micronotes

Microeconomic Study Notes (17/7/2012 Houston H. Stokes

1

Preliminary Lecture notes for a Micro Course Based on

Microeconomics 8ed

by Pindyck & Rubinfeld

Prepared by Houston H. Stokes.

Goal of the Notes: Allow the student to have an outline of the key ideas and solutions

to a number of problems that will be discussed in class. Since the notes are distributed

in WORD format, students can edit the notes.

Introduction

Quote from Robert Mundell Man and Economics 1968

"Economics is the science of choice. It began with Aristotle but got mixed up with ethics in the

Middle Ages. Adam Smith separated it from ethics, and Walrus mathematized it. Alfred Marshall

tried to narrow it, and Keynes made is fashionable. Robbins widened it, and Samuelson dynamized it,

but modern science made it statistical and tried to confine it again.

But the science won't stay put. It keeps cropping up all over the place. There is an economics of

money and trade, of production and consumption, of distribution and development. There is also an

economics of welfare, manners, language, industry, music, and art. There is an economics of war and

an economics of power. There is even an economics of love.

Economics seems to apply to every nook and cranny of human experience. It is an aspect of all

conscious action. Whenever decisions are made, the law of economy is called into play. Whenever

alternatives exist, life takes on an economic aspect. It has always been so. But how can it be?

It can be because economics is more than just the most developed of the sciences of control. It is a

way of looking at things, an ordering principle, a complete part of everything. It is a system of

thought, a life game, an element of pure knowledge.

Chapter 1 Preliminaries

Economics is concerned with scarcity. If something is not scarce, there is no economic problem.

Microeconomics => Study of behavior of individual economic units. How they react and how they interact to form larger units.

Economics uses theory to explain actions and predict future actions. For example if: the Bulls are in the playoffs, then there will be a larger number of people wanting tickets

than if they have a poor season. If there is high unemployment, then at the university

more students enroll in business courses because their opportunity costs (pay loss due

to being in class) are less.

Theory does not work well all the time. The market test of theory is how well it does in comparison to another theory. A theory must have the possibility to being proved wrong.


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The statement "all unmarried men are bachelors" is a tautology and cannot be proved

wrong. The statement "If American Airlines lowers the ticket price to Bermuda, an

increased number of people will fly this weekend." Can be proved wrong or right.

Marginal utility theory can be used to derive the demand curve. However it will be shown later that to get a downward sloping demand curve the only assumption needed is

that consumers buy randomly along the budget line. => a minimalist approach to

deriving an important economic concept - downward sloping demand.

Normative Economics => What should be done. "Microsoft should be allowed to bundle the IE with Windows XP because it benefits consumers."

Positive Economics => What will happen, not what should be done. "An increase in the property tax in the area of UIC will tend to lower the price of apartments, everything

else equal."

Many decisions involve multiple assumptions. Book example of 1985 decision of Ford to produce the Taurus involved:

1. Consumer tastes vs demand "would they like the car?"

2. How sensitive would demand be to price changes? (elasticity),

3. What would be the production costs? (Depends on assumptions of #'s of cars produced, union demands, inflation, how fast workers learn).

4. How would competitors react (market structure).

5. How much new capital would be needed? (interest rates, engineering).

6. How would the decision be changed if oil prices moved favorably, unfavorably?

7. How should Ford organize the production?

8. How might anticipated Government regulation changes influence the decision (Gas mileage requirements).

What is a Market. A market is the collection of buyers and sellers that, through their actual or potential interactions, determine the price of a product or set of products. A

market includes more than an industry (a collection of firms that sell the same or closely

related products). Key business decision: Determining the market for the product!

If prices differ in two markets, arbitrage may be possible. If the price of a T-bill maturing in period t in NY is > than the price of the same T-bill in Chicago => people


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will buy in Chicago and sell on the NY market. If the price of a Big-Mac is less in

Norfolk VA than Chicago, arbitrage is NOT feasible, even with fast planes.

Markets can be competitive (wheat) or noncompetitive (electric power) due to entry costs.

In a competitive market with many producers no one producer can change the industry price. Product differentiation => power to alter price within limits. Successful

advertising => in perceived product differentiation.

Extent of the market => the boundaries, both geographical and physical of a market.

Real vs Nominal Price. Economic decisions should be made on the basis of real prices. Money illusion => consumer looks at the nominal price not the real price. Assume two

groups: debtors and creditors. Creditors and debtors set the interest rate depending on

their expectations of price movements. Unexpected price increases (decreases) favor

debtors (creditors).

Measuring Price The CPI measures price changes by buying a market basket of goods at different times. Three known problems are:

1. Tastes may change over time but same basket is bought.

2. Relative prices may change but the same basket is bought

3. Price changes involve subtle income changes that give rise to income effects that will alter the mix of goods bought.

The CPI for period t, Pt is calculated with the Laspeyres formula:

P p q p qt tii

n

i i

i

n

i

1

1 1

1

1/ (1)

If in place of the above equation the quantities could have been adjusted every year as in the Paasche formula

P p q p qt tii

n

ti i

i

n

ti

1

1

1

/ (2)

which is not possible to calculate but would avoid the tastes bias and the relative price bias.


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Table 1.2 lists the CPI and education and egg prices in both nominal and real terms. How

you get data in 2010 prices? See file ch1_1.xls for the answer? Why would one want to

make this calculation?

Study Questions:

1. Over the past year the price inflation has been 10%. The price of a used Ford SUV has fallen from $6,000 to $5,000. How much as the real price fallen:

((1.1 * 6000) - 5000)/(1.1*6000) = 24.24

Since last year the price of gold has risen from $120 to $420. What annual rate of

inflation would hold the price of gold fixed in rea1 terms?

(420-120)/120 = 250%

If this was over 5 years and we assume yearly compounding, what would the rate of

inflation have to be?

420 = 120(1. + r)5

(1. + r)5

= (420/120)=3.5, = > ln(1.+r) * 5 = ln( 3.5), => ln(1. + r) = ln(3.5)/5

or (1. + r) = exp(ln(3.5)/5),

(1.+ r) = 1.2847 or 28.47% annual inflation.

Check: (1.2847)5 = 3.5, 120*3.5 = 420

2. Suppose that the Japanese yen raises against the U. S. dollar; that is, it now takes more dollars to buy any given amount of Japanese yen. Explain why this simultaneously

increases the real price of Japanese cars for U. S. consumers and lowers the real price of

U. S. automobiles for Japanese consumers.


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Chapter 2 Basics of Supply and Demand

The basic model postulates that Supply responds positively to price and Demand

responds negatively to price. Qs = Qs(P) and Qd = Qd(P). At equilibrium P (P0) = Q (Q0)

and the market clears. Qs(P) > Qd(P) implies excess supply while Qs(P) < Qd(P) implies

excess demand. This is shown below

S

P

P1

P0

P2

D

Q

Points where price is above P0 represent excess supply, while points below P0 represent

excess demand. The laws of motion of Walrus state "If there is excess demand, price will

rise." The laws of motion Marshall state "If there is excess demand, quantity will rise." P0

is the "market clearing price." Here supply = demand. Assume that somehow the price goes

to P1. Now demand < supply. According to Marshall adjustment will proceed by a reduction

in supply, while according to Walrus price will fall. Similar arguments can be made for P2.

In a market for Old Master Paintings clearly Walrus adjustment is the only legal adjustment

mechanism. In 1969 the first man walked on the moon. The New York times printed the

edition showing this historic moment for three days until everyone got a copy. This was

Marshall adjustment.

In the above diagram it does not matter which adjustment model you use, price will go to P0.

Assume that supply now is negatively sloped or that economics of scale exist. The producer

can increase his production and lower his price. Two Models are possible.


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P D P S

D

S

Q Q

The left graph is stable according to Marshall and unstable according to Walrus.

The right graph is stable according to Walrus and unstable according to Marshall. Why?

There is a shift in supply if one of the variables held constant (not on the axis) changes and

that in turn changes the amount supplied. Assume the supply of wheat is a function of P and

R where R = rainfall.

Qs = a + 1 P + 2 R (3)

where 1 > 0 and 2 > 0. An increase in R would, everything else equal move the supply curve right and lower the price for wheat assuming the demand curve is not flat. Assume the

demand for wheat is a function of price and income.

Qd = a' + 3P + 4Y (4)

Where 3 < 0 and 4 > 0. An increase in Y moves the demand curve right and results in an

increase in price assuming that the supply curve is not flat and that Y => quantity

demanded .

Demand and supply curves hold tastes, prices of all other good, incomes and technology etc

constant. Over time supply and demand usually shift right. An exception would be the

demand for buggy whips! Why?

Key Concept: Given a demand curve, it can be said that there is a change in demand or

shift in the demand curve if the price of another good changes, income changes or tastes

change. If the price of the good itself changes, then there is a change in the quantity

demanded or a movement along the demand curve. In the above example Y will cause a change in demand while P will cause a change in the quantity demanded. For supply, P causes a change in the quantity supplied while R causes a change in supply. It is

always important to understand the difference with what moves a curve and what

causes a movement along the curve.


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.

