Economics 352: Intermediate Microeconomics Notes and ...faculty.metrostate.edu/BELLASAL/352/Lec12new.pdfChapter Twelve: The Partial Equilibrium Competitive Model and Applied Competitive

EC 352: Intermediate Microeconomics, Lecture 12

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Economics 352: Intermediate Microeconomics Notes and Sample Questions Chapter Twelve: The Partial Equilibrium Competitive Model and Applied Competitive Analysis

This chapter will investigate perfect competition in the short run and in the long run. The

difference between the short run and long run here will be that new firms can enter the

market in the short run and, as a result, economic profits for firms will be driven to zero

in the long run, regardless of what they are in the short run.

Market Demand

Market demand is the sum of the individual demand curves of each person. In a graph,

this looks like:

Three graphs, side by side, showing that the horizontal sum of two individual demand

curves is the market demand curve.

Total market demand, Dt, is the horizontal sum of the demand functions of person a (Da)

and person b (Db). Also, note that the lower case letters q are used for individual

quantities while the upper case Q is used for the market quantity.

In terms of demand functions expressed mathematically, if each person has individual

demand function for good x of xi = xi (px, py, Ii) where xi is the quantity demanded by

person i and Ii is the income of person i, then the total market demand where there are n

people is:

n

1i

iyxi I,p,pxX


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Changes in the price of x will cause movement along the demand curve and are referred

to as a change in the quantity demanded.

Changes in anything else result in a shift in the demand curve and are a change in

demand. Events that could result in a change in market demand would include:

-a change in the price of another good

-a change in incomes

-a change in weather

-new information about health effects of the good

-a tax or subsidy on the good

You should work through Example 10.1 to see how this all plays out with equations.

This can also be generalized to multiple goods and multiple people, as shown on page

282 of the text, but I don’t believe that this sort of generalization will be exploited further

in the chapter.

Some Notation

xi is the quantity of good x demanded by person i

QD is the total quantity demanded in the market

P is the market price of the good in question

P’ is the prices of other goods (or for you math fans, a vector of the prices of other goods)

I is the incomes of all the people in the market (again, a vector of incomes)

What’s up with the vectors?

P’ and I are one symbol that stand for multiple values. So, if we’re talking about good 1,

then P’ is the set of all the other prices in the market, so it would be [p2, p3, …, pn].

Similarly, I is the set of all of the incomes of people that are potential customers in the

market, so I is really [I1, I2, …, Im].

Elasticities of Market Demand

These are definitional and given in terms of partial derivatives:

Price Elasticity of Market Demand

D

D

Q

P

P

I,'P,PQ

Cross Price Elasticity of Market Demand

D

D

Q

'P

'P

I,'P,PQ


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Income Elasticity of Market Demand

D

D

Q

I

I

I,'P,PQ

Short Run and Long Run

Discussion of supply responses in a market really depends on the time frame involved.

As more time is allowed, the magnitude of suppliers’ response to a price change can

increase.

The very short run is defined as the time period over which the quantity supplied is fixed,

so no supplier can alter the quantity that she will offer for sale. The market supply curve

is vertical in the very short run.

The short run is defined as the time period in which suppliers who are currently in the

market can change the quantity that they supply. However, new firms cannot enter the

market and existing firms cannot leave the market.

In the long run it’s all in play. Existing firms can leave the market and new firms can

enter.

The important thing about this will be that if economic profits are positive in the short

run, new firms will be attracted to the market and supply will expand in the long run,

driving prices down and driving profits toward zero.

How long the very short run, short run and long run might be depends on the industry in

question. It might take a couple of weeks or a month to get a new espresso cart up and

running, but it could take a decade to bring a new automobile plant on line.

Assumptions of Perfect Competition

The following are the assumptions about perfectly competitive markets. They actually

describe only a few markets, generally financial markets and some commodity markets.

However, the analysis is perfect competition is important, even though it doesn’t

perfectly describe all that many real-world markets, because lots of markets are

sufficiently similar to perfectly competitive markets that the conclusions we get from

analysis of perfect competition can be applied. Also, perfect competition is an ideal

against which other types of markets can be compared.

