Lecture 4: Elasticity of Supply

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Econ 1000 lecture 4:Elasticity

C.L. Mattoli

(C) Red Hill Capital Corp, Delaware USA 2008

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This week

Mod 2, part 3 Chapter 5: Elasticity


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Learning objectives: Mod 2On successful completion of this module

(lecture 3 of the module), you should be able to:

Explain the concept of elasticity Calculate and interpret price, income and

cross-price elasticity of demand Calculate and interpret

price elasticity of supply .


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Introduction We have talked, in general terms, about

demand and supply schedules and curves. We have discussed opportunity costs: 1. When a consumer buys one thing, he will

not have money for others. 2. When a producer decides to produce one

thing, he will forego the opportunity to produce other things.

The real question is how important is one thing versus the other opportunities.


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Producer motivations Producers (suppliers) are in business to

make a profit. In that regard, they would like to get as high a

price as they can for a good or service. On the other hand, they know what minimum

price they can offer goods in certain quantities and still make a profit.

They need to understand how consumers will react to different prices, in order to arrive at proper prices for marketing their wares.


Psychology & Logic of Econ Think about how things affect each other,

how they interact. Think about how people are. For example, if the price of coca cola goes

up, some people will just switch to Pepsi, if it’s price didn’t change … it’s just human nature.

Thus, the availability of substitutes will affect how demand will change as prices go up and down.

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Psychology & Logic of Econ You don’t have much of a choice about who

will supply your electricity, if you live in a city … you can’t get by on batteries.

If there are barriers to entry for an industry, high prices will be charged, until other people break into the market and compete and lower the excess profits.

A change in the price of one vegetable will affect the supply of other vegetables. There is only so much farming land, and farmers will allocate according to their profit expectations.


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Psychology & Logic of Econ With a lot of things, the more you do

it, the less pleasure you get out of it. You eat out, and you eventually get saturated with eating out. But if the price was lowered, you might go back for more.

You only have so much money, and you have to allocate it according to your needs and desires.


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Revenue and how is it shown in the market model

Price

Quantity

S0

P0

Q0

D0

Q1

P1

D1

What happens to revenue when demand changes?


Revenue goes up when demand goes up

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Revenue and how is it shown in the market model?

Price

Quantity

S0

P0

Q1

D0

Q0

P1

S1

What happens to revenue when supply changes?


Not as clear

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The importance of percentages Often, in finance and economics, we

are more concerned with percentages and percentage changes than with raw numbers or absolute number changes.

That is because percentages give us a better basis for comparison, in many cases.


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The importance of percentages For example, it is not so important that

someone made $100 on an investment. What is more important is to ask how much did she invest to earn the $100. If she invested $100 to earn $100, then the return on investment was Income/investment = $100/$100 = 100%. If the investment was $10,000, the return on investment was $100/$10,000 = 1%. The percentage number was much more interesting.


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The importance of percentages The same is true about growth in GDP

(gross domestic product). If one country’s GDP growth was $100 million last year and another country's growth $1 trillion, the next question to ask is how much total did the countries have in GDP. Then, we can compute a percentage growth rate, and we will better be able to compare the growth rates in GDP of the two economies.


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The importance of percentages We looked at the general concepts of supply and demand: quantity demanded should be a decreasing function of price, while quantity supplied should be an increasing function of price.

But how will those quantities vary exactly with price: that is an important question.


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The importance of percentages To begin our next stage of economic

analysis, elasticity, we will look, more precisely, at how quantities vary with. To do that, in a meaningful way, we will …. You guessed it…. Use percentages.

Elasticities look at percentage change of one variable with respect to percentage change of another.


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Elasticity of Demand


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Price Elasticity of demand The law of demand says that the quantity

demanded, QD(P), is a function of price, P, and QD(P) is decreasing with increasing price.

The question is: how much will QD change when price changes. That will be a valuable piece of information for suppliers to know. Then, they can pick up their own pencils, and figure out whether or not production should be done, at what price, quantity, and what cost.


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Price Elasticity of demand Instead of using the ordinary variation of QD

with P, i.e., ΔQD/Δ P, consider the percentage change of quantity, ΔQD/ QD, versus the percentage change in price, Δ P/P.

ED = Elasticity of demand

= [percentage change in quantity demanded ]/ [percentage change in

price](C) Red Hill Capital Corp, Delaware USA 2008

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Price Elasticity of demand

= [ΔQD/ QD ]/[Δ P/P]

In that regard, we are looking at percentage change in the number of units purchased caused by a one percent change in price.