Solve simple system:

Qs= 1800 + 240P

Qd= 3550 - 266P

In equilibrium Qd = Qs. or 1800 + 240P = 3550 - 266P

506P = 1750 => P = $3.46 and Q = 1800 + (1750/506)*240 = 2630

Excel file ch2_1.xls solves this system. Using this technology. Solve the system assuming:

- An advertising campaign raises 3550 to 4023. - A lack of rainfall lowers 1800 to 1500 - A change in taste changes 266 to 280

This is the basic template for micro analysis of supply and demand. A major research

objective is to determine what will change a, a', 1,4. It will be made more complex as we move forward.

Ed = elasticity of demand

= (%Q)/(%P)

= (Q/Q)/(P/P)

= (Q/P)*(P/Q) (5)

Usually d is used in place of Ed. The price elasticity is measured at a point. On a linear

demand curve the slope (Q/P) is constant.

Q = 8-2P => (Q/P) = -2

As Q 0 => Ed -

As P 0 => Ed 0

If |Ed| > 1 => P => Total Revenue (TR) up.

TR = P * Q (6)

A firm should never operate where |Ed| < 1.

Advertising is designed to make |Ed| decrease for every price. After a successful

advertising campaign the firm will have more product differentiation and can either raise

price or increase sales at the current price. Careful analysis will tell us what to do.


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S

b

a

P2

P1 c d

O

Q1 e f

Firm started with demand curve a e which implied price P1 and Q1. A major advertising

campaign moved the demand curve from a e to b f. For purposes of this example a e is | | to

b f. Price rises to P2.

Proof that |d | at d is more inelastic than at c.

At c d = (Q/Q)/(P/P)

= (Q1e/OQ1)/(OP1/OP1)

= (Q1e/OQ1)

= ce / ac (| | lines produce proportionate segments)

At d d = (Q/Q)/(P/P)

= df / bd

Since df = ce and bd > ac = > at d |d| is less than at c

Note that at a d = - while at e d = 0.

A parallel shift right of a demand curve makes is more inelastic at each price.

Income elasticity measures the percent change in the quantity of a good for a percent

change in income.


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EI I = (Q/Q)/(I/I) = (Q/I)(I/Q) (7)

A good is normal if I > 0 and inferior if I < 0 . Baked beans are the classic inferior good and the BMW car a classic normal good.

Assume an individual faces goods a to n. Let Pa be the price of good a, Pb be the price of

good b. Let A be the change in the amount of A bought and B be the change in the

amount of B bought. Assume the individual gets an increase in income I.

Pa A + PbB + .. + PnN = I (8)

If we assume I = 0, the above equation defines the budget line which will be used in indifference curve analysis.

Divide (8) through by I and then multiplying all terms on the left by I A / I A gives a key expression. In steps

[ / ] [ / ] ,...,[ / ] [ / ]P A I P B I P N I I Ia b n

[ / ] [ / ] ,...,[ / ] [ / ]P A AI I A I P B BI I B I P N NI I N I I Ia b n

Finally

Ka Ia + Kb Ib + + Kn In = 1 (9)

Or the sum of the weighted income elasticities = 1

The cross price elasticity of demand APB measures the effect of the price of good B on

the quantity of good A.

(10)

If A is a substitute for B, then APB is > 0 or an increase in the price of B => the quantity

of A . If A is a complement of B then APB is < 0. Coke is a substitute for Pepsi while

gas is a complement for an auto.

In the long run demand is usually more elastic. When the price of gas went up in the 70's

people did not just dump their cars that got poor gas mileage BUT when they replaced them

they made sure they got a car with a higher MPG rating.

In the long run the supply of a product is usually more elastic than in the short run since in

the long run fixed factors can be changed.

AP A A B B A B A BB Q Q P P Q P Q P ( / ) / ( / ) /


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Given QD = a - bP (11)

QS = c + dP (12)

And P* and Q

* are equilibrium P and Q, then at equilibrium the elasticity of demand D and

elasticity of supply S are

D = -b(P*/Q

*) (13)

S = d(P*/Q

*) (14)

=> if we know D , S, P* and Q

* we can get the supply curve and the demand curve. In the

market we observe P* and Q

*.

Book shows P*

and Q*

are $.75 and 7.5 million D , S are -.8 and 1.6 respectively. From equation (13) and (14) we get -b = (-.8) * (7.5/.75) = -8. and d = (1.6)*(75/.75) = 16.

Excel file ch2_2.xls solves the general case of determining the supply and demand functions

given the elasticity and P* and Q

*.

In the long run supply and demand are usually more elastic. When OPEC raised price =>

discoveries went up. Users shifted to more efficient cars over time.

An effective price control will cause a shortage. If the supply curve is NOT vertical, the total

consumed will go down.

Demand for E

Problem 1.

P Qd Qs

60 22 14

80 20 16

100 18 18

120 16 20

d = (Q/P)*(P/Q)

Q/P -2/20 => d = (-.1)*(80/20) = -.40

at 100 d = (-.1)*(100/18) = -.56

Problem 2. T or F "Since tuition has doubled in real terms in the last 15 years this implies

the demand curve for education is vertical." FALSE may be seeing shifts of both supply

and demand.


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Problem 3. File Ch2_3.xls contains simulated Data from 25 Families obtained from Stigler

Theory of Price Edition 4 page 37. Variables are expend = expenditure, pincome =

permanent income, Tincome = transitory income, oincome = observed income.

The data was generated from the model expend = f(1+.02*pincome). Tincome was

randomly added such that pincome + tincome = oincome

Run expend=f(constant pincome)

Expend=g(constant oincome)


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Chapter 3 Consumer Behavior

Key Assumptions of Theory of Consumer Behavior:

Preferences are complete => Consumers can rank market baskets.

Preferences are transitive => If consumer prefers basket A to B and B to C then the

consumer prefers A to C.

More of any good is always better.

Indifference Curve - Locus of points showing different combinations of goods to which the

consumer is indifferent.

X

II I

a

III IV

b Y

Consumer starts with a of X and b of Y. Points in I => more satisfaction. Points is III => less

satisfaction.

Indifference curves must be in II and IV.

X Complements X Substitutes

Y Y


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Y

Usual Case Utility along b > than along a

2

b

1 a

X

Indifference curves cannot cross unless there is a change in tastes.

Ordinal ranking => A is better than B but cannot tell by how much.

Cardinal ranking => Can tell how much better A is than B.

Slope of indifference curve measure marginal rate of substitution between goods. In

terms of above example = ( / ) Y X .

At 1 ( / ) Y X 0

At 2 ( / ) Y X

=> along an indifference curve there is diminishing marginal rate of substitution.

Given you have relatively more X than Y => will give less Y for every additional X.

Budget line = locus of points showing different combinations of goods that can be bought

given income. Where budget lines is tangent to highest indifference curve => desired point

(a).

Y

A

a

3

2

1

B X


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A = I / Py, B = I / Px. At a on highest indifference curve. MRS = Y/X =Px / Py

1 2

if income increases budget line moves out.

If price of X falls budget line rotates

Y

a

I => Budget line moves from 1 to 2 above

PxB => Budget line moves from ab to ac on left.

b c X

Total spending fixed along budget line. Object is to reach highest Indifference curve (not

drawn).

Unless there is a corner solution, MRS = Px / Py. Of in words slope of the indifference curve

= slope of budget line.

Corner solution => consume only one good

Utility = satisfaction one gets for consuming a good.

Marginal Utility declines as consumption of a good increases unless lumpyness problem (4

tires on a car).

MRSxy = MUx / MUy

In equilibrium

MUx / MUY = PX / PY

MUx / PX = MUY / PY

(MUx / PX) > (MUY / PY) => Have too much Y relative to X

Marginal utility per dollar last dollar spent must be the same for all goods.


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Gas rationing => loss of welfare. Rationing done to maintain price. In NYC rent controls

led to vast sections of the city being abandoned. Rationing once in place is hard to remove.

See Figure 3.22

Other

Goods

O A C Gas

Consumer wants OC of gas. The government forces person to take OA and thus be on a

lower indifference curve.

The Laspeyrse price index is defined as

P p q p qt tii

n

i i

i

n

i

1

1 1

1

1/

which overstates the amount of a price increase because the person is given enough money

to buy their old bundle even though this is NOT what they will buy since relative prices

have changed.

a

Y

1

2

3

II III I

X

Consumer was on indifference curve 2 and budget line I. The price of X increases and the

consumer ends up on indifference curve 3 and budget line II. A subsidy is given to allow

consumer to buy old bundle of goods BUT consumer now buys relative more of good Y and

less of good X since Px/Py has risen.


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# 2 page 99 Draw indifference curves for:

Al likes beer, hates hamburgers

U3

beer U2

U1

U3 > U2 > U1

Hamburger

Betty indifferent between 3 beers or 2 hamburgers. Nothing changes no matter what

the level of consumption.

beer

9

6

3

2 4 6 Hamburger

Chris eats one hamburger and one beer in fixed proportions.

beer

Hamburger


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1. Antonio buys 8 new college textbooks at a cost of $50.00 each. Used books were $30.00

each. Next year prices for new books go up 20% and used books go up 10%. Antonio's Dad

sent him $80.00 more. Is he better off?