1. A large number of firms

2. A homogeneous product – every firm produces exactly the same thing

3. Each firm maximizes its own profits

4. Each firm takes the market price as given


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5. All prices are known by all market participants

6. There are no secrets about the production of the product

7. There are no transactions costs

8. There are no barriers to the entry of new firms or exit of existing firms

The short run market supply curve is the horizontal sum of the individual supply curves

of the existing firms in the market. This is just like the market demand curve assembled

above. The total supply curve is the sum of the quantities supplied by each individual

firm at each price.

Three graphs, side by side, showing that the market supply curve is the horizontal sum of

individual firms’ supply curves.

In mathematical terms, if each firm has the supply function qi(P,v,w) then the market

supply is given by:

n

1i

iS w,v,Pqw,v,PQ

To see how this all works out, you should work through Example 10.2 in the textbook,

knowing that the real start of this is back in Example 8.1 with cost minimization of the

Cobb-Douglas production function:

lk)l,k(fq

In Example 8.5 we get the cost function

1

1

11 kwqvk)k,q,w,v(SC

And in Example 9.3 we get the short run supply function for one firm


5

11

1

1

Pkw

q

Short Run Equilibrium in A Perfectly Competitive Market

In a perfectly competitive market, the short run equilibrium price will be the price for

which the market quantity supplied is equal to the market quantity demanded. This

should come as no surprise.

In math terms, this is that the equilibrium price P* satisfies:

QD(P*,P’,I) = QS(P*,v,w)

In terms of a simple diagram of a market with 1000 firms and an equilibrium price of $8,

this could be:

Two diagrams, side by side, showing supply and demand in the market generating a price

that an individual firm takes as given in determining its profit maximizing quantity to

produce. The profit maximizing quantity is the quantity for which marginal cost is equal

to the market price.

That is, the equilibrium price is determined in the market to be $8, and the resulting

market quantity is 10,000 units. For an individual firm, the price of $8 causes it to

produce 10 units. The 1000 identical firms together produce the 10,000 units in the

market.

If market demand increases, the market price will rise and, in the short run, all of the

existing firms will increase production.


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If market demand falls, the market price will fall and, in the short run, all of the existing

firms will decrease production.

Each of these events will be represented in the market diagram by a shift in the demand

curve, but by a movement along the existing supply curve. There will be a change in

demand, but a change in the quantity supplied.

You should work through Example 10.3.

Mathematical Model of Market Equilibrium

This is shown on page 293 of the text. I’ll try to work through it a bit more carefully

here.

We start with the demand and supply functions, except that the quantities to be supplied

and demanded are expressed as a function of the price and just one other factor. This

other factor (which we won’t name right now) is called α in the case of the demand

function and is called β in the case of the supply function.

,PSQ

,PDQ

S

D

If we totally differentiate each of these we get:

dSdPSdS

dPP

SdQ

dDdPDdD

dPP

DdQ

PS

PD

In equilibrium we have QD=QS and, totally differentiating this we get:

dQD=dQS

And combining these we get:

dSdPSdDdPD PP


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Now, if β doesn’t change (that is, if β is held constant) we have dβ=0 and this equation

becomes:

PP

PP

DS

D

d

dP

dPSdDdPD

So, this describes the effect of an increase in α on the equilibrium price, P. The

denominator, SP – DP is positive (you should know why this is positive), so if the effect

of an increase in α on demand is positive, then an increase in α will increase the price.

Similarly, if the effect of an increase in α on demand is negative, then an increase in α

will lower the price.

α might be something like income, and if the good is a normal good then an increase in

income will increase demand for the good and its equilibrium price will rise.

You should work through Example 10.4 and be sure it makes sense to you.

