Download Overview of perfect competition: Sessions 1–6

MBA, P1 Sep–Oct 2012
Prices & Markets
Timothy Van Zandt
Overview of perfect competition: Sessions 1–6
The purpose of this handout is to outline the approach I have taken in class and
explain where the readings fit in. Some sections are extensive and detailed—the parts
that cover the framing of the sessions in a way that differs from the readings. Other
sections are skeletal because the readings and slides fill in the details.
1. Students selling textbooks: unit demand and unit supply
Our first double sessions 1 & 2 followed closely Chs. 1 & 2.
Our starting point for the course was thus trade in a market when each buyer wants
to buy only one unit and each seller has only one unit to sell. The motivating example
in class was of P4 students selling used Corporate Finance textbooks to incoming P1
students.
We approached it from this perspective:
• What gains does trade bring to the buyers and sellers?
• What kind of trade maximizes those gains?
Eventually we reached this picture:
Figure 1
$
Consumer surplus
MC ↔ Supply
P ∗ → 35
Producer
surplus
MV ↔ Demand
Q∗ →500
Q
The points on the MC/supply curve are the costs of the individual sellers. It is a
marginal cost curve because, at a quantity on the horizontal axis, it measures the extra
cost to the sellers (collectively) when one more unit is taken from them. It is a supply
curve because, starting at a price on the vertical axis, it tells us how many sellers would
sell at that price.
The points on the MV/demand curve are the valuations of the individual sellers.
It is an MV curve because, at a quantity on the horizontal axis, it measures the extra
valuation to the buyers (collectively) when one more unit is given to them. It is a demand
curve because, starting at a price on the vertical axis, it tells us how many buyers would
purchase at that price.
Furthermore, we can read the following from this picture:
Prices & Markets • Overview of perfect competition: Sessions 1–6
1. The efficient quantity is given by MC=MV, so it is at the intersection of these two
curves.
2. The equilibrium price is given by supply=demand, likewise at the intersection of
these two curves.
3. The area of the rectangle P ∗ × Q∗ is the revenue of the sellers and the expenditure
of the buyers.
4. The sellers’ total cost is the area under the MC curve; subtracting this from their
revenue leaves the producer surplus.
5. The buyers’ total valuation is the area under the MV curve; subtracting out their
expenditure leaves the consumer surplus.
Understanding that supply comes from MC and that demand comes from MV helps
us in several ways:
• Price movements are due to shifts in either the supply or the demand curve. We
understand that such shifts come from changes in costs or changes in valuations.
We thus understand, for example, that a tax on sellers of $10 per unit will shift the
MC curve (hence supply curve) up by exactly 10 units.
• The impact on prices of a shift in a demand or supply curve depends on the elasticity
(price sensitivity) of each of these curves. We understand, for example, that the
supply curve is elastic (flat) when sellers have very similar costs.
• We can see the gains that traders get. We can see that a seller ends up selling because
his cost is lower than that of other sellers, and the amount of his surplus equals his
cost advantage over the marginal seller.
2. From students selling textbooks to real firms
There are some interesting markets in which sellers have only one unit to sell. In a labor
market, the sellers are workers. Although some workers may flexibly choose how many
hours to work, as a first approximation the basic unit is a “full-time job” and the most
important decision a worker makes is whether and in which industry to work. Likewise,
though illegal in many countries, there are markets for kidneys. A person can live a
healthy life with one kidney but not zero, so each potential kidney donor—such as I, or
you if you still have both kidneys—has only one kidney to sell.
However, in this course, we are most interested in markets in which the sellers are
firms. A firm’s level of output may be quite large and is always an important decision;
we must understand it to have a model of markets with firms. There are further complications: regulations, market power, entry and exit decisions, and adjustment lags and
costs that affect market dynamics. In this section, I outline how we deal with each of
these complications throughout the course so that we can understand markets in which
the sellers are firms.
For context, let us consider the market for electricity in Kazakhstan. The electricity production in Kazakhstan has been 85% privatized, the distribution of electricity is
through a market (with distributors sharing the same state-owned transmission grid), and
the market price fluctuates according to supply and demand. There are 71 power plants,
some owned by the same owners. Vestas, a Danish company that manufactures and installs wind turbines, is an example of a firm considering entry into this market. How can
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Prices & Markets • Overview of perfect competition: Sessions 1–6
Figure 1 help us understand this market?