Cost last year for new books 8 * $50.00 = $400.00

Cost last year for used books 8 * $30.00 = $240.00

Relative price of new and used books last year 50/30 = 1.67

Relative price of new and used books this year (50*1.20)/(30*1.1) = 60 / 33 = 1.82

New books are relative more costly.

Cost this year for the two choices would be 8*60 = $480

8*33 = $264

Dad gave him money to buy 8 new books this year. Will he still buy this bundle now that

prices of new books are relatively higher?

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

2. Jane has a utility function U(F,c) = FC. Set up a table for U=12 and U = 24

Suppose Jane has $12.00 to spend and Pf = $1.00 and Pc = $3.00 Show budget line

What should she buy? (F=6 C =2 ).

Ch3_1.xls

Jane U(Fmc)=FC

U(F,C) = FC P food 1 P Cloth 3

U=12 U=24

F C Cost F C Cost

1 12 37 1 24 73

1.5 8 25.5 2 12 38

2 6 20 3 8 27

3 4 15 4 6 22

4 3 13 6 4 18

6 2 12 8 3 17

8 1.5 12.5 12 2 18

12 1 15 24 1 27

Budget line is Y = Pf * F + Pc * C

MRS = -1/3


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Chapter 4 Individual Market Demand

Demand Curve holds constant:

Prices of other goods

Income

Tastes

Assume Income available is I:

A = I /P1y ,

B = I / P1x, C = I / P2x, D = I / P3x

As Px falls the budget line moves from AB to AC to AD. The possible set of goods

increases. The consumer increases x purchases and Y purchases. The above diagram is

same as figure 4.1.

Points to remember: As price of X falls there is a substutution effect that is due to the

relative price change and an income effect which is due to the increase in real income


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due to the price decrease. If the price of X falls, the consumption of Y can increase, or

decrease.

Income Consumption Curve Traces out points of consumption of X and Y that occurs

as income increases.

If X and Y are both superior goods, as I increases the consumption of X and Y increases.

=> Demand curves for both goods shift right.

Y

ICC

X

Here X is inferior at high income = > as I increases, consumption of X eventually falls.

Y

3

2

1

X

As Income rises X consumption first increases, then falls. As income rises the

consumption of Y increases.


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Y is a normal good. X is a normal good for low incomes, an inferior good for high

prices.

In an N good world all goods can be normal goods. As a upper limit only N-1 can be

inferior. => In a 2 good world cannot have two inferior goods.

Income and substitution effects can be drawn 4 ways for a price fall and 4 ways for a

price rise assuming normal goods. For the inferior not giffen and inferior giffen there are

8 other ways each. Total number of cases = 24.

Inferior not Giffen = > good is inferior but not so inferior that the income effect out

weighs substitution effect.

Four ways to draw cases:

Hicks method (American assumptions). => Assume base case. Prices change

causing the budget line to rotate (See figure 4.6). Helping budget line drawn tangent to

old indifference curve but parallel to new budget line.

Slutsky method (American assumptions) => Assume base case. Prices change

causing the budget line to rotate . Helping budget line drawn through old basket but

parallel to new budget line.

Hicks method (European Assumptions). => Assume base case. Prices change

causing the budget line to rotate . Helping budget line drawn tangent to new indifference

curve but parallel to old budget line.

Slutsky method (European Assumptions) => Assume base case. Prices change

causing the budget line to rotate . Helping budget line drawn through new basket but

parallel to old budget line.

For a price fall Hicks (Slutsky) method with American assumptions looks like a price

increase for Hicks (Slutsky) with European assumptions.

We assume American assumptions for this course!!!

Define AB = substitution effect using Hicks

AB* = substitution using Stutsky

BC = income effect using Hicks

B*C = income efffect using Stutsky

AC = Total Effect

Assume P X falls.


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Normal good = > ABB*C

Inferior not Giffen => ACB*B

Inferior Giffen -> CB*BA

Y

a

2

1

II III

I

A B B* C c d

X

We assume income is fixed. Original budget line is ac. Consumer consumes A of X.

Price falls => budget line shifts out to ad. Consumer now obtains C of X.

Hicks method draws helping budget line 1 tangent to old indifference curve I but

parallel to new budget line. AC broken into AB (Hicks substitution effect) and BC Hicks

income effect.

Slutsky method draws helping budget line 2 through old point. Consumer is

overcompensated and substitution effect is now AB* and income effect B

*C.

Slutsky American method is how Lasperse price index ( P Q P Qjt j j j1 1 1/ ) is constructed.

Slutsky European method is how Paasche price index ( P Q P Qjt jt j jt/ 1 ) is constructed.

Figure 4.6 shows Hicks method for a price fall of a normal good. In terms of

ABC, F1 = A, E = B and F2 = C. Figure 4.6 can be used to show the Hicks method using

European assumptions for a price increase.

Figure 4.7 shows Hicks method for an inferior good not Giffen good.


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Figure 4.8 shows Hicks method for an inferior good that is Giffen.

Figure 4.9 shows the effect of a Gas tax with total rebate. Gas tax => relative price of gas

rises => relative consumption of gas falls. BUT the gas tax involves an negative income

effect. State elects to rebate the full tax to each person on an average basis. => heavy

users of gas will be at less utility, low users of gas will benefit since they will be over

compensated. Graph shows effect on heavy user. For all users relative price of gas has

increased.

Market demand = sum of all private demands

Price A B C Market

1 6 10 16 32

2 4 8 13 25

3 2 6 10 18

4 0 4 7 11

5 0 2 4 6

At price > 3 consumer A is out of the market.

Assuming demand curve is elastic (inelastic) => price fall inplies that revenue increases

(decreases).

Point elasticity = (P/Q)*(1/slope)

For straight line demand curves elasticity = point elasticity. Not all demand curves are

straight lines.

Arc elasticity = ( / )( / ) Q P P Q

Arc Income elasticity = ( / )( / ) Q I I Q

Demand curves have kinks as consumers jump into the market. See figure 4.11

P

Domestic Demand

World D Market Demand

Q


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Consumer surplus = total benefit of consuming = difference between what a consumer

is willing to pay for a product and what consumer actually pays.

A

B E

C D

Consumer surplus = area ABE

= AB * BE / 2

= (P * Q) / (d * 2)

d = BC / AB,

P*Q = BC * CD

=> (P * Q) / (d * 2) = (BC * CD)/(2*BC/AB) = (BC*CD*AB)/(2*BC)

= (AB*BE/2)

Value of clean air: Would consumers maintain their cars better if the exhaust was on

front of car? Why?

Bandwagon effect => You like the good better if others get it. Bandwagon effect

makes market more elastic. Retail marketing based on creating bandwagon effect. MJ

paid to wear a special shoe.

Snob Effect => You like the good less the more others have it. Snob effect

makes market demand less elastic.

Table 4.5 data is in Excel file Table4_5. Estimate

Q a B P B I 1 2


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and

ln( ) ln( ) ln( )Q a B P B I 1 2

Do you get what the book gets? (Hint I do not!!!)

Math Treatment

Assuming goods X and Y and income I, Customer wants to

(1) Max U(X,Y)

Given budget constraint

(2) I = PxX + PyY

Form Lagrangian or the function to be maximized

(3) U X Y P X P Y IX Y( , ) ( )

If the budget constraint is satisfied => second term = 0. Differentiate Lagrangian with

respect to X, Y and and set to zero. Obtain

(4) MU X Y PX X( , ) 0

(5) MU X Y PY y( , ) 0

(6) P X P Y IX Y 0

where MU X Y U X Y XX ( , ) ( , ) / etc

Equations (4) and (5) indicate that the consumption of X and Y will proceed until the

marginal utility is a multiple of P or

(7) [ ( , ) / ] [ ( , ) / ]MU X Y P MU X Y PX X Y Y

or

(8) MU X Y MU X Y P PX Y X Y( , ) / ( , ) /

Equation (8) expresses an equilibrium condition. This equation is satisfied where the

indifference curve is tangent to the budget line.

Along an indifference curve the utility is fixed or


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(9) U X Y U( , ) *

As we move along the indifference curve

(10) MU X Y dX MU X Y dY dUX Y( , ) ( , )* 0

can express the MRSXY as

(11) dY dX MU X Y MU X Y MRSX Y XY/ ( , ) / ( , )

or the ratio of the marginal utilities.

Practical case using Cobb-Douglas utility function. This section based on Appendix

to Chapter 4.

(12) U X Y X Ya a( , ) 1

which can be estimated as

(13) log( ( , )) log( ) ( ) log( )U X Y a X a Y 1

forming the Lagrangian and solving we find

(14) a X a Y P X P Y IX Ylog( ) ( ) log( ) ( )1

(15) / /X a X PX 0

(16) / ( )Y a Y PY1 0

(17) / P X P Y IX Y 0

Solving (15) and (16) for PXX and PYY and substituting in the budget equation gives

(18) a a I/ ( ) / 1 0

which implies that 1/ I . Form the first two equation we get

(19) X a P IX ( / )

and

(20) Y a P IY [( ) / ]1 .


26

The Cobb-Douglas utility function implies that the consumption of each good depends

only on the price of that good and income, not the price of the other good or that cross

elasticities of demand are zero.