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Elasticity of demand exampled Suppose that we made observations that

found that Kangda college’s enrollment will drop by 20%, if the price of tuition increases by 10%.

Then, we could calculate the elasticity coefficient of demand =[percentage change in quantity demanded ]/ [percentage change in price] = [ΔQD/ QD ]/[Δ P/P] = %ΔQD/%ΔP = (-20%)/(10%) = -2.


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Elasticity of demand exampled It will always be a negative number

since, if price goes up, quantity demanded goes down, and vice versa.

That’s just human nature. So, we usually just say that the

elasticity coefficient is equal to 2.


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What it means to a supplier What that means to the supplier is that, if

he increases or decreases the price by 1%, he will experience a an opposite change of 2% in the number of units that he will be able to sell.

That will affect his total revenues, which are equal to QxP = Total Revenue = RT.

For example, assume that the price for tuition at Kangda is currently $50,000 per year = P0, and that there are 5,000 students = Q0. Then, RT

0= Q0xP0 = $50,000x5,000 = $250 million.


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What it means to a supplier Next, suppose that we try to increase the

price by 1% = $50,000 x 0.01 = $500 to P1 = $50,500.

Then, according to the elasticity coefficient of 2, enrollment will decrease by 2% = 100 to 4,900.

In that case total revenue will be RT = $50,500x4,900 = $247,450,000, which means that the supplier has lost revenue of about $2.5 million, which is no small amount of money.


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What it means to a supplier What that means is that, in order to be

ahead of the game by raising prices, he will also have to raise his profit margin enough to more than compensate for his loss in revenue.

For example, assume that he had a profit margin of 10%, originally. Profit margin = PM = profit/revenue = 10%. Then, his original profit would be profit = E0 = RTxPM = $250,000,000x10% = $25,000,000.


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What it means to a supplier For the supplier to break even on profits,

his new profit margin needs to be $25,000,000/$247,450,000 = 10.1%.

Therefore, the supplier will have to look at his pro-forma profit margin before he can make a decision to raise or lower prices.

In the end, it will be his own internal costs and marginal cost considerations that will allow him to make a decision about what price he should charge to maximize his profits


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Mathematically: total revenue change Total revenue equals price time quantity

demanded: RT0 = Q0xP0

Q1 = Q0 + ΔQ ; P1 = P0 – ΔP since price and quantity demanded will have opposite signs.

The variation of total revenues with respect to price is given by: Δ RT /ΔP = P x[ΔQ/ΔP] + QxΔP/ΔP = P x[ΔQ/ΔP]

And Δ RT /ΔP = [Q0xP0 – Q0xΔP – ΔQxΔP + ΔQxP0 – Q0xP0]/ΔP = – Q0 – ΔQ + ΔQxP0/ΔP = – Q1 + P0x ED. So what?...


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Mathematically: total revenue & elasticity If we want to find the condition for

increasing total revenue, that means that the change in revenue should always be a positive number. In algebra, we require: Δ RT /ΔP > 0.

So, Δ RT /ΔP = P x[ΔQ/ΔP] + Q >0 Rearranging the symbols in the equation,

we get ΔQ/(ΔP/P) > – Q


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Mathematically: total revenue Or, (ΔQ/Q)/(ΔP/P) = %ΔQ/%ΔP = ED >

– 1 Thus, in order for R to increase with

increasing P, E must be less than 1 in size.

Demand must be price inelastic. We shall take a closer look at revenues, in

the next module.


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The problem with elasticity calculations When we actually do calculations, we are

not dealing in abstract equations or perfect continuous curves. We will usually deal with a finite number of pairs of quantity and price, (Qi,Pi), in a demand schedule or a table.

Suppose we know two points in the demand schedule between which we want to calculate elasticity: (Q1,P1) = (400,$10) and (Q2,P2) = (440,$9.50).


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The problem with elasticity calculations Then, we can calculate the percentages

two different ways. If we assume that prices fall and we want

to know how much demand will rise, we quite naturally choose the starting points as (Q1,P1) = (400, $10) and calculate the percentages changes from those starting points of price and quantity, so elasticity = ED = [(440 – 400)/400]/[($9.50 – $10)/$10] = 2.