2.1. Regulation
In our market for used textbooks, equilibrium trade is efficient. However, inefficiencies
can arise in other markets for a variety of reasons, leading to market regulation. In the
electricity market in Kazakhstan, there are regulatory caps on the market price, there
are subsidies for renewable energy such as wind, and any generation project must pass
through a complicated approval process.
We deal with the regulatory environment in an easy way: leave it for later courses,
such as your International Political Analysis core course and the Business and Public
Policy elective. The tools in Prices and Markets remain critical: you cannot understand the regulated electricity market in Kazakhstan without understanding the underlying market forces that exist under the regulatory layer and without understanding the
objectives of the regulators.
2.2. Market power
A supply curve measures how much sellers choose to sell at any price, when each seller
presumes that he has no influence over the price. This means that the sellers are price
takers. Such price-taking behavior makes sense in our textbook market in Sessions 1 &
2. A seller might nudge the equilibrium price up by choosing not to sell, but then that
seller could not benefit from the higher price.
We can also relate to price-taking behavior as consumers. I eat about 0.00000727%
of the tomatoes sold in France. When I buy tomatoes near my home in Fontainebleau,
I see a price posted for tomatoes and I figure that I can buy as few or as many tomatoes
as I want without affecting that price.
In contrast, a typical firm faces a trade-off between volume and price: if it sells
more, it does so at a lower price. This trade-off—which means also that the firm can get
a higher price by selling less—is called market power. A firm has market power to the
extent that either it is a big player in the market or its product is differentiated in the eyes
of the buyers.
In the electricity market in Kazakhstan, there is no product differentiation: buyers
view all electricity as the same and hence there is a single market price. However, one
of the 71 plants generates 13% of the electricity. If this plant cut its production by onethird, the supply of electricity in the market would drop by over 4% and the market price
would rise noticeably. In particular, the price at which the plant would sell its remaining
two-thirds capacity would be higher. Market power is precisely such a trade-off between
a firm’s volume of production or sales and the price at which it sells its output.
Even a large wind farm built by Vestas in Kazakhstan would represent a small share
of the electricity market. Hence, Vestas’ market power would be negligible if it entered.
However, suppose that Kazakhstan created a separate market for green energy. Vestas
would be the sole supplier of this differentiated good. Some buyers—either firms seeking
carbon credits or consumers who want to reduce their personal carbon footprint—would
be willing to pay a premium for such green energy. The size of this premium would vary
across buyers. Thus Vestas—like any firm whose product is differentiated—would also
have market power: if it sells less, it can charge a higher price because it sells only to
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Prices & Markets • Overview of perfect competition: Sessions 1–6
higher-valuation customers.
Market power will be an important topic in this course, starting in Session 7—the
part of the course that we call pricing with market power when we study firms’ individual decisions and then imperfect competition when we study firms’ interaction. In the
meantime, we ignore market power up through Session 6 by assuming that each firm
is a price taker. As a model of firms’ interaction, this is called perfect competition and
means simply the model of supply and demand. In summary, our course is divided into
two parts:
Sessions 1–6
Sessions 7–15
Perfect competition
Imperfect competition
(firms are price takers)
(firms have market power)
I chose the word “ignore” meaningfully. Of course, perfect competition is good for
quantitatively measuring markets in which firms have little market power. However,
it is useful for understanding any market. By first abstracting from the market power
that might exist, prices are driven entirely by cost and valuation, with MC = P = MV.
When we take into account market power, there is a mark-up over marginal cost: MC <
P = MV. Yet cost and valuation remain the most important drivers of prices and market
dynamics, in ways that are simple to see with the model of perfect competition but harder
to visualize with imperfect competition.
2.3. Entry and exit
Unlike consumers, the entry of a firm into a market happens as a discrete jump due
to economies of scale. Vestas would not enter Kazakhstan with a single turbine—the
generation cost per megawatt–hour would simply be too high. Instead, the minimum
scale with which it would enter might be a wind farm with 50 turbines—and it would
still face the choice of exactly how large to be: 50, 60, 120 turbines?
