


Putting Together a Demand Curve: In Pictures

P

Q


With Many Steps, Imagine a Curve

P

Q


Why the Shape of the Curve Matters: Avocados!

• 1914 US puts limits on imports of Mexican avocados• 1994 North American Free Trade Agreement (NAFTA) passes• 2004 USDA agrees to year-round avocado imports from

Mexico

• Domestic producers of avocados• form expectations from part of demand curve they observe• except that increase in Q will lead to decline in P

• What happens?

Almost no change in P, big increase in Q


Why the Shape of the Curve Matters: Avocados!

• 1914 US puts limits on imports of Mexican avocados• 1994 North American Free Trade Agreement (NAFTA) passes• 2004 USDA agrees to year-round avocado imports from

Mexico

• Domestic producers of avocados• form expectations from part of demand curve they observe• except that increase in Q will lead to decline in P

• What happens? Almost no change in P, big increase in Q


Three (Not Mutually Exclusive) ExplanationsOr, Is Everything We’ve Learned Wrong?

1. Demand curve is not linear

2. “Price” for big customers includes reliability of supply, so true“price” fell → Q ↑

3. Demand increases


E.1.: Demand Curve is Not LinearThe World Before NAFTA

P

Q

SUSA, weather good

D


E.1.: Demand Curve is Not LinearWhere Is World Supply?

P

Q

SUSA, weather good

SUSA, weather bad

D


E.1.: Demand Curve is Not LinearIf You Think Demand is Linear, What Happens?

P

Q

SUSA, weather good

SUSA, weather bad

D

SWorld


E.1.: Demand Curve is Not LinearWhy Is This Unlikely to Have Been the Case?

P

Q

SUSA, weather good

SUSA, weather bad

D

SWorld


E.1.: Demand Curve is Not LinearCurved Demand Is One Explanation

P

Q

SUSA, weather good

SUSA, weather bad

D

SWorld


E.2.: “Price” for big customers falls

• Elsewhere, I learned that after the introduction of Mexicanavocados, big chains considered putting them in menus

• Major cost component for big chain input is reliability• Mexican supply guarantees year-round supply• And more reliable supply

• Thus, for big firms, outward supply shift understates truedecrease in price, and can explain large change in Q


Elasticity

• Elasticity measures the change in quantity for a given changein price

• Absolutely crucial for policy decisions• Formally, percentage change in one value relative to

percentage change in another

• In math, elasticity is

E =%∆Q

%∆P


Perfectly Elastic and Inelastic Supply and Demand

Draw the usual supply and demand axes.

• If demand (or supply) is perfectly inelastic, what does thecurve look like?

• If demand (or supply) is perfectly elastic, what does the curvelook like?


Drawing Perfectly Inelastic and Perfectly Elastic Demandand Supply


Numerical Examples

• “Among the models that CBO uses to analyze the economiceffects of changes in federal fiscal policy is a life-cycle growthmodel. That model requires an estimate of [the elasticity oflabor supply with respect to price]. .... CBO incorporates intoits analyses an estimate of the [this] elasticity that rangesfrom 0.27 to 0.53, with a central estimate of 0.40.”

• → a 1% change in wages causes a 0.4% change in labor supply• Short-run (< 1 year) price elasticity of demand for gasoline:

-0.26 (see Espey, Energy Journal)• → a 1% change in gas price causes a 0.26% decrease in gas

demanded

• Long-run (> 1 year) price elasticity of demand for gasoline:-0.58


Many Types of Elasticities

• Price elasticity of demand and supply• Elasticity terms• Income elasticity of demand• Cross-price elasticity of demand


Elasticity of Supply and Demand Reminder

• In general, we expect ED

< 0

• And ES > 0



• In general, we expect ED < 0• And ES

> 0



• In general, we expect ED < 0• And ES > 0


Useful Elasticity Terms

• Unit elastic, |E | = 1: any percent changes in prices areequally matched by percent changes in Q

• Elastic, ∞ > |E | > 1: responsiveness of numerator greaterthan change in denominator

• Inelastic, 0 < |E | < 1: responsiveness of numerator less thanchange in denominator

• Perfectly inelastic, |E | = 0: no change in numerator forchange in denominator

• Perfectly elastic, |E | =∞: infinite change in numerator forchange in denominator


Income Elasticity of Demand

Calculating

• We are interested in the income elasticity of demand

EDI =%∆QD

%∆I=

∆QD

∆I∗ IQD

• What do you consume more of as your income increases?These are normal goods, and E > 0 (but E ≤ 1)

• What do you consume less of as your income increases?These are inferior goods, and E < 0.

In groups: Examples

• What is the sign of the income elasticity of demand for freshfruit and vegetable consumption?

• Give an example of a normal good and an inferior good



Calculating


EDI =%∆QD

%∆I=

∆QD

∆I∗ IQD

• What do you consume more of as your income increases?

These are normal goods, and E > 0 (but E ≤ 1)• What do you consume less of as your income increases?

These are inferior goods, and E < 0.

In groups: Examples





Calculating


EDI =%∆QD

%∆I=

∆QD

∆I∗ IQD


• What do you consume less of as your income increases?

These are inferior goods, and E < 0.

In groups: Examples





Calculating


EDI =%∆QD

%∆I=

∆QD

∆I∗ IQD


• What do you consume less of as your income increases?These are inferior goods, and E < 0.

In groups: Examples




Cross-Price Elasticity of Demand

How much does your demand for pluots change when the price ofapricots increases?

Policy examples, please!

EDXY =%∆QDX%∆PY

=∆QDX∆PY

∗ PYQDX

• The responsiveness of quantity demanded of good X to priceof good Y

• If EDXY is positive, are X and Y substitutes or complements?


Cross-Price Elasticity of Demand

How much does your demand for pluots change when the price ofapricots increases?Policy examples, please!

EDXY =%∆QDX%∆PY

=∆QDX∆PY

∗ PYQDX

• The responsiveness of quantity demanded of good X to priceof good Y

• If EDXY is positive, are X and Y substitutes or complements?


Paper Overview


What We Did This Class

1. Corner Solutions

2. Non-linear demand curves

3. Many kinds of elasticity


Next Class

• Turn in Problem Set 4• GLS, Chapter 5

Course AdministrationRipped from the HeadlinesCorner SolutionsDemand Curves Are Not LinearMany Types of ElasticityPaper AssignmentRecap

lecture 4: elasticitylfbrooks/leahweb/teaching/pppa6085/...short-run (< 1 year) price elasticity of...

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