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The problem with elasticity calculations If, on the other hand, we want to look at

what would happen to a price increase from $9.50 to $10, we would naturally use starting point of (Q2,P2) = (440,$9.50). Elasticity is, then, [(400 – 440)/440]/[($10 – 9.50)/$9.50] = 1.72.

So, we get two different answers, depending on how we calculate: which point we start at.


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Elasticity: Mid-point approximation The simple cure to this problem, in

economics, is to use an average of some sort,

After all, right now we are imagining that we do not care if price goes up or if price goes down by 1%, we want one number for the percentage quantity that will either be retracted from or added to demand, as a general result.


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Elasticity: Mid-point approximation Moreover, since we are using 2 discrete,

separate points, not even in a real curve, what we are really doing in our actual calculation of elasticity is to measure an approximate value at the mid-point on the actual curve that would exist, if we had mounds of minutely-detailed data for quantity and price.

Thus, economics, as done in this course, will use a mid-point average value that is calculated in the following manner:…….


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Elasticity: Mid-point approximation1. Take the mid points for both quantity and for

price, which are simple averages ΔQD/ [(Q1D + Q2D)/2] and ΔP/ [(P1 + P2)/2].

2. Then, use percentages based on the mid-point as: mid-point elasticity approximation: %ΔQD/%ΔP = {ΔQD/ [(Q1D + Q2D)/2]}/{ ΔP/ [(P1 + P2)/2]} ={ΔQD/ (Q1D + Q2D)}/{ ΔP/ (P1 + P2)} because the 2’s on top and bottom cancel.

3. We demonstrate some of these concepts, pictorially, in the next slide


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Graphical Approximations First, look at elasticity along the dashed line. That is actually what we are using to calculate

the approximate elasticity.

$9

$10

$9.50

400 440 520

$10.50

P

QD

Demand Curve

480


It is approximately the same line as the dotted line that is tangent to the actual curve at the mid-point, more or less, so we use the mid-point to calculate it. Notice, also, that on a real demand curve the elasticity will change at different points o the line.

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Graphical Approximations

$9

$10

$9.50

400 440 520

$10.50

P

QD

Demand Curve

480(C) Red Hill Capital Corp, Delaware USA 2008

For example, if we calculate mid-point Elasticities between $9.50 and $10, we get E = [(440-400)/ ((440+400)/2)]/[($9.5-$10)/ ((9.5+10)/2)] = 1.86

If we calculate between $9 and $9.5, we get E = [(520-440)/((530+440)/2)]/ [(9-9.5)/((9.5+9)/2)] = 3.08.So, demand is more responsive to changes in price as price decreases, in this case.

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Elasticity classifications We classify elasticity into 3 basic categories:

1. Elastic demand, ED > 1, means that the percentage change in quantity demanded changes more than the percentage change in price. Thus, a reduction in price will cause total revenues to increase; a rise in price will cause total revenues to fall.

So, if elasticity of demand for Kangda college is 1.5, enrollment is 5000, and the price increases by 10% from $50,000/year to $55,000, then, enrollment will decrease by 1.5x10% = 15%.


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Elasticity classifications Enrollment will fall to 5000x85% = 4250, and

total revenues will fall to from 5,000x$50,000 = $250 million to 4250x%55,000 = $233,750,000.

2. Unitary elasticity, ED = 1, is a special case in which the percentage change in quantity exactly equals the percentage change in price. In this special case, total revenues are completely insensitive to changes in price.

Total revenue for Kangda will remain at $250 million, no matter what price is charged for tuition.


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Elasticity classifications3. Inelastic demand, ED < 1, means that the percentage

change in quantity demanded will be less than the percentage change in price. That means that total revenues will increase when price increases but will decrease when price decreases.

In this case, if Kangda has an elasticity of 0.75, and it decides to raise its tuition from $50,000 to $60,000, a 20% price hike, it will only lose 15% (=0,75x20%) in enrollment, from 5000 to 4250, and total revenues will rise to $255 million.

We show graphical examples of the three cases in the next 2 slides.


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How does the relative elasticity affect changes in producer revenue?

Price($)

Quantity/wk

70

1400

D0

90

1000

Inelastic = revenue increase with price increase & vice versa


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3 Types of elasticity The general shapes of elasticity graphs (see page

120 of the textbook) and their causal chains.