The Lagrange multiplier represents the extra utility generated by one more dollar. Taking the total derivative

(21) dU dI MU X Y dX dI MU X Y dY dIX Y/ ( , )( / ) ( , )( / )

since any increase in income is spent

(22) dI P dX P dYX Y

since from (4) and (5) P MU X YX x ( , ) and P MU X YY Y ( , ) then

(23) dU dI P dX dI P dY dI P dX P dY dIX Y X Y/ ( / ) ( / ) ( ) /

substituting for dI gives

(24) dU dI P dX P dY P dX P dYX Y X Y/ ( ) / ( )

An example. Assume a 1 2/ , PX=$1.00 and PY=$2.00 and I = $100. From (19) & (20)

X a P IX ( / ) and Y a P IY [( ) / ]1 . Thus X = 50 and Y = 25. Since 1/ I , then

=1/100. If income were to increase to $101, X=50.5 and Y=25.25. The original utility was . *log( ) . *log( ) .5 50 5 25 3565 while the new utility was

. *log( . ) . *log( . ) .5 505 5 2525 3575 . was .01 which is the exact difference in utility.

(12) implies that if the consumption of X and Y were to increase by , then total utility

goes up by . In a more general case

(25) U X Y X Y( , )

where in general 1 . Here if X and Y increase by , then utility goes up by

( ) . Direct differentiation of (25) with respect to X and Y gives

(26) MU X Y dU X Y dX aX Y aU X Y XXa B( , ) ( , ) / ( , ) /( ) 1

(27) MU X Y dU X Y dY X Y U X Y YYa( , ) ( , ) / ( , ) /( ) 1

Equations (27) and (28) show that if Y is fixed and X is increased the marginal utility of

each additional X will decline. An additive utility function will not have this property.


27

Duality in Consumption Theory states that maximizing utility for a given budget is

equivalent to minimizing the cost of obtaining a given level of utility. This can be best

seen with indifference curves and budget lines.

Discussion Problem # 1

Sally Henin has an arc price elasticity of demand for gasoline of -.8. Her income

elasticity for gas is .5. Sally has a current income of $40,000 per year and spends $800

per year for gas. The current price of gas is $1.00.

a. The government is concerned about energy usage and is contemplating an excise tax which will cause gas prices to increase to $1.40. What will happen

to Sally's consumption?

b. The Government is considering a $200.00 tax rebate. How will this impact Sally?

c. Assume both the tax and the rebate are implemented. Is Sally worse off or not?

a. Solve arc elasticity formula for new Q b. Using new Q and arc income elasticity formula sub in new income and recalculate Q c. See how much she spends before and after

2 2

2 2

( 800) /(1.40 1.00) ( 800) (1.00 1.40).8

(1.00 1.40) /( 800) ( 800) (1.40 1.00)

Q Q

Q Q

. ( ) ( )8 800 800 62 2Q Q

680 41602. Q

Q2 61176 612 .

. (( ) / ( , , ))(( ) / ( ))5 612 40 200 40 000 40000 40200 6123 3 Q Q

. ( ) ( )5 612 612 4013 3Q Q

4005 306 2454123. Q

Q3 61353 .

On final indifference curve she spends 613.53 * 1.40 = $858.94 . With her income and the

rebate she would have 40200-858.94 = $39,341 to spend on goods.

If she bought 614 at the old price she would have had 40000-614 = $39386

Sally is NOT happy with the government!!


28

Problem # 2

The San Francisco Chronicle reported that the toll on the Golden gate bridge was raised

from $2.00 to $3.00. Following the toll increase traffic fell 5%.

What is the point price elasticity of demand?

Steve Leonoudakis chairmen of the bridge's finance auditing committee

warned that the toll increase could cause toll revenues to decrease by $2.8

million per year. Is this statement consistent with Economic Theory?

Elasticity = ( / )( / )Q Q P P = -.05/.50 = -.1 or inelastic demand

Steve is wrong. Inelastic demand => revenue increases as price increases.

Chapter 5 Uncertainty and consumer behavior not covered in detail.

Fines: Individual balances gain from breaking the law against expected fine

Double park => utility gain $5.00

Fine => $50.00 where probability of getting caught = .1

Fine => $500.00 where probability of getting caught = .01

These cases imply enforcement costs = 0.0. Most drivers who do not like risk will not

double park.

In case of music piracy difficult to catch. => can have very high fines.


29

Chapter 6 Production

Firms turn inputs or factors of production into outputs via a production function

Q=F(K,L).

A production function implies a given technology.

Firm uses each input as efficiently as possible. Isoquant (production indifference curves)

show different quantities of inputs (say L and K) such that output is fixed.

L

Q=30

Q=20

Q=10

K

In short run not all inputs can be changed. In the long run all inputs can be changed.

Given K, Average product = Q/L, Marginal product = Q/L. Q = Total product.

When Marginal Product > Average Product => average product is increasing.

Figure 6.1 shows relationship between AP, TP and MP. Why would a firm never operate

where MP < 0? MP reaches a peak at point of inflection. of TP curve.

Figure 6.2 shows how output per time period goes up as technology improves.

Figure 6.4 shows that cereal yield and the food price index appear to be negatively

related. Why might this be so? Except for a brief period in the 70's, food prices have

declined.

Law of diminishing returns => with other inputs fixed, MP of an input declines as the

amount of that input used increases.

Malthus believed that the earth would not support population growth. To date he has been

wrong.


30

Table 6.3 shows Annual Growth of Labor Productivity in various countries. It is shown

below: Year US Japan France Germany UK

1960-1973 2.29 7.86 4.70 3.98 2.84

1974-1982 .22 2.29 1.73 2.28 1.53

1983-1991 1.54 2.64 1.50 2.07 1.57

1992-2000 1.94 1.08 1.40 1.64 2.22

2001-2009 1.90 1.50 .90 .80 1.30

GDP per hour worked in 2009 dollars

$56.90 $38.20 $54.70 $53.10 $45.80

A technological change raises the production function. Here it is occurring over time.

Q Ae L Kt

In any particular year the aggregate value of goods and services produced by en economy

is equal to the payments made to all factors of production.

We can estimate a production function in log form with Excel. Take Data from 6.4 and fit

model. See ch6_1.xls

ln( ) ln( ) ln( ) ln( )q a L k

Production Function data from Table 6.4 of Pindyck-Rubinfeld (2005)

Q L K lnq lnL LnK

20 1 1 2.995732 0 0

40 1 2 3.688879 0 0.693147

55 1 3 4.007333 0 1.098612

65 1 4 4.174387 0 1.386294

75 1 5 4.317488 0 1.609438

40 2 1 3.688879 0.693147 0

60 2 2 4.094345 0.693147 0.693147

75 2 3 4.317488 0.693147 1.098612

85 2 4 4.442651 0.693147 1.386294

90 2 5 4.49981 0.693147 1.609438

55 3 1 4.007333 1.098612 0

75 3 2 4.317488 1.098612 0.693147

90 3 3 4.49981 1.098612 1.098612

100 3 4 4.60517 1.098612 1.386294

105 3 5 4.65396 1.098612 1.609438

65 4 1 4.174387 1.386294 0

85 4 2 4.442651 1.386294 0.693147

100 4 3 4.60517 1.386294 1.098612

110 4 4 4.70048 1.386294 1.386294

115 4 5 4.744932 1.386294 1.609438

75 5 1 4.317488 1.609438 0


31

90 5 2 4.49981 1.609438 0.693147

105 5 3 4.65396 1.609438 1.098612

115 5 4 4.744932 1.609438 1.386294

120 5 5 4.787492 1.609438 1.609438

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.961637

R Square 0.924745 Adjusted R Square 0.917903 Standard Error 0.118085

Observations 25

ANOVA

df SS MS F Significance

F

Regression 2 3.769633 1.884817 135.1693 4.38E-13

Residual 22 0.306771 0.013944

Total 24 4.076404

Coefficients Standard

Error t Stat P-value Lower 95% Upper 95%

Lower 95.0%

Upper 95.0%

Intercept 3.394232 0.061017 55.62726 3.66E-25 3.267689 3.520774 3.267689 3.520774

lnL 0.483056 0.041549 11.62623 7.28E-11 0.396889 0.569223 0.396889 0.569223

LnK 0.483056 0.041549 11.62623 7.28E-11 0.396889 0.569223 0.396889 0.569223

RESIDUAL OUTPUT

Observation Predicted

lnq Residuals Yhat Actual Error

1 3.394232 -0.3985 29.79175 20 9.79175

2 3.72906 -0.04018 41.63997 40 1.639968

3 3.924923 0.08241 50.64917 55 -4.35083

4 4.063889 0.110498 58.20024 65 -6.79976

5 4.17168 0.145808 64.82428 75 -10.1757

6 3.72906 -0.04018 41.63997 40 1.639968

7 4.063889 0.030455 58.20024 60 -1.79976

8 4.259752 0.057736 70.79241 75 -4.20759

9 4.398718 0.043933 81.34655 85 -3.65345

10 4.506509 -0.0067 90.60499 90 0.604987

11 3.924923 0.08241 50.64917 55 -4.35083

12 4.259752 0.057736 70.79241 75 -4.20759

13 4.455614 0.044195 86.10902 90 -3.89098

14 4.594581 0.010589 98.94665 100 -1.05335


32

15 4.702372 -0.04841 110.2082 105 5.208238

16 4.063889 0.110498 58.20024 65 -6.79976

17 4.398718 0.043933 81.34655 85 -3.65345

18 4.594581 0.010589 98.94665 100 -1.05335

19 4.733547 -0.03307 113.6982 110 3.698178

20 4.841338 -0.09641 126.6387 115 11.63871

21 4.17168 0.145808 64.82428 75 -10.1757

22 4.506509 -0.0067 90.60499 90 0.604987

23 4.702372 -0.04841 110.2082 105 5.208238

24 4.841338 -0.09641 126.6387 115 11.63871

25 4.949129 -0.16164 141.0521 120 21.05206

The above Excel output shows how data can be used. Figure 6.4 graphs this data.