We therefore need to understand simultaneously firms’ entry/exit decisions and their
quantity (i.e., scale or volume) decisions. Here is where we reach the difference between
the division of material in the FPM lectures notes (Chapters 3, 4 and 5) and my division
of material in class (Topics 3, 4, and 5).
In class, I divided the material as follows:
• Topic 3: Entry/exit in isolation.
• Topic 4: Quantity decisions in isolation.
• Topic 5: Entry/exit and quantity combined.
For each topic, I integrated the relevant parts of Ch. 3 (costs), Ch. 4 (supply, equilibrium),
and Ch. 5 (short-run vs. long-run dynamics). Furthermore, I explained that Figure 1
continues to provide a summary, even if the interpretation of the upward-sloping supply
curve differs across topics: in Topic 3, it comes solely from the entry of new firms; in
Topic 4, it comes solely from the expansion of output by firms in the market; in Topic
5, it comes simultaneously from the entry of new firms and the expansion of output by
firms already in the market. This schema is illustrated in Figure 2.
4
Aggregate
supply
45
40
35
30
25
20
15
10
5
$
MC↔supply
€
5
10
15
20
25
Supply goes up via
entry of new firms
30
Q (100MW)
€
10
20
30
20
100
200
Qi
300
Q
MC ↔ Supply
Supply goes up via expansion
of output by firms in market
40
20
40
…
MCi ↔ Supplyi
Quantity ← MC
Entry ← break-even price
(economic cost)
Individual
firm
Re-interpret unit supply from
Sessions 1 & 2 as entry
Fix which firms are in the market,
only decision is how much to prod.
Fix size of a firm,
only decision is whether to enter
Topic 4
Isolate
quantity
How
Topic 3
Isolate
entry/exit
Figure 2: Understanding the entry/exit and quantity decisions of firms
40
50
5
10
15
20
25
30
P
10
20
30
ACu
€
10Qu 15
20
25
30
35
MC
100
200
300
Supply goes up via entry
and exp. of firms in market
5
Entry ← AC
Quantity ← MC
Q
Q
400
AC
Firms decide both whether to enter
and how much to produce
Topic 5
Combine
entry/exit & quantity
and resulting market equilibrium
Prices & Markets • Overview of perfect competition: Sessions 1–6
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Prices & Markets • Overview of perfect competition: Sessions 1–6
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2.4. Market dynamics: short run vs. long run
Firms’ entry and exit from markets and their changes to output can involve long lead
times and costs. As a consequence, when the demand in a market shifts unexpectedly,
the dynamic response of the firms and hence of the market unfolds over time. Even with
no further surprises in the market, things will look differently one week from now, a
month from now, and a year from now, and so on.
Though there are a continuum of time horizons, we try only to compare a shorter and
a longer time horizon. Thus, we speak of a loosely-defined “short run” and “long run”.
We consider two types of adjustments that differentiate the short run from the long run:
1. It may take time for firms to enter or exit the market.
2. Firms already in the market may have trouble adjusting production.
In Topic 3, we consider the time it takes firms to enter and exit the market. In the
long run, there is exit and entry; in the short run the set of firms and hence output are
fixed. This is not presented in FPM but is simple; we do it here in Section 3.6.
In Topic 4, we consider the difficulty firms have in adjusting production. This is
covered in FPM §5.2–§5.4. In the long run, all inputs are adjustable; in the short run,
one or more inputs is fixed.
In Topic 5, when we integrate entry/exit and quantity decisions, there is another
possible comparison: in the long run, exit and entry is possible and all inputs are variable;
in the short run, the inputs remain variable but there is no exit and entry.
Whatever the source of adjustment delays and costs, the basic implications for market dynamics are the same:
Adjustment delays and costs imply that supply adjusts less in the short run than
in the long run—hence, prices are more volatile in the short run than in the
long run.
I now give a graphical treatment of these general market dynamics. When we then look
at a specific source of adjustments costs, all that changes is the interpretation.
Figure 2 shows our “leading example” of a market, in long-run equilibrium.