Long Run Competitive Equilibrium

In the long run, if economic profits in an industry are positive, new firms will be attracted

to the industry and supply will increase. The increase in supply means that prices will

fall and, as a result, profits will fall, too. This will continue to happen until profits in the

industry are driven to zero, giving us the long run competitive equilibrium condition that

profits are equal to zero or, alternatively, that P=AC. If we combine this with the firm’s

profit maximizing condition that P=MC, we get P=MC=AC and profits equal zero.

Similarly, if economic profits are negative, firms will exit the industry (shut down, or

maybe start making something else, it doesn’t matter), causing the supply to diminish and

the price to rise. This will continue to happen until the price rises enough to bring

economic profits up to zero, at which point firms will stop exiting.

The standard, simple graph of long run equilibrium is:


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Two graphs, side by side, showing long run equilibrium in which the market price is

equal to the minimum average cost. The individual firm produces a quantity such that

price is equal to minimum average cost, which is equal to marginal cost.

Example

Imagine that a perfectly competitive industry has firms whose cost functions are given

by:

C(q) = 5000 + 5q + 2q2

and that there are currently 1000 firms in the industry. Demand in the industry is given

by:

P(Q) = 1000 – (Q/1000)

Which may be rewritten as:

P1000000,000,1QD

Solve for the short run equilibrium price and for the long run equilibrium price. Discuss

how the market will move from the short run equilibrium to the long run equilibrium.

The short run supply curve for a typical firm will be given by the firm’s marginal cost

function, which is:


9

4

5pq

p)q(MC

q45dq

dC)q(MC

s

That is, the marginal cost function is MC(q)=5+4q and, at a profit maximizing quantity

the marginal cost equals the price, so we set marginal cost equal to the price and solve for

the quantity to get the function for the quantity supplied.

Now, there are 1000 firms, so the market supply function is:

1250p250)5p(2504

5p1000q1000Q ss

We can combine this with the market demand function to get

199,000QQ

801*P

P1250250,001,1

1250P250P1000000,000,1

QQ

SD

SD

So, in the short run the quantity sold in the market is 199,000, so each of the 1000 firms

in the market produces 199 units.

Now, in the long run, P=MC=AC. It also happens that MC=AC at minimum average

cost, so there are a number of ways to solve for minimum average cost. You could either

find the average cost function and find its minimum (take the derivative and set it equal

to zero) or you could set the marginal cost function equal to the average cost function and

solve for q. Let’s do both.


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205)50(2550

5000)50(AC

50q

2500q

02q

5000

dq

dAC

q25q

5000)q(AC

q

q2q55000

q

)q(C)q(AC

2

2

2

205)50(45)50(MC

50q

q25000

q2q

5000

)q(MCq45q25q

5000)q(AC

2

So, the long run equilibrium has a price of 205 and each firm is making 50 units.

Total market demand at a price of 205 is:

1,000,000 – 1000(205) = 795,000

If each firm is producing 50 units, this means that in the long run there will be

795,000/50 = 15,900 firms.

Increasing, Decreasing and Constant Cost Industries

There’s a question about how well new firms in an industry can compete with previously

existing or incumbent firms.

If new firms tend to have higher average costs, either because they lack some advantage

that previously existing firms enjoy or because they just don’t know the business as well,

then in the long run as the quantity supplied increases, average costs in the market will

increase. Such an industry is known as an increasing cost industry, because as the

market quantity increases in the long run, the price or average cost will rise. In this case,

the long run supply curve will be upward sloping. The long run elasticity of supply will

be positive.

If prices or average costs don’t rise with the entry of new firms in the long run, then long

run supply will be infinitely elastic. That is, the long run supply curve will simply be a

horizontal line at the level of a typical firm’s minimum average cost. This is called a

constant cost industry. The long run elasticity of supply will be infinite.

If prices or average costs fall as more and more firms enter the industry, perhaps due to

positive externalities in production, then the long run supply curve will be downward

sloping and this will be a decreasing cost industry. The long run elasticity of supply will

be negative.


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The Effects of Shocks to the Market on the Structure of the Market

Market structure, in the case of perfect competition, basically means how many firms

there are and how much each firm produces.