Elastic Unitary Elastic Inelastic

Price decrease

TotalRevenues Increase

Price decrease

Total Revenues unchanged

Price decrease

Total Revenues decrease


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Elasticity extremes There are also extreme cases for elasticity:

perfectly inelastic, ED = 0, and perfectly elastic, ED = ∞. These are limiting cases for the index.

Perfectly elastic demand corresponds to a demand curve that is perfectly horizontal (slope of Q(P) = ∞). So, if tuition is $50,000 and is perfectly inelastic, a change in tuition to $50,000.01 will result in zero enrollment.

Perfectly elastic is the limiting case in which an infinitesimally small change in price will result in an infinite change in quantity demanded.


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Elasticity extremes Perfect inelasticity is the opposite

extreme. In that case a change in price results in no change in quantity demanded. The demand curve is totally vertical (slope of Q(P) = 0), and demand is limited to an exact quantity.

Perfect inelasticity is the limiting case in which a change in price causes no change at all in quantity demanded.

We show example graphical representations of these extremes, in the next slide.


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Graphical Perfect elasticity Perfect elasticity

can be represented by a flat demand curve. Then, change in price results in an infinite change in demand.

There is only one price

ED = ∞

P

Q(C) Red Hill Capital Corp,

Delaware USA 2008

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Graphical Perfect inelasticity Perfect inelasticity

can be represented by a vertical demand curve. Then, change in price results in no change in demand.

There is only one quantity

ED = 0

P

Q(C) Red Hill Capital Corp,

Delaware USA 2008

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Elasticity variations on a line Since elasticity is percentage change versus

percentage change, it is different from the slope of a line, and elasticity may vary along demand curves.

Thinking at the extremes, when price is very high and quantity demanded is small. Then, a change of one unit of quantity demanded is a large percentage change, while a change of price by $1 will be a small percentage change, so that demand is very elastic.


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Elasticity variations on a line When price is low and the quantity

demanded is already large numbers of units, a $1 change in price is a large percentage change, while a unit change in quantity demanded is a small percentage change. Thus, demand at that end of the curve will be very inelastic.

In between those extremes will come a turning point at which elasticity of demand will be unitary.


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Elasticity variations on a line Actually, it will, in particular, vary

along a straight-line demand curve. We show this varying type of elasticity

for a line, in the next slide. In the slide we show demand for

DVD’s from a street vendor. In the upper region, it is elastic; in the

lower, inelastic(C) Red Hill Capital Corp,

Delaware USA 2008

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Elasticity variations on a line

0

5

10

15

20

25

30

35

40

0 10 20 30 40 50

0

50

100

150

200

250

300

350

400

450

0 10 20 30 40

Demand Schedule

Total Revenues

Elastic: E>1

Inelastic: E<1

Unitary elastic: E=1Price

Quantity demanded

Total Revenues

Mid-point

Elasticity

$40 0 $0

35 5 175 15.00

30 10 300 4.33

25 15 375 2.20

20 20 400 1.29

15 25 375 0.78

10 30 300 0.45

5 35 175 0.23

Demand for DVD’s


Break time

Please take a 10 minute break. Come up and ask questions, if you have any.


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Determinants of Price Elasticity of Demand


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Elasticities for goods and services In truth, at least because of inflation, prices

of most things change over time. Thus, we can expect that most things will have long-term and short-term elasticities that might be very different.

Elasticities are one thing that economists like to keep track of, so we can look at elasticities of some common goods and services to see some real examples (see, also, page 126 of the textbook).


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Elasticities for goods and services According to some estimates, we have the

following approximate elasticities of demand:

1. Automobiles: 2, elastic

2. Gas for automobiles: 0.5, inelastic

3. Automobile tires and tubes: 1, unitary elastic

4. Jewelry and watches: 0.5, inelastic

5. Movies: 0.9, short-term inelastic; 3.7, long-term elastic

6. Medical care: 0.3–0.9, inelastic


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ED: availability of substitutes The most important element of electricity

of demand is the availability of substitutes.

Demand, quite naturally, will be more elastic for goods and services for which there are close substitutes.

Then, if the price of the good or service changes, people can and will switch to the substitute.

Again, it is simple human nature, logic & psychology.


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ED: availability of substitutes For example, if the price of cars goes up,

people can switch to riding buses, trains, bicycles, or they can walk.

Indeed, the more public transportation that is available, the more elastic will be the demand for automobiles.