Marginal rate of technical substitution = K L/ for a given Q (K on vertical axis).

MRTS K L MP MPL K / ( / )

since along isoquant

( )( ) ( )( )MP L MP KL K 0

When inputs are substitutes => isoquants are straight lines.

When inputs are complements => isoquants are right angles

Assuming a Cobb-Douglas production function sum of coefficients determines returns

to scale. Assume all inputs increase by . Get

Q ae L K ae L K Qt a t a a a* ( ) ( )( ) ( )

Example: MPL= 50, MRTS = .25. What is MPK? . / /25 50 MP MP MPL k k .

=> MPK 200

Example: Determine whether decreasing, constant or increasing returns.

A. Q KL Q K L Q Q . , . ( )( ), **5 5 2 or increasing returns.

B. *2 3 , 2 3Q K L Q K L Q or constant returns.

Example: Assuming Q=100(K.8

L.2

) starting K=4 and L=49 show MP of labor and K are

declining


33

K L Q 4 49 100 4 49 660 218 2, , * * .. .

K L Q MPK 5 49 100 5 49 789 25 129 048 2, , * * . , .. .

K L Q MPK 6 49 100 6 49 91319 123948 2, , * * . , .. .

K L Q MPK 7 49 100 7 49 103304 119858 2, , * * . , .. .

K L Q 4 49 100 4 49 660 218 2, , * * .. .

K L Q MPL 4 50 100 4 50 66289 2 688 2, , * * . , .. .

K L Q MPL 4 51 100 4 51 66552 2 638 2, , * * . , .. .

K L Q MPL 4 52 100 4 52 66811 2598 2, , * * . , .. .


34

Chapter 7 Cost of Production

Accounting Cost - concerned with historical expenditures.

Economic Cost takes into account opportunity cost that has to be taken into

consideration in the decision process (It is more costly for a doctor to mow the lawn on

Monday at 10:00 than a janitor).

Sunk costs - costs that cannot be recovered.

Valuable Alternative use of land => high opportunity cost of present use.

Zoning in many cases reduces opportunity cost.

Total Cost (TC) = Variable Cost (VC) + Fixed Cost (FC)

Marginal Cost (MC) = VC Q TC Q/ /

Average Cost (AC) = TC Q/

Table 7.1 illustrates FC, AC VC MC, AFC, AVC, ATC

In the short run can change labor to increase output. Given the wage w ,

MC VC Q w L Q w MPL / / /

Assuming labor is the only variable input

AVC wL Q w APL / /

where APL is the average product of labor.

Figure 7.1 The MC curve goes through the minimum of the ATC and AVC but not the

AFC. As Q AFC , 0 .

In the long run all inputs are variable.

Isocost line (= production budget line) is locus of points shows different combinations of

inputs such that cost is fixed.

C wL rK


35

solving for K gives

( / ) (( / ) )K C r w r L

Isocost slope

K L w r/ ( / )

of ratio of wage rate to rental cost of capital.

Want to maximize production for a given total cost TC.

K

A=TC/Pk

A B=TC/PL

Q

B L

The MRTS K L MP MPL K / / . In equilibrium the slope of the isocost P PL K/ =

MRTS

MP MP P P w rL k L K/ / /

or

MP w MP rL K/ /

Figure 7.5 show effect of an effluent fee raising the relative price of the input water.

Production moves to be less water intensive.


36

Expansion path shows the amounts of labor and capital used as firm grows (figure 7.6).

This is a long run concept.

K

Long Run

Short Run

L

Economies of scale includes increasing returns to scale as a special case. Increasing

returns to scale requires inputs be used in fixed proportions. Economies of scale allows

the ratio of inputs to change.

Figure 7.6 Long-Run Cost with Constant Returns to scale

Figure 7.10 Long-Run Cost with first Economies then Diseconomies of Scale. The LAC

traces tangency points of SAC curves.

At minimum point of LAC the LMC and SMC intersect.

Economics of scale => MC < AC. Diseconomies of scale => MC > AC. Define

EC = elasticity of total cost

E TC TC Q Q TC Q TC Q MC ACC [ / ] / [ / ] [ / ] / [ / ] /

Economics of scale => Ec 1, of MC < AC.

Economies of scope are present when joint output of a single firm producing two

products is greater that the output of two firms each producing one product. Define

C Qi( ) as cost of producing Qi of the ith

good. Economies of scope => SC > 0

SC C Q C Q Q C Q Qii

n n [ ( ) ( ,..., )] / ( ,..., )1 1

Diseconomies of scope SC < 0


37

Learning Curve => Over time labor costs go down as more units are produced. Define L

as labor per unit, A> 0, B>0, 0< A to B

Learning Curve => A to C

A

B

C AC1

AC2

Q

In the early life of a product the learning curve is steep. After while the "learning" slows

down. In chip business had a 20% learning curve. => 10% increase in cumulative

production => costs fall 2%. In aircraft industry learning curve rate was 40%.

Estimating a cost curve

Linear Model used if MC is constant at . MC

VC Q


38

Quadratic Model used if have straight line MC. MC Q 2 .

VC Q Q 2

Cubic cost function used if have U shaped MC curve of form

MC Q Q 2 3 2

VC Q Q Q 2 3

Can use Excel and other software to estimate the MC curve.

Problem 12 page 272. Computer firm cost is AC CQ Q 10 1 3. ( ) . where CQ is

cumulative quantity, and Q is quantity per year.

a. There is a learning curve effect since -.1 b. There is decreasing returns to scale?

TC Q CQ Q Q 10 1 3 2. ( )( ) .

MC TC Q CQ Q / . ( ) .10 1 6

Since . .6 3Q Q => decreasing returns to scale

c. CQt=40,000, Qt = 10,000, Qt+1= 12,000 AC ACt t 10 1 40 3 10 9 10 1 50 3 12 861. ( ) . ( ) ., . ( ) . ( ) .

Problem 13 page 272.

Assume TC a bQ cQ dQ MC TC Q b cQ dQ 2 3 22 3, ( ) /

AC a Q b cQ dQ [ / ] 2 . AC not defined for Q=0. For a U shaped cost

curve we want c0. At minimum point of AC, MC=AC. Set a=0 to normalize y

axis and equate MC=AC. => b cQ dQ b cQ dQ 2 3 2 2 or c dQ 2 . If c=-1 and

d=1 then Q=1/2

Key Question: How do we use this theory to solve a practical problem?

Firm has a production function F K L AK L( , ) which could be estimated using Excel

when we note that log[ ( , )] log( ) log( ) log( )F L K A K L . Want to determine a

general case that shows the optimum K and L given the cost of capital r and the wage w.

The following is a simpler treatment than 273-278. In equilibrium we note that

(1) [ / ] /MP MP r wK L


39

Given the production function

(2) Q AK L0

(3) [ / ] [ / ]A K L A K L r w 1 1

(4) [ / ] / L K r w

(5) L r K w [ / ]

Substituting (5) into the production function (2) gives

(6) 0 [ / ]Q AK r K w

(7) K w r Q A( ) ( / ) / 0

The equilibrium amount of capital is

(8) K w r Q A [( / ) ]( / )/( ) /( ) 01

If the cost of capital, r, increases or the marginal product of capital, , falls K will fall. Direct substitution of (8) into (5) gives

(9) L r w Q A [( / ) ]( / )( /( )) ( /( )) 01

If the wage rate, w, increases or the marginal product of labor, , falls then less labor

will be used. The firms cost function is

(10) C wL rK

At equilibrium

(11) C w r Q A ( /( )) ( /( )) ( /( )) ( /( )) ( /( ))[( / ) ( / ) ]( / ) 1

Equation (11) shows how C is related to wages, w, cost of capital, r, and returns to scale

( ) . MATLAB can be used to calculate the appropriate derivatives

Equation (11) shows how costs are related to the production function of the firm as well

and input costs.

See ch7_1.xls for solution.


40

Chapter 8 Profit Maximization and Competitive Supply

Firms want to maximize revenue.

Competitive supply => many firms, all price takers, no product differentiation, free entry

Profit is the difference between revenue and cost for a given level of output q.

(1) ( ) ( ) ( )q R q C q

To maximize profit differentiate and set to zero. => MR(q) = MC(q)

(2) / ( ) / ( ) /q TR Q TC Q 0

For a competitive firm P is given => d and P=MR. It can be proved that

(3) MR AR Pd d [ ( / )] [ ( / )]1 1 1 1

(4) / [( ) / ] [( ) / ]TR q qp pq q p qp pq qp

p pq qp p d[ ( / )] [ ( / )]1 1 1

Figure 8.1 shows profit maximization. Figure 8.2 shows firm in competitive market is a

price taker.