If demand increases, the equilibrium price will rise in the short run, but it will fall back to

the minimum average cost in the long run. In a constant cost industry, this will result in

the entry of new firms and, in the long run, each firm will produce just as many units as

they did before the demand increase.

If producer costs rise, the effect on the number of firms and on each individual firm’s

output will be ambiguous. If the cost increase is an increase in the firm’s fixes costs, this

will shift the average cost function up but will leave the marginal cost function

unchanged. It will likely be the case that there will be fewer firms in the market, but that

the remaining firms will produce more units than they did previously. If the cost increase

takes the form of a large increase in marginal cost, then the optimal (average cost

minimizing) quantity might fall enough that each firm will produce fewer units and the

number of firms could actually rise.

Producer Surplus in the Long Run

In a constant cost industry, producer surplus or profit will go to zero in the long run as

new companies come in and drive the price down to minimum average cost.

The applicable principle here is that if firms in an industry without significant barriers to

entry are making extranormal profits, these profits won’t last long because new firms will

enter the industry and take those profits away. Put somewhat differently, if firms in

industries without barriers to entry have highly priced stocks, the value of those stocks

will probably fall over time as a result of new firms entering.

In an increasing cost industry, incumbent firms will have some cost advantage over new

entrants and the profits of incumbent firms can remain higher than normal (that is, they

can enjoy positive economic profits on a sustained basis), but these extra profits will

really be returns to the advantage that they possess.

For example, a farmer who owns particularly fertile land will be able to produce crops

more cheaply than a farmer working less fertile land. The extra profit earned as a result

of the superior fertility of the land might show up as extra profit for the farmer, but it is

really a rent accruing to the very fertile land that he owns and works. In fact, the

opportunity cost of his working the land is the rent that he could charge to someone else

to work the land.


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Practice Problems

1. Recreate the analysis on page 293, except that you should assume that supply shifts

and that demand is held constant. Explain how changes in β affect equilibrium price

and why this makes sense.

2. For the short run and long run competitive example presented in these notes, fill in the

appropriate numbers in the following diagrams.

Short run:

Long Run


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Applied Competitive Analysis

In this chapter, we will do some fun stuff with supply and demand and competitive

analysis.

There is one potentially important caveat offered at the beginning of the chapter that I

will echo here. The analysis offered here is partial equilibrium analysis, that is, it only

looks at one market and doesn’t consider effects in other markets. A more complete

analysis that looked explicitly at other markets and considered the interactions between

markets might generate different results.

A large part of the focus of this chapter is on the gains from trade, which are a measure of

the benefits to society of the exchanges that take place in a market. Gains from trade are

divided into the gains to consumers, or consumers’ surplus, and the gains to producers, or

producers’ surplus. These are shown for a market equilibrium in the following graph:


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A graph showing the triangles that are consumer surplus (CS) and producer surplus (PS) from the standard supply and demand graph with a market equilibrium.

To see why gains from trade are maximized at q*, it helps to think of the supply curve as

a marginal cost curve, that is, the height of the supply curve gives the cost of making and

selling one additional unit at each quantity, and to think of the demand curve as a

marginal value curve, that is, the height of the demand curve gives the consumers’

marginal willingness to pay to get another unit of the good at each quantity. The supply

curve is upward sloping because marginal cost is rising, at least in the short run. The

demand curve is downward sloping because marginal value diminishes.

At quantities less than q*, the marginal value is greater than the marginal cost, so there

are gains to be had by producing and selling additional units because consumers’

willingness to pay is greater than the marginal cost. For example, if I’m willing to pay

$10 to get another unit of something and it costs you only $3 to make and sell it, there is

the potential for an additional $10-$3=$7 in gains if an additional unit is made and sold.

So, at quantities less than q*, it is reasonable to increase production.

At quantities greater than q*, the marginal value is less than the marginal cost, so there

are gains to be had from reducing production because consumers’ willingness to pay is

less than the marginal cost. For example, if I’m willing to pay $4 to get another unit of

something and it costs you $12 to make and sell, making and selling that unit would

result in a loss of $12-$4=$8. So, at quantities greater than q*, it is reasonable reduce

production.