If you live in the middle of nowhere, and you have no car, your opportunity cost will involve all of the time that you spend walking from one place to another.


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ED: availability of substitutes

Of course, the question of available substitutes depends on how broadly or narrowly we define the market.

For example, the elasticity of demand is different for Ford automobiles than for some other automobile makers and automobiles, in general, because all of the other automobiles by other manufacturers are additional substitutes for Fords.


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ED: percentage of consumer budgets On the other hand, if there are no close

substitutes, then, demand will be more inelastic.

For example, there are no close substitutes for gasoline for automobiles. Thus, the demand for gasoline is fairly inelastic.

For an item, like salt, which represents a very minor item in a person’s budget, the price could double, and most consumers would not bat an eye: it is so inexpensive and will remain so, in comparison to an overall consumer budget.


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ED: percentage of consumer budgets Thus demand for small percentage items

will be inelastic. On the other hand, if the price of home

purchase or meals at expensive restaurants were to double, demand for those items would drop substantially.

They have very elastic demand because they represent a larger portion of a person’s budget.

In general, the elasticity coefficient varies directly with the percentage that an item represents in the budget.


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Response to price changes over time As we have seen in examples in the

lecture and can see on page 126 of the text, there are short-term and long-term elasticities.

Elasticity can even change character between the short run and the long run, going from, e.g., inelastic in the short-run and elastic in the long-run.


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Response to price changes over time The explanation of this can be looked at in

terms of people’s mentalities and the availability of substitutes.

In some cases, people cannot accept change, immediately, but over time they can adjust, mentally.

Because they are used to driving back and forth to work, alone, the immediate response to a hike in gasoline prices is to keep going the way they have been.


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Response to price changes over time As the high price persists, they will begin

to cut back on little trips to the store. They will slow speed to save gasoline. They may form car pools and drive

together. They might stop being so stubborn and

decide that a bus or a train is not such a bad alternative to driving.


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Response to price changes over time The next time they buy a car, they will

seek one that is more fuel efficient. Thus, their demand elasticity while fairly

inelastic in the short-run, becomes less inelastic in the long-run.

Demand for movies is inelastic in the short-run (0.87) because everyone wants to see the new movie when it previews.


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Response to price changes over time Over time, however, the excitement

diminishes. Friends tell you about their experience at the movie. You keep thinking that someday, maybe you should see it, but it becomes less important, and demand becomes very elastic (3.67).

Indeed, as a price change persists, there might be greater efforts to find substitutes or to invent them.

In general, the price elasticity of demand increases with time the longer a price change persists.


Opportunities You have a certain amount of earnings each

month. You allocate that among choices. The choices

that you give up to take others are your opportunity costs.

For a particular good, a substitute that you gave up to get that good is your opportunity cost.

As the price of a good goes up relative to substitutes, the opportunity cost of continuing to buy that good increases in terms of the others.

(C) Red Hill Capital Corp, Delaware USA 2008 64

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Airline ticket pricing: an example of complicated elasticity of demand to price Airline ticket pricing can seem particularly

complicated and convoluted, but, if we think in terms of price elasticity of demand, people’s convenience, and inflexibility, we will understand that the designers of the pricing scheme are very crafty.

Most people might not like the idea of getting up early in the morning to ride on a plane, so unit demand at those hours is very flexible to changes in price.


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Airline ticket pricing: an example of complicated elasticity of demand to price Thus, demand is elastic, and the airlines make

prices cheap at such slow times of the day to induce people to fly.

At busy times of the day, demand is inelastic, so airlines can charge higher prices.

Similar pricing patterns can be observed on longer time scales. For example a trip from GZ to Xi’an was 40% of the normal price in early January, but as the Chinese New Year approached, the price went up to 90%. If you book ahead three months before the May holiday, you can get 40%.


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Airline ticket pricing: an example of complicated elasticity of demand to price Those longer term pricing policies reflect

inelastic demand for urgent, last-minute travel and more elastic demand for longer term travel planning. The airline induces people to book early and penalizes those that it can: those who have no choice but to travel on last-minute plans.


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Other Elasticities


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Elasticity, in general

As we discussed, earlier, elasticity is simply a specialized measure of change in one variable with respect to another.

Sometimes, the ordinary slope, ΔY(X)/ΔX, the change in Y, a function of X [Y(X)], with respect to a change in X is an appropriate measure.