Figure 8.3 shows a competitive firm (MR=AR) making extra normal profits and

operating with decreasing returns.

In long run new firms will enter and firm will earn normal profits or those profits such

that no firms enter or no firms leave industry.

Figure 8.5 show that in the short run the firms MC curve is the firm supply curve.

If an input increases in price => AC curve shifts up => MC curve shifts up and firm

produces less output.

Book indicates that short run MC of petroleum has flat sections until other refineries get

on the line. See figure 8.8. ComEd's costs are constant until they start jet engine

generators.

Industry supply curve is the sum of firm MC curves in the short run.


41

Producer Surplus = area above firm supply curve and below price. See figure 8.11.

In long run firm can alter all inputs. If industry is making extra normal profits in the short

run => new firms will enter such that in the long run all firms are making normal profits.

The long run competitive equilibrium point is P=SMC=LMC. Firm is at the minimum

point of its AC curve. Given the firm's technology, it is most efficient. It earns economic

profit (normal profit). See figure 8.13.

In long run firm tries to equate LRMC to price BUT new firms can enter the industry and

drive down price.

Economic profit = R - wL - rK where rK is the opportunity cost of capital. A firm

making zero economic profits may still stay in business.

Economic rent = return to factors of production in limited supply. MJ earns economic

rent. Songs and books are copyrighted to allow economic rent to be earned for a limited

number of years.

The long run supply of a constant cost industry is a straight line. This is a partial

equilibrium argument. As Q increases input prices will increase at some time. General

Equilibrium has all assumptions variable. Some industries are so small that they can be

assumed to have no effect on input prices. See figure 8.15

Increasing Cost Case => If extra normal profits are earned new firms will enter the

industry and input prices will increase. See figure 8.17.

Taxes. An output tax raises the MC curve. A Lump Sum Tax (such as a liquor license)

does not change the MC since it is paid no matter what. The effect of a n output tax in the

long run is to reduce industry supply.

Perfectly Competitive Markets Assume:

- Price Taking - Product Homogeneity - Perfect Mobility of Assets - Perfect Information

Even if only one firm in the market it may pay to act as if the firm was in a competitive

market since extra normal profits => others firms may enter to bid away profit.

Problem # 1 The Conigan box company is in a competitive market. It sells boxes in

batches of 100 for $100.00. TC Q 3 000 000 001 2, , . .

What is profit maximizing output? Want MC=MR=AR. => 100 002 50 000 . , ,Q Q


42

What is profit?

TR TC, *( ) ( . *( ) $500,100 50000 3000000 001 50000 0002

The firm should stay in business in the short run since AVC < P:

AVC TVC Q TVC TC TFC / , ,

TVC 55 00 000 3 000 000 2 500 000, , , , , , ,

AVC ( , , ) / , $502 500 000 50 000

Example: Restaurant stays open in off hours if it can cover labor costs.

Problem # 2 Competitive market has a market demand curve of

P Q 75 15.

and supply curve of

P Q 25 5. .

where Q = where a typical firm has MC q 25 10. .

What is market price and rate of sales? We set S = D or

25 5 75 15 25 75 15 25 5 . . , , . * $37.Q Q Q P

Each firm sells where MR = MC . Since perfect competition MR=AR=P=$37.50

375 25 10 35. . , . q q

Note: If you use ch2_1.xls template to solve system remember that the template is set up

as: *( ), ( ) , 50 2 , 50 (1/1.5)s d s dQ f P Q f P Q P Q P


43

Chapter 9 Analysis of Competitive Markets

Want to look at welfare and efficiency effects of a competitive market.

Figure 9.1 shows producer (area between supply curve and market price) and consumer

(area between demand curve and market price) surplus.

Price Controls: Figure 9.2 and 9.3 show changes in producer and consumer surplus

when the government put on a price control.

The more inelastic the demand curve the more the deadweight loss.

If supply is fixed there is no dead weight loss.

Looking at figure. Producer surplus loss = A+C. Consumer net gain = A-C-B.

Unless demand is totally inelastic a price control => a shortage.

Price controls can have a serious long term effect on market as was case with NY

housing.

Figures 9.4 & 9.5 contrast the effects to price being held below and above the market

price.

Kidney Market. (See figure 9.6) Supply function of 16000 .4sQ P implies that if the

price is held to $0.0 by the 1984 National Organ Transplantation Act, and you cannot

sell an organ, only 16000 will be supplied. The demand function is 32000 .4dQ P .

Equating

16000 .4 32000 .4 , $16000 / .8 $20,000

16000 (.4*20000) 16000 (.4*20000) 24000

P P P

Q

On figure 9.6 suppliers lost A+C. If supply is reduced due to not being able to sell

kidneys, the market clearing price is $40,000 and many consumers are rationed on a

"willingness to pay" A+D = total value of kidneys at new market clearing price.

Middlemen and hospitals get gain NOT donators.


44

Minimum Prices (Government restricts market from lowering prices. Fair trade laws.

Tariffs.) (See figure 9.7).

P1

A B

P2

C

Q3 Q0 Q1

Government raises price from P2 to P1. Supplier produces Q1 not Q3 > "glut"

From free market consumer surplus loss = B. Producer surplus loss = C (Assuming

producer produces Q3)

Minimum Wage Figure 9.8 shows the analysis for minimum wage which causes

unemployment of L2-L1.

Price Supports. In contrast to minimum price laws, price supports require that

government buy farm products. Figure 9.11 shows that as a result of the purchase

program production when from Q0 to Q2 and price from P0 to Ps. Consumer surplus

reduced by = B+A. Producer gain = A+B+D. Government cost = Ps(Q2-Q1).

Change in welfare (A+B+D)-(A+B)-[Ps(Q2-Q1)].

Production Quotas. Government reduces supply (taxi licenses, bar permits). NYC has

113,150 taxi licenses. Roughly same as 1937. Medallion costs $880,000. Cost in 1947

was $2,500. In 1980 was $55,000. If supply went up current medallion owners would see

a loss of value of their medallions. Drives cab ride prices very high. See Figure 9.13. In

NYC cabs are run 24/7, not shut off at night.

Acreage limitation programs give farmers money incentive to leave land idle. Causes

farmers to farm their land more intensively. Figure 9.11 suggests cost to government

must at least equal B+C+D of the gain from planting since farmer sees new higher price

as given.

CS A B PS A C payments to stop producing at least B C D , ( )

Thus PS A C B C D A B D

Total change in welfare


45

( ( )) ( ) ( ) ( ) CS PS Cost to gov A B A B D B C D B C

Society would be better off if Government just gave producers A+B+D since what

government would lose farmers would gain for a zero net effect.

Book Example page 336 figure 9.12 shows how to use above theory:

In 1981 1800 240 , 3550 266s dQ P Q P

(240 266) (3550 1800), $3.46, 2630P P Q

Government must increase demand to raise the price. Let Qg be government demand

3550 266 1800 240 506 1750 P Q P Q Pg g,

Given desired P, Qg is determined. If P=$3.70, => government buys 122 million 2688-

566) bushels at cost of $451.4 million. Inspect figure 9.12. Customers lose A((3.7-

3.46)*2566) + B(.5*(3.70-3.46)(2630-2566) or 616+8=624 million. Note that A is

substantially bigger that B in this problem. Total cost = 624+451.4=1075.4

Exact answers for this problem and related ones are in ch9_1.xls.

As an exercise run the problem where the desired price is $3.80. Adjust demand and

supply and see what happens.

If P = $4.00, => government buys 506*4-1750 = 274 at a cost of $1096 million.

Calculate A and B here.

Quotas and Tariffs. Figures 9.14 and 9.15 shows basic setup. (9.14 shows a tariff that

eliminates all imports). Consider figure 9.15. With free trade the price is Pw domestic

supply is Qs, domestic demand is Qd. Imports are (Qd.-Qs). After a tariff (or quota).

Domestic supply jumps to Q's, domestic demand falls to Q'd and imports fall to

Q'd-Q's. Trapezoid A = gain to producers. Due to higher price consumer loss is

A+B+C+D. If a tariff is imposed, Gov gains revenue D. Net domestic loss is B+C+D.

Excel file ch9_2 shows setup to analyze Sugar Case. A tariff of 83% gives book case.

Can adjust tariff to eliminate imports and thus tariff revenue (area D).

Product Taxes. Figure 9.16 and 9.17 shows effect on producers and consumers of a per

unit tax on producers. Area A + B = what buyers lose. Area D + C = what sellers lose.

Are A + D = what government collects. s = elasticity of supply. d = elasticity of

demand. A tax falls mostly on the buyer (seller) if d s/ is small (large).

Pass-through (to consumers) fraction is s s d/ ( ) .


46

Fraction of tax producers bear is d s d/ ( )

NOTE: These formulas make use of fact that d 0 .

Most luxury goods have inelastic demand => luxury good tax hits consumers hard.