If production is at some level other than q*, the gains from trade will be reduced. This

reduction in gains from trade is called a dead weight loss or an efficiency loss.


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For example, at a smaller quantity, qs, there is the potential to produce additional units for

which the marginal value is relatively high and the marginal cost is relatively low.

Stopping at qs results in the dead weight loss shown in the diagram below:

A graph showing the dead weight loss (or the foregone gains from trade) that result from

too small a quantity being exchanged in a market.

Similarly, at too big a quantity, qb, the last few units produced had a relatively high

marginal cost and a relatively low marginal value and society would have been better off

if they had not been produced at all. Production should be reduced at quantities greater

than q*.

A graph showing the deadweight loss (or losses in gains from trade) that

result from too large a quantity of goods being exchanged in a market.


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Calculating This Stuff

The book goes through a couple of calculations examples (Example 11.1) but I’ll offer a

more complete set of examples here.

Imagine that you have supply and demand functions given by

QD=1200 – 2P and QS = 3P – 200

We will solve for the equilibrium price and quantity and then calculate the dead weight

loss resulting from quantities of 550 and 700.

First, to solve for equilibrium:

QD = QS

1200 – 2P = 3P – 200

1400 = 5P

P* = 280, Q*=640

Diagramming this, we have:

A graph showing the numerical values from this example as they look in a

supply and demand graph.

Further, we can calculate CS and PS:


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68,1606402132

1)0640()67280(

2

1PS

102,4006403202

1)0640()280600(

2

1CS

Now, if for some reason the quantity produced is restricted to 550 units, there will be a

resulting dead weight loss that can be calculated. To do this, we need to know the height

of the demand and supply curves at the quantity Q=550. To calculate these values, we

need to rewrite the supply and demand functions as marginal cost (MC) and marginal

value (MV) functions:

QD=1200 – 2P QS = 3P – 200

MV = P = 600 – Q/2 MC = 200/3 + Q/3

At Q=550 we have:

MV = 600 – 550/2 MC = 200/3 + (550/3)

MV = 600 – 275 MC = 66.67 + 183.33

MV = 325 MC = 250

Now the calculation of the dead weight loss is simply a matter of finding the area of a

triangle:

A graph showing the numbers and calculated dead weight loss from this

example.

The dead weight loss (DWL) can be calculated as:


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337590752

1)550640()250325(

2

1DWL

This is the value by which gains from trade would increase if the market were allowed to

trade 640 units instead of 550.

You might be wondering if you could go one step further and describe how the dead

weight loss or the extra gains from trade might be divided between consumers and

producers. This could be done if you knew the market price when Q=550. If the market

price at Q=550 is P=280, then figuring out the extra CS and extra PS from moving to

Q=640 would be a fairly straightforward calculation of two triangles’ areas. However,

the price at Q=550 is P=325, then moving to market equilibrium would represent a big

increase in consumers’ surplus and, most likely, a decrease in producers’ surplus.

Now, if the quantity were 700, we would recreate the calculations from above:

At Q=700 we have:

MV = 600 – 700/2 MC = 200/3 + (700/3)

MV = 600 – 350 MC = 66.67 + 233.33

MV = 250 MC = 300

A graph showing the numbers and resulting dead weight loss resulting

from too much production in this example.

The dead weight loss (DWL) can be calculated as:

150060502

1)640700()250300(

2

1DWL


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This is the value by which gains from trade would increase if the market quantity was cut

from 700 back to 640. There would be increased gains from trade because the extra

units, from unit 641 to unit 700, were all produced at a marginal cost that was greater

than the associated marginal value. In other words, the resources that went into

production of these extra sixty units would have been better used elsewhere.

Now, this sort of example can be re-done using the slightly more realistic constant

elasticity demand functions. I say that these are more realistic because it is likely that

you won’t know a linear equation for some real world market demand function, but you

will probably have access to an estimate of the price elasticity of demand and will know a

recent price and quantity and can come up with a combination of the two to get a demand

function. I will duplicate the example from the book.