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Elasticity, in general In other case, however, especially in

economics and finance, percentages and percentage changes are more appropriate measures to analyze a problem.

Thus, the general concept of elasticity, percentage change of a variable with respect to percentage change of another variable, can arise as an appropriate measure in other circumstances.


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Income elasticity of demand

An important non-price financial factor in demand is income.

Indeed, we have discussed that there are even two separate categories of goods, normal and inferior, that respond in opposite manners to changes in income.


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Thus, in order to examine how consumption responds to changes in income, economists look at income elasticity of demand.

Income elasticity of demand is defined as the percentage change in quantity demanded with respect to percentage changes in income, Y (the standard symbol for income in econ), EY = %ΔQD/%ΔY ={ΔQD/ (Q1D + Q2D)}/{ ΔY/ (Y1 + Y2)}.


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Positive and negative income elasticity Unlike the case of price elasticity of demand, which was

always a negative number, income elasticity of demand will be positive for normal goods, EY>0, and negative for inferior goods, EY<0.

In that regard, we could classify normal goods as those whose income elasticities of demand are positive and inferior goods as those whose income elasticities are negative.

In any event, it will be useful to know what will happen to demand for any good or service when income changes since income changes all the time, and it can particularly change in times of general economic downturns: recessions.


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Income demand elasticity exampled Suppose that it is found that the quantity demanded of

illegal DVD’s in Guangzhou increases from 10,000 per month to 15,000 per month when monthly income increases from $1,000 to $1,250 or inferior.

Then, we can find both the income elasticity and its sign to discover the good’s true nature: normal or inferior…

EY = %ΔQD/%ΔY ={ΔQD/ (Q1D + Q2D)}/{ ΔY/ (Y1 + Y2)}

= [(15000–10000)/(15000+10000)]/[(1250-1000)/(1250+1000)]

= +1.8(C) Red Hill Capital Corp,

Delaware USA 2008

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Income demand elasticity exampled Thus, in this mid-point approximation, an 11%

average change in income results in a positive 20% average change in quantity of DVD’s sold.

Thus, illegal DVD’s are a normal good with fairly responsive demand versus income changes in a positive manner.

In the end-point calculation, the elasticity is 2, which is fairly positively elastic, and elastic, in the case of a positive elasticity is a good thing.

Income elasticity can be different in the long and short runs, becoming either more or less elastic.


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Recessions: not necessarily a bad thing. Although the bite of a recession, a downturn in

economic activity, causes many people to suffer decreases in income, others prosper.

While sellers of luxury automobiles, expensive jewelry, and ritzy restaurants will see lower income in recessions, sellers of so-called inferior goods, like cheap used cars or generic brands of food and drugs, will see a rise in their unit sales.

Normal goods have a negative income elasticity of demand: when income falls, unit demand rises.

At least recessions can be good for sellers of inferior goods.


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Normal or inferior In the table on page 129 of the textbook, only one good,

potatoes, showed a negative elasticity of income for the long-term.

For most of the other limited items on page 129, elasticity is positive, and, except for automobiles and furniture, most of the elasticities are larger in the long-run than in the short-run.

Other goods and services that we might imagine as having negative income elasticity are bus rides, used cars, cheap restaurant meals, retread tires, hamburger helper, and other things that people buy because they cannot afford to buy a better substitute.


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Children: normal or inferior It has been observed, especially over the last

century, that two trends have emerged in the world.

As the world entered the industrial age, people’s incomes have grown substantially, on the one hand, and the number of children in families has decreased.

As economists, we would conclude, ceteris paribus, that the demand for children seems to react opposite to change in income.


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Children: normal or inferior If that is truly the case, then, children would seem

to be inferior goods. Some economists might argue that there are so

many other factors that affect family size, others would point out that there might be a connection to the prices of complementary goods for children, like clothing, food and education, have also risen, and that these price changes have also contributed to the decrease in demand for children.


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Children: normal or inferior You might also think of other factors that can affect

demand for children. Children provide satisfaction for parents, but with rising income, there are many other choices of satisfying goods available for parents to purchase, like expensive vacations and luxury automobiles. In the past, children were also a free source of labor to, for example, help with farming, but with farms gone, and better jobs supplied by other people, again, the demand for children is diminished.

In any event, we might conclude that children are inferior goods.


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Cross-elasticity of demand

Another factor that we learned can affect demand for one good or service is prices of other goods or services.