Example 9.7 Tax on Gas. See figure 9.20 and Excel 9_3.xls

We are given that d s P Q . , . , $1. ,* *5 4 00 100 . From Chapter 2 and excel

ch2_2.xls we know that

Given QD = a - bP (11)

QS = c + dP (12)

And P* and Q

* are equilibrium P and Q, then at equilibrium the elasticity of demand D and

elasticity of supply S are

D = -b(P*/Q

*) (13)

S = d(P*/Q

*) (14)

This implies 150 25 , 60 20d sQ P Q P . With no governmental tax

150 25 60 20

90 45 $2.00. 100

P P

P P Q

After Government places a $1.00 tax the new price is $2.44 and the new quantity is 89.

The producer price falls to $1.44. The steeper the supply curve the less quantity falls and

the more the producer price falls. The more inelastic the demand curve the more the

consumer price increases. In this case a greater proportion of the tax is passed on. The

following calculations replicate the figure 9.20

0supply price, no tax price, price including tax

1.00

150 25

60 20

150 25( 1) 60 20

(150 25 60) 45 65 / 45 1.444

$2.44. 60 20*1.44 88.8

s b

b s s

d

b

s

s

d s

s s

s s

b

p p p

p p tax p

Q p

Q p

Q Q p p

p p

p Q


47

Problem # 12 page 354 has the demand and supply of hula beans. See p354_12.xls

Q P Q Ps d 50 100 5, . . The world trade price is $.60. Congress puts on a tariff of

$.40. Use of ch9_2.xls implies that Equilibrium P and Q are $1.00 and 50 if there was no

foreign supply. If the tariff is imposed at .666666 then the domestic producer will

produce 10. The domestic consumption will be 50 (instead of 70 at world trade price of

$.60). Deadweight loss = (70-50)*$/40*.5= area C = $4.00. Before the tariff since

domestic production is 10 and consumption is 70 => import 60. After tariff there is no

imports. Consumer surplus loss =$24.


48

Chapter 10 Market Power: Monopoly and Monopsony

Monopoly => One producer MR AR.

Monopsony => One buyer

Assuming P=6-Q

P Q TR MR AR TR 6 0 0 - - - 0

5 1 5 5 5 inf 5

4 2 8 3 4 -4 8

3 3 9 1 3 -1.5 9

2 4 8 -1 2 -.667 8

1 5 5 -3 1 -.25 5

Key Formulas: MR AR [ ( / )]1 1

[ / ( )]AR MR AR

If || < 1 => as quantity increases TR decreases. See figure 10.1

A

At B =-1. AB=BD, AE=EO, OC=CD

E B

O C D

Equilibrium at max profit requires MC=MR where MC hits MR from below. Figure 10.2

is the basic diagram. Various points:

- If normal profits are made => AC curve will be tangent to AR curve at a point to left of minimum point. Normal profits with MR < AR =>

operating at less than optimum capacity.

- If MR=AR => perfect competition. Can have three cases: 1. If making loss in short run => less than optimum capacity. 2. If making normal


49

profits => at minimum point of AC curve. 3. If making extra normal

profits => operating at greater than optimum capacity.

- If MR < AR can

Possible Cases Table: Study below listed tables and be able to draw all possible cases

and prove that the I cases are not possible.

MR=AR

MC=MR

MCAC

_____________________________________________________________________

AC>AR Case 1 P Case 2 I Case 3 I

AC=AR Case 4 I Case 5 P Case 6 I

AC


50

A firm always maximizes profit if MC=MR and MC hits MR from below.

A firm makes an extra normal profit if AR>AC, a normal profit if AR=AC and a short

term loss if AR C'(Q)=R'(Q) or 2 40 2 10 30Q Q Q P , ,

Solution is illustrated in figure 10.3. This is case 18 . a firm making extra normal profit

operating at greater than optimum capacity.

Since in equilibrium MC=MR and MR AR d [ ( / )]1 1 the markup model for pricing

is MC AR AR or AR P MCd d ( / ), [ / ( ( / ))]1 1 1

The "markup model" fails if d 1 . If | |d 1 the implied price is negative! No firm

will ever operate here!

In a competitive market d and in equilibrium (case 5) P=MC.

Figures 10.4a and 10.4b show special cases where demand can shift and leave Q fixed

and demand can shift and leave P fixed. This is usually not the case.

A per unit tax of increases MC by the same amount. Here profit is where

MR MC

Unless there is a vertical demand curve, A BQ . If | | 1,d P

The more inelastic the demand curve the higher the price after the tax. This can be tested

using toolbox file ch9_4.xls. To make the demand curve more inelastic, reduce the

coefficient on price. Toolbox file ch9_4.xls must be used in place of ch9_3.xls since the

former holds the percent tax fixed while the latter holds the dollar amount of the tax

fixed.


51

In a multi-plant firm the profit maximization condition is

MC MC MC MRn1 2 ,...,

Figure 10.6 shows MC horizontal sum of MC MCT i ii

n

1

for a n plant system.

Q QT i

Monopoly Power. A firm in an industry with few sellers will face a more elastic demand

curve than the industry as a whole. The greater the product loyalty for that firms product,

the more inelastic the demand curve. The more inelastic the demand curve the more the

firm can raise price. Lerner's measure of monopoly power L P MC P ( ) / . L is in the

range 0-1. P=MC => L=0 and demand curve has . Since MR P [ ( / )]1 1 and

MR=MC as | | .B AP

1. in food industry, =-10 in store.

Manager sets P MC MC MC / ( ( / )) / ( . ) .1 1 1 1 111 or a 10%-11% markup. The

better the quality of the store the smaller | | and the more price can be raised. If 5

prices could be raised (1.-(1./5)) of 25%.

Designer label clothing => | | B or higher prices. Advertising is designed to lower the absolute value of the demand elasticity. To make the consumer less sensitive to a price

change. See figures 10.8a and 10.8b

Firm's elasticity of demand due to:

- Market elasticity of demand - Number of firms in the market - Interaction between firms

The firm will face a more inelastic demand if the number of firms in the market is small

and there is less interaction between firms (i.e. firms do not follow a price lowering with

a price lowering). If firms collude, then prices will go up. OPEC limited supply. Some

countries cheated!!

Figure 10.10 shows Deadweight loss of monopoly power. Monopolist wants to equate

MC=MR to maximize profit. Consumers lost A+B. Producer gains A loses C.

Deadweight loss = -B-C.

Figure 10.11 shows "kink" in MR curve due to a price ceiling due to regulation. If price

is set at Pc , can get perfect competition solution. What is interesting is MC can move

within the kink and prices will not change. Problems:


52

- How do we know where that it? - By price control will we be removing incentives?

Figure 10.12 shows a Natural Monopoly ( are in range of declining MC as Q increases.).

Here want one firm. If left alone firm wants to sell Qm at Pm. Government lowers MR as

seen by firm by setting Pr or the lowest price where the firms stays in business. If price

were set to Pc firm will make a loss since here MC=MR but MC two monopolists facing each other. Hard to tell what will

happen. Think of auto producers and parts suppliers.

Problem Firm has a

demand curve P Q 100 01.

supply curve TC Q 50 30000

What is P and Q to maximize profit? MC = 50. MR Q Q Q Q ( . ) / .100 01 100 022

50 100 02 2500 100 01 2500 75 . , , (. )* $.Q Q P

Problem


53

Given P= 27 24 21 18 15 12 9 6 3 0

Q=0 2 4 6 8 10 12 14 16 18

MC=10

What is P and Q to max profit?

Inspection or regression analysis (See p365_5.xls) indicates

227 1.5 , 27 1.5 , ( ) / 27 3P Q TR PQ Q Q MR TR Q Q

TR ( . )( . ) $104.185 567 83

Profit = 10483 10 567 17. ( )( . ) $48.

Problem Firm faces demand P Q 700 5 and has two factories.

C Q Q MC Q1 1 12

1 110 20( ) , 2

2 2 2 2 2( ) 20 , 40C Q Q MC Q

Q Q Q MC MC MCT 1 2 1 220 40 3 40[ / ] [ / ] /

MC Q MC MR Q Q QT T 40 3 40 3 700 10 30/ , [ / ] ,

Monopoly price = 700 5 30 550 ( )( )

MR MC MC 1 2 700 10 30 400( )( )

Q Q1 2400 20 20 400 40 10 / , /

Firm produces less in higher cost plant!!


54

Chapter 11 Pricing with Market Power

Figure 11.1 suggests that if one price is charged it would be P.* If firm was able to price

discriminate, it would charge a higher price to more inelastic market. It has been reported

that McDonald's charges more for the same item at Water Tower Place than on the South

Side!

A firm that practices first-degree price discrimination charges each customer his/her

reservation price or the maximum that the consumer would pay. Figure 11.2 shows how

in such a world the firm expands production from Q* to Q

**. In this word all consumer

surplus is captured by the firm. In practice this is hard to do. Universities try to

practice this approach by giving just enough aid to get the student. If firm does not have

perfect knowledge, then a number of prices can be charged. See figure 11.3

Second-degree price discrimination occurs when price is reduced if additional amounts

are bought. (See figure 11.4) Big box vs small store.

Third-degree price discrimination occurs when firm packages same product under two

different labels and sells at a different price. Using formula MR Pi i di [ ( / )]1 1 and

MC MR MR 1 2 , then

1 2 2 1[ / ] [1 (1/ )]/[1 (1/ )]d dP P

Figures 11.5 and 11.6 illustrate third-degree price discrimination.