Imagine that you know that the price elasticity of demand for automobiles is –1.2 and you

suspect, for whatever reason, that the price elasticity of supply is 1. This suggests that

the demand and supply functions will be of the form:

2.1

D PAQ PBPBQ 0.1

S

Based on recent price and quantity information, you could come up with values to put in

for A and B. The book uses A = 200 and B = 1.3. We can calculate the equilibrium as:

825.12866.93.1*Q

866.9846.153*P

846.153P

PPPP

P

3.1

200

P3.1P200

QQ

2.2

1

2.2

2.22.10.1

2.1

0.1

0.12.1

SD

In a diagram, this looks like:


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A graph showing the equilibrium price and quantity from this example.

Now, if the quantity exchanged in the market is restricted to 11 (million) units, there will

be a dead weight loss. While this won’t exactly be a triangle, we’ll approximate the dead

weight loss as a triangle. To do this, we need to calculate the MV and the MC at a

quantity of 11:

21.11200

11)11(MV

200

QPMV

200

QP

P200Q

2.1

1

2.1

1

2.1

2.1

D

46.83.1

11)11(MC

3.1

QPMC

P3.1QS

The area of the triangle is given by:

51.275.2825.12

146.821.1111825.12

2

1DWL

In a diagram, this looks like:


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A graph showing the dead weight loss that occurs if the quantity is

restricted to 11 in this example.

Finally, the example in the book talks about restricting the sale of new automobiles to

control emissions of pollutants. This is a terrible idea for a pollution control policy and I

need to tell you why. As the supply of new cars is restricted and their price rises from

9.866 to 11.21, demand for older, used cars will rise. Older cars, which tend to have

more emissions that new cars, will be driven more and will be driven longer and this, if

anything, will tend to make emissions problems worse rather than better.

Price Controls and Shortages

Figure 11.2 in the textbook is way more complicated than it needs to be. A more

reasonable version looks like this:


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A graph showing a simplified version of Figure 11.2 from the textbook,

which shows the dead weight loss resulting from a price ceiling.

Imagine that a market is subject to a price ceiling at pc, which is below the equilibrium

price. At the restricted price, pc, the quantity demanded is qd and the quantity supplied is

qs, resulting in a shortage equal to qd – qs. The resulting dead weight loss is shown. The

dead weight loss occurs because at qs, additional units could be produced for which the

MV is greater than the MC. So, producing and selling additional units would generate

some additional gains from trade.

As an example, imagine that we have a linear system in which demand is given by QD =

120 – P and supply is given by QS = 2P – 30. The equilibrium is P=50 and Q=70.

Imagine that this market is subject to a price control of PC=40. At this price, qd=80 and

qs=50, with the resulting shortage of 80 – 50 = 30. The calculation of the dead weight

loss requires knowing the height of the demand curve or the marginal value at qs=50.

This is given by:

300)4070()5070(2

1DWL

7050120)50(MV

Q120MVP

P120QD

This looks like:


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A supply and demand graph showing the deadweight loss and the shortage

resulting from a price ceiling.

Non-price Rationing

More should be said about price ceilings and shortages. When there is a shortage of

some good, there must be some process to determine who gets the goods. Waiting in line

is sometimes used as the rationing process, so that those who are willing to wait in line

the longest get the stuff. In the above diagram the controlled price is $40 but the

marginal willingness to pay at the quantity of 50 is $70. If people have a value of time of

$10/hour, you might expect that the different between the marginal value and the price

will be made for by the time cost of waiting in line. $30 at $10/hour means an

equilibrium waiting time of three hours. The resulting consumer surplus, including the

cost of waiting in line, will be the small triangle at the top of the demand curve. The

value of the time wasted waiting in line is the rectangle to the left of the dead weight loss

triangle.