Again, in this case, we have two different categories of goods: substitutes and complements.

Thus, we can apply the elasticity concept to examine responsiveness of quantity demanded of one good based on price changes of other related goods.


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Cross-elasticity of demand

Given those circumstances, we can define the cross-elasticity of demand as the percentage change in quantity demanded of one good corresponding to a percentage change in the price of a related good or service:

EC = %ΔQX/%ΔPY ={ΔQX/ (QX1 +

QX2)}/{ ΔPY/ (PY

1 + PY2)} is the cross-

elasticity of demand for good X versus change in price of good Y (mid-point formula).


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Complement or substitute: what’s your sign?

Thus, the general rule is that cross elasticity for substitutes is a positive number.

As in the case of income elasticity, cross elasticity can be positive or negative: the sign will distinguish between the two categories of goods whose prices can affect the quantity demanded of the good in question.


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Complement or substitute: what’s your sign? Consider that if Coke raises its price by 10%

and as a result, ceteris paribus, consumers buy 5% more Pepsi. Then, the cross elasticity of demand for Pepsi with the price of Coke is EC = +0.5.

Next, suppose that the price of motor oil to lubricate automobile engines rises by 50%, and as a result the quantity demanded for gasoline declines by 1%.


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Complement or substitute: what’s your sign? Motor oil and gasoline are complements. You

need to keep your engine lubricated, if you are going to drive your car. The more you drive, the more motor oil you need.

The characteristic of complement is also displayed in the cross-elasticity result as a negative sign.

Thus, the cross elasticity of demand for gas with respect to price of motor oil is EC = (– 1%)/(50%) = – 0.02, a negative number.


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Elasticity of Supply


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Elasticity of supply

In studying elasticity of demand we already discovered some useful information for suppliers: how total revenues will vary with price.

Just as price affects consumer sentiment about purchasing goods and services, price is an important factor to a supplier.


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Elasticity of supply Indeed, in the case of supply, the price will

determine whether or not the supplier can make a profit on his sales. That is why he has chosen to be in business, and if he cannot make profits, he will exit the business, and supply will decrease definitely.

In the next chapter, we will begin to study the cost side of production and supply and see how cost interacts with price and profits.


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Elasticity of supply For now, we can look at things from the

outside by defining the elasticity of supply as the percentage change in quantity supplied resulting from a certain percentage change in price: ES ={ΔQS/ (Q1S + Q2S)}/{ ΔP/ (P1 + P2)}.

Intuitively, elasticity of supply should always be a positive number. If price increases, a supplier should be willing to supply more, not less. The same for a price decrease: if the price is cut, a supplier should be willing to supply less, not more.


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Supply is elastic when ES>1, unit elastic when ES=1, and inelastic when ES<1.

As in the case of elasticity of demand, supply elasticities will be different in the sort-run and in the long run. Price elasticity of supply will, in general, be more elastic in the long run, so the long-run supply curve will be flatter.


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In chapter 7, we discuss how the time factor is a major determinant in the shape of the supply curve.

Here, we will look at one cost in supply, taxation, how it affects supply, and how governments use elasticity to design taxation schemes that will bring them a lot of revenues.


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Graphical supply elasticity We show the 3 general cases of price elasticity of

supply, in the extremes.

P

QS

Perfect Elastic Unit Elastic Perfect Inelastic

10%

10%


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Taxation and supply elasticity Governments get the bulk of their income from

taxes. Comprehensive coverage taxes, like the GST, the

goods and services sales tax, are generally a small percentage, like 5% so as not to be too large a factor in discouraging demand. They usually also exempt necessities, like food, clotting, and shelter, to name a few, so as not to affect demand for things that people need to live.

Thus, governments consider welfare and other economic factors when designing tax systems.


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Taxation and supply elasticity Excise taxes are taxes imposed on sellers of

certain goods and services, and they are usually substantially higher than sales tax on regular goods.

These taxes are on items that the government has deemed as harmful or in some way bad for society, anyway, like alcohol, cigarettes, and gasoline, but they also display inelastic demand.

So demand will be little affected by the additional tax on the item, and tax revenues can be fairly certain.


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Excise tax: who really pays?

You could say that the seller pays since he is the one who pays the tax.

Economists use the elasticity concept in this problem to analyze the question of who really pays: the consumer or supplier?

Tax incidence is the portion of tax paid by consumer or seller.