Table 11.1 suggests that coupon users have higher elasticity of demand than non coupon

users. Assume the non coupon users have elasticity of demand d1 . If P1 = P2, and V =

value of coupon, then in an optimum world

1 2 2 1[( ) / ] [1 (1/ )]/[1 (1/ )]d dP V P

Airlines price discriminate. Table 11.2 on page indicates that industry price elasticity for

First-Class, Unrestricted Coach and Discount are -.3, -.4 and -.9. Income elasticities are

1.1, 1,.2 and 1.8. Firm elasticities are > in absolute value.

Intertemporal Price Discrimination => firm charges first consumers more. Hard cover

edition of a book comes out first. Before too long soft cover comes out at a lower price.

Library buys hard cover! Nikon does this with new models! See figure 11.7

Peak-Load Pricing => charge more at a certain time in the day. See figure 11.8

Two-Part Tariff => pay to get into Great America, then, pay for each ride.


55

Figure 11.9 shows single consumer. Usage fee is set to marginal cost. Entry fee is set to capture entire consumer surplus. Here firm captures all surplus

Figure 11.10 Profit making usage fee is set > MC. Entry fee T* set to surplus of customer with smaller demand. Profit = 2*T

* + (P

*-MC)*(Q1 + Q2).

For n customers this becomes (see figure 11.11) n(T)*T* +(P-MC)*Q(n),

Polaroid Camera cost was entry fee. Film was price.

Bundling. When customers have heterogeneous demands that are negatively

correlated => pays to bundle products. Figure 11.12 and 11.13 show cases

A

II I I Consumers buy both

II Consumers buy only A

III Consumers buy neither A or B

IV Consumers buy only B

III IV

B

By forcing consumer to get both => move to section I

Effectiveness of bundling depends on how negatively products are related.

Mixed bundling. Sell as a package or alone. MS Office 97 is sold this way. Figure 11.18

shows that with zero MC this is even more profitable.

Luxury cars are sold with standard options bundled into the car. Vacation package

another example. Restaurants sell items a la carte and as dinners.

Tying => force customer to buy all items from one source. McDonalds at one time

required owners to get supplies from one source. Gas station has to carry full range of

products.

Advertising. Want marginal revenue of an additional dollar spent on advertising to equal

full marginal cost of that advertising. We define profit as a function of amount sold Q and

advertising A.

( , ) ( , ) ( )Q A PQ P A C Q A

/ ( / ) ( / ) 1 0A P Q A MC Q A

We rearrange and get the marginal revenue from advertising.

( / ) 1 ( / )ad sMR P Q A MC Q A


56

[ ][ / ] , [( ) / ][( ) / ( )] [ / ]P MC Q A P MC P A Q Q A A PQ 1

Given elasticity of demand = [( ) / ( )]A Q Q A A , in equilibrium

then

[( ) / ] [ / ]

1 1[1 ] [( ) / ]

a

p p

P MC P A PQ

MC P P MC P

[ / ] [ / ]A PQ A P

Which determines how much advertising should be purchased.

The more inelastic the demand for the firm's output, the more advertising. In perfect

competition since p , no advertising is done.

This logic takes into account the effect of advertising on increasing sales but also adding

to costs as added units have to be produced.

Transfer Pricing is between units of a vertically integrated firm. Will show that

profits are maximized if transfer price equals marginal cost of respective upstream

division.

( ) ( ) ( ) ( ) ( )Q R Q C Q C Q C Qd 1 1 2 2 where each term represents revenue from sales,

firm production costs, costs from intermediate production inputs from plant 1 and costs

from intermediate production inputs from plant 2.

To maximize the net marginal revenue firm earns from one more input of Q1 and Q2

differentiate ( )Q with respect to Q1 and Q2.

d dQ dR dQ Q Q dC dQ Q Q dC dQd / ( / )( / ) ( / )( / ) /1 1 1 1 1 0

NMR MR MC MPP MCi d i i ( )

Each upstream firm takes price Pi as given and equates it to their marginal cost MCi.

NMR MR MC MPP Pi d i i ( )


57

Engine problem consists of an auto firm assembling cars with the option of getting

engines from an upstream firm. Demand for autos

2

20000

20000 2

Cost of assembly

( ) 8000

8000

engine costs

( ) 2

( ) 4

Net marginal revenue of engines given

20000 2 8000 12000 2

12000 2 4 2000

A

A

E E E

E E E

E

E A

E E

E E

P Q

MR Q

C Q Q

MC

C Q Q

MC Q Q

Q Q

NMR MR MC Q Q

NMR MC

Q Q Q

Optimal transfer price is marginal cost of the 2000 engines or 4 $8000EQ

If engines can be bought outside for $6000, then a case can be made that the firm should

buy all engines outside BUT remember the engine dept has an upward slope to MC. This

suggests equate

6000

12000 2 6000 3000

Here we have since we set ( ) 6000

4 6000

1500

Firm buys 1500 outside and uses 1500 of its own engines.

E

E

E E E

E

E

NMR

Q Q

Q Q MC Q

Q

Q


58

Chapter 12 Monopolistic Competition and Oligopoly

Monopolistic Competition => Large number of sellers each with some market power

due to selling a differentiated product. At the model level in the automotive industry we

have monopolistic competition. d in monopolistic competition.

- Many sellers - Each seller selling a slightly differentiated product - Entry by new firms is NOT restricted

Note: Trade theory suggested that trade would be between countries that were not

similar. However most trade is between countries such as Canada and US and Germany

and France which are similar. Krugman used monopolistic Competition Theory to rescue

trade theory.

Oligopoly => Few sellers each with market power. If one firm in an oligopoly market

were to raise price, the others would not follow and that firm would find sales fall off

rapidly. If the same firm were to lower price hoping to increase sales at the expense of the

other firms, then all other firms would lower price and the expected increase in sales

would not be realized.

- Few sellers - Each seller selling a differentiated product. - Each with substantial market power - Entry is restricted by barriers (example aircraft industry)

Cartel=> Firms work together. (GE in 50's until they got caught.)

- Like a monopoly BUT members tempted to cheat.

- Cartel usually does not control complete market

Under Monopolistic Competition free entry =>

- No extra normal profits in long run.

- Firms in long run operate at less than optimum (minimum average cost) capacity (see case 13) and figures 12.1 and 12.2.

Table 12.1 lists Elasticities

Royal Crown -2.4

Coke -5.2 to -5.7 (more close substitutes)


59

Folgers -6.4

Maxwell House -8.2

Chock Full oNuts -3.6

In perfect competition and monopolistic competition When a market is in equilibrium

firms are doing the best they can and have no reason to change their price or

output.

In oligopoly each firm is doing the best it can, given what its competitors are doing.

Cournot Model. Two firms (duopoly) each making its decision at the same time.

Decision rule: Each treats the output level of its competitor as given.

See figure 12.3 where MC is constant

Firm 1 Q Firm 1 thinks Firm two produces

50 0 25 50 12.5 75

Firm # 1 profit-maximizing output is a decreasing schedule of how much it thinks firm 2 will produce. This defines the reaction curve.

Cournot equilibrium => Intersection of firm 1's and firm 2's reaction curve => how

firms divide up quantity. (See figure 12.4).

Assume problem on page 461-462 where there are 2 firms

MCi = 0

P=30-Q

Define R1 = total revenue of firm 1


60

1 1 1

1 1 2 1

2

1 1 2 1

1 1 1 1 2

2 2 2

2

2 1 2 2 1 1 2 1

2 2 2 2 1

(30 )

30 ( )

30

/ 30 2

(30 )

30 ( ) 30 ( )

/ 30 2

R PQ Q Q

Q Q Q Q

Q Q Q Q

MR R Q Q Q

R PQ Q Q

Q Q Q Q Q Q Q Q

MR R Q Q Q

Firms 1 and 2 have reaction curves

Q Q Q Q1 2 2 115 5 15 5 . , .

which are derived by setting MR1 and MR2 to zero and solving for Q1 and Q2.

at equilibrium Q Q Q Q Q1 1 1 215 5 15 5 10 20 . [ . ], ,

If firms could work together => 2

1 2

(30 ) 30

/ 30 2 , 15, 7.5

PQ Q Q Q Q

MR R Q Q Q Q Q

Note that MC=0 and 1 2 15Q Q defines the contract curve.

For graphical analysis see Figure 12.5.

Stackelberg Model => One firm moves first BUT has to take into account what other

firms will do.

Firm 2 has reaction curve Q Q2 115 5 . . Firm 1 knows this and knows its revenue

is PQ Q Q Q Q1 1 12

2 130 . To get solution substitute form 2's reaction curve in firm 1

revenue curve

R Q Q Q Q Q Q1 1 12

1 1 1 1

230 15 5 15 5 [ . ] . . MR1 = 15 151 1 Q Q,

Firm 2 will produce 15 5 7 51 . .Q

Going first gave firm 1 the advantage.

Stackleberg Model good when one firm is dominant and can move quickly to set

quantity.


61

Cournot Model good when have more firms with no one firm dominant. Cournot model

is stable because e

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