Tax Incidence Analysis

A fun question to ask is who bears the burden of a tax. Microeconomic theory says that it

doesn’t matter on whom the tax is actually levied, the real burden of the tax depends on

the relative elasticities of the consumers and suppliers in the market. When demand is

relatively inelastic consumers will bear most of the burden of taxes. When supply is

relatively inelastic suppliers will bear most of the burden of taxes. The standard diagram

is shown below for cases of inelastic demand and of inelastic supply.


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Two diagram, side by side, demonstrating that the distribution of the burden of a tax

depends on relative slopes of demand and supply curves. The first shows that when the

demand curve is relatively steep the consumer will bear most of the burden of a tax. The

second shows that when the supply curve is relatively steep the supplier will bear most of

the burden of the tax.

The first diagram shows relatively inelastic (steep) demand. A tax imposed shifts the

supply curve upward by the amount of the tax, leading to a reduction in the quantity

exchanged and creation of a dead weight loss equal to the shaded area. After the tax

there is a higher price paid by the consumer (PPBC) and a lower price received by the

supplier (PRBS), with the difference between these being equal to the per unit tax (PPBC

– PRBS = tax). The two rectangles to the left of the dead weight loss triangle represent

the total tax revenue. The top rectangle is the portion of the tax revenue taken from

consumers in terms of reduced consumer surplus. The bottom rectangle is the portion of

the tax revenue taken from producers, in terms of reduced producer surplus. The PPBC

rises a lot as a result of the tax while the PRBS falls only slightly, so consumers, as a

result of their inelastic demand, bear most of the burden of the tax. This is evidence by

the fact that their tax revenue rectangle (the top rectangle) is larger than the lower,

suppliers’ rectangle.

The second diagram shows a relatively flat demand curve and a relatively steep supply

curve, with the result being that suppliers bear most of the burden.

As an example, imagine that demand is given by QD = 120 – P and supply is given by QS

= 2P – 30. The equilibrium is P=50 and Q=70. For a tax of $6, find the new equilibrium

quantity, the new PPBC and PRBS, the total tax revenue raised, the reduction in

consumers’ surplus, the reduction in producers’ surplus and the dead weight loss.

To find the new equilibrium, it is necessary to add the tax to the supply curve, but to do

this you need to re-write the supply curve to get price in terms of quantity, add the tax,

and then re-write the new supply curve in terms of quantity:

QS = 2P – 30

P = Q/2 + 15


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Tax: P = Q/2 + 15 + 6

P = Q/2 + 21

QS = 2P – 42

The new equilibrium is given by:

2P – 42 = 120 – P

3P = 162

P = PPBC = 54, Q = 120 – 54 = 66

PRBS = PPBC – 6 = 54 – 6 = 48.

The diagram and resulting areas are:

A graph showing the numbers for the tax example given here.

Total tax revenue = ($54 - $48) x 66 = $396

Reduction in CS = 272$2

667050$54$

Reduction in PS = 136$2

667048$50$

Dead Weight Loss = 12$)6670()48$54($2

1


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The relationship between these is that the sum of the reduction in CS and the reduction in

PS is equal to the sum of the tax revenue and the dead weight loss, which are both $408

in this example.

Put more clearly, the total damage to consumers and producers will be greater than the

tax revenue collected, so taxes result in a welfare loss despite the fact that the money

collected in tax revenues is merely transferred from one part of society (private

individuals) to another part of society (the government).

The book goes through and establishes that how the tax burden is divided between

consumers and suppliers depends on their elasticities. For example, if the price elasticity

of demand is –1.2 and the price elasticity of supply is 0.6 the division of a $10 per unit

tax to consumers and producers will be:

67.6$2.16.0

2.110$t:Suppliers

33.3$2.16.0

6.010$t:Consumers

DS

D

DS

S

So, the price paid by consumers, who are more flexible as evidenced by their elasticity of

–1.2, will see the price that they pay rise by $3.33.

The price received by suppliers, who are less flexible as evidence by their elasticity of

0.6, will see the price that they receive fall by $6.67.

The textbook also gives an equation for dead weight loss as a function of the amount of

the tax (dt) and the elasticities of supply and demand, eS and eD, respectively. The

equation is on page 324 and there is a related example, Example 11.2.