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Who pays example Tax incidence will depend on both

elasticities of supply and demand. The more inelastic supply, the more is

paid by seller. The more inelastic demand, the more is

paid by the buyer. Suppose that there is initially no excise tax

on gasoline, and the equilibrium price is $1.00/liter.


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Who pays example Next, suppose that the government installs

an excise tax of $0.50/liter. Elasticity of demand with respect to price will

tell part of the tale. If demand is completely inelastic, then, all

of the cost will be born by the buyer, even though the tax was imposed on the seller

If demand has elasticity, the tax burden will be shared between consumer and the seller. (see next slide)


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Who pays example Who pays excise tax? Supplier adds excise tax to his price and shifts the

supply curve up $0.50 at every price

BuyerSeller

Buyer

More Inelastic demand Total inelastic demand

More paid by buyer All paid by buyer

Less paid by seller None paid by seller


Who pays Example As elasticity of supply becomes more vertical

(inelastic) and elasticity of demand becomes more horizontal (elastic), the tax burden is shifted to seller

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0

2

4

6

8

10

12

0 25 50 75 100 125 150 175 200

Paid by seller

Paid by buyer


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Who pays example Thus, if demand is completely inelastic, the buyer

will bear all of the tax burden. If the demand curve is upward sloping, the new

supply curve will intersect the old demand curve at a quantity that would have been supplied at a price, $0.50 lower than where the new equilibrium is.

In that sense, the final equilibrium price will be below $1.50, and the cost of the tax will be split between consumer and seller.


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Taxes and markets In general, taxes will distort market outcomes and

result in prices that are too high and output that is too low.

Thus, imposing taxes can lead to inefficient markets when the object is tax revenue and disincentive for consumers to engage in bad things.

However, we have also seen the case, in the last section, whereby taxes are used as a disincentive for suppliers to stop doing bad things or at least pay for the damage that they are inflicting on others, like in the case of pollution.


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Tax, Equilibrium P&Q, and Revenues

Price

Quantity

S0

P0

Q0

D0

PT

QT

P-T

Initial producer revenue

Revenues after tax

S1


Tax Revenues

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Summary of Elasticities

%ΔQD/%ΔP %ΔQA/%ΔPB %ΔQD/%ΔY %ΔQS/ %ΔP

Price elasticity of demand

Cross-elasticity



Profit change with price change

Substitute/ Complement

Normal/ Inferior

Greater in Long Run


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In the end In the end, economics is about wants

being fulfilled by businesses. The price charged for something will

cause less people to want it, as price increases, while a higher price will be viewed favorably by business.

The market, left to its own devices, will find an agreeable price at which sellers are willing to supply exactly the amount that buyers wants. Then, the market will clear.


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In the end Although we might think that as price

increased, indefinitely, suppliers would be better and better off, in this lecture, we learned that there will be a maximum price, after which total revenues begin to, again, decrease.

That is a result of the demand equation. The limit to total revenue is strictly a result of demand, and is out of the immediate control of the seller, although he might try to create more demand.


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In the end That maximum revenue means that

profit margins must be able to be increased, enough, by the unit price rise, to overcome the decrease in total revenues since RT = Price x Quantity , profit margin = PM = profits/revenues , profits = profit margin x revenues.

Our next step will be to examine the cost side of the supplier’s equation.


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In the end Then, we will have to find out if there is

a maximum point for profits, beyond which a supplier will not increase supply.

We will have to see how costs, on the supply side, interact with revenues generated by the demand side.

Then, we will have a more clear picture of economics, through the operation of the businesses at its base.


Exam-caliber questions

1. For excise taxes, If supply is vertical, all tax is paid by consumer; if demand is horizontal, all tax is paid by the producer. Can you describe, in words, and show, in pictures, how tax incidence varies with changing elasticities of supply and demand?

2. Governments tend to impose excise taxes on social or economic “evils”, like smoking, alcohol, and traffic violations. Discuss at least 3 general reasons that a government would want to tax such things.


Delaware USA 2008

How Smart are You

3. We said that it is a concave curved demand line that can display unit elasticity everywhere. Can you show that any straight-line supply curve that passes through the origin (P=Q=0) is everywhere unit-elastic?

(C) Red Hill Capital Corp, Delaware USA 2008 109

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Homework Chapter 5


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End


Lecture 4: Elasticity of Supply

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Transcript of Lecture 4: Elasticity of Supply