International Trade and Restrictions

Imagine that a small country that has not traded with the rest of the world in some good

(wheat, perhaps) is considering opening up their market to international trade. The world

wheat price is less than their domestic wheat price, so the price that consumers pay for

wheat in the country will fall. Producers, of course, are opposed to opening trade to

foreign producers and claim that they will all be driven out of business.

If the country is small, its entry into the world market won’t affect world prices, so world

prices can be taken as given. The effect of the entry into world trade on the domestic

wheat market is shown in the following diagrams:


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Three graphs, side by side, showing the impact of opening trade on a domestic market.

The first graph shows the increased consumer surplus for domestic consumers, the

second shows the decreased producer surplus for domestic producers, and the third

shows the difference between the two, or the domestic net gains.

As the price within the country falls from p* to the world price pw, the total quantity

purchased will rise from the domestic equilibrium q* to q1 and consumer surplus will

increase.

As the price within the country falls, the quantity supplied by domestic suppliers will fall

from q* to q2 and producer surplus will fall.

The net effect on domestic gains from trade will be the area shown in the third diagram,

the difference between the consumer surplus gains and the producer surplus loss. It

should be noted that the gains to consumers will outweigh the losses to producers, so the

net benefits to opening up trade will be positive.

Analysis of Tariffs

Tariffs are often imposed on the import of foreign goods. In fact, this is how the U.S.

government raised most of its tax revenue until the early 20th

century.

The book presents this analysis graphically. The book’s analysis will be presented here

with some additional explanation.

Let’s start with the original picture of international trade:


28

A simple supply and demand graph showing the net gains from the opening of a domestic

market to international trade.

The shaded area represents the net gains from international trade and the fact that

consumers can buy at the lower world price, pw.

Now, imagine that a tariff equal to t per unit is applied to the imported good. This will

raise the effective price of the imported, world market goods from pw to pw+t. This will

make the net gains triangle smaller. The reduction in the net gains triangle can be

divided into two parts. The rectangle is the tax revenue from the tariff, and is equal to the

amount of the tariff multiplied by the quantity imported after the tariff is imposed. The

remaining two triangles are the deadweight loss from the imposition of the tariff.

That is, the tax revenue is a transfer from domestic consumers to the government, so it

isn’t a welfare loss. However, the reduction in gains from international trade that occurs

as a result of the tariff is a welfare loss.


29

A graph showing the tax revenue and the net welfare loss that result from imposing a

tariff on international trade.

Practice Problems and Stuff

1. For a market with supply and demand given by QS = 3P – 30 and QD = 90 – P, find the

following:

a. equilibrium price and quantity

b. CS and PS at the equilibrium

c. shortage and DWL resulting from a price ceiling of P=$20.

d. surplus and DWL resulting from a price floor of P=$40

e. tax revenue and DWL from a tax of $12 per unit.

2. For a market with supply and demand given by QS = 1.2P and QD = 20P-1.5

, find the

following:

a. equilibrium price and quantity

b. shortage and pproximate DWL resulting from a price ceiling of P=$3.

c. surplus and approximate DWL resulting from a price floor of P=$4.

d. tax revenue and approximate DWL from a tax of 10%. Note: this will require

rewriting the supply curve so that it is 10% higher than it is originally. To do this, solve

the supply curve for P and multiply by 1.10, the re-solve for Q.

e. for the tax revenue question in part d, is the tax burden distributed as theory predicts it

should be? Explain.

3. In general, how the distribution of the burden of a tax depend on elasticity?

4. In general, how does the dead weight loss associated with a tax depend on elasticity?


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5. If demand is given by QS = 3P0.5

and demand is given by QD = 12P-1.5

and a tax is

imposed on the market, how will the burden of this tax be shared between suppliers and

consumers?

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Economics 352: Intermediate Microeconomics Notes and ...faculty.metrostate.edu/BELLASAL/352/Lec12new.pdfChapter Twelve: The Partial Equilibrium Competitive Model and Applied Competitive