Figure 2
$
Slong
P1∗ → 35
D1
500
Q
Prices & Markets • Overview of perfect competition: Sessions 1–6
7
This picture is familiar, but I have labeled the demand curve D 1 and the equilibrium
price P1∗ , anticipating that we’ll see a shift in the demand curve. Furthermore, the supply
curve has been labeled Slong , anticipating that we consider also short-run responses of
supply.
Consider an upward shift in the demand curve. This would come from an increase
in the buyers’ valuations for the good sold in this market (for example, because the price
of a substitute good has gone up). Such an upward shift by $10 is shown in Figure 3,
with the shifted demand curve labeled D 2 .
Figure 3
$
Slong
P2∗ → 40
P1∗ → 35
D2
D1
500 570
Q
We see the new equilibrium with a price of P2∗ = 40. This exercise is very similar to
the one we did in Sessions 1 & 2 when there was a shift in the supply curve due to an
increase in cost or to a tax, but we model instead a shift in demand.
The long-run supply curve is telling us how firms respond to other prices when they
have a “long time” to enter or exit and otherwise adjust output. What is a “long time”?
It depends on the horizon that we are interested in. If we want to see the market price
one year down the road, for example, then this long-run supply curve shows how firms
respond to prices when they have one year to enter and exit the market and adjust their
output.
Consider instead how price evolves over a shorter horizon, say 3 months from now.
With a tighter time frame, the firms’ adjustments are harder—it is harder or may be
impossible to enter or exit the market; some changes in production are impossible to
make quickly, others are costly. Therefore, supply responds less in the short run than in
the long run.
Take, for example, Vestas after it has entered the market with a windfarm. (For
simplicity, I speak as if Vestas would actually operate the windfarm; more likely there
would be a distinct operator.) Suppose that its price forecast at time of entry was correct
and so it is operating the windfarm at its design capacity. As long as the price does not
change, it would keep its output at this level, whether a week or a year from now.
Suppose, however, that the price of green energy jumps up and is expected to stay
at the higher price. Even at design capacity, Vestas can squeeze out more output right
away by increasing the maintanence cost, but this is very expensive. It would take more
than a year for Vestas to be able to add turbines to the windfarm, and even longer for
Vestas or another entrant to develop another site.
Prices & Markets • Overview of perfect competition: Sessions 1–6
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On the flip side, suppose that the the price drops and is expected to stay low. When
Vestas designed its capacity, it factored in all the marginal costs, especially the construction and installation cost of each turbine. If it had expected such a lower price, it would
have built a much smaller windfarm or not entered at all. However, if it now lowers
output by idling some turbines, its actual savings will be small; therefore, Vestas would
likely continue to operate the farm close to design capacity.
Let’s visualize this by drawing in a short-run supply curve for Figure 3. Our starting
point is the initial long-run equilibrium: The market price is $35 and firms collectively
produce 500 units. The short-run supply curve depends crucially on this status quo. If
the price remains at 35, output will still be 500, whether a week or a year from now. The
short-run response differs from the long-run response only when the price moves away
from 35 and firms try, but find it costly, to adjust their output. Thus, the short-run supply
curve passes through the long-run supply curve at the current equilibrium.
At prices above 35, supply expands less in the short run than in the long run. Likewise, at prices below 35, supply contracts less (and hence remains higher) in the short
run than in the long run. This is shown in Figure 4.
Figure 4
$
Sshort
Slong
P1∗ → 35
D1
500
Q
In Figure 5, I put the new demand curve back in the picture to visualize how prices
respond in the short run and long run following the shift in demand. The intersection of
the short-run supply curve with the new demand curve is the short-run equilibrium.
Prices & Markets • Overview of perfect competition: Sessions 1–6
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Figure 5
$
Sshort
Slong
Pshort → 43
P2∗ → 40
P1∗ → 35
D2
D1
500
570
530
Q
The graph is getting busy, so approach it slowly.
1. Pick out the initial long-run equilibrium where D 1 (red) intersects Slong (blue). The
price is 35.
2. Then the demand curve shifts to D 2 (orange). Pick out the short-run equilibrium
where D 2 intersects the short-run supply curve (green). The price goes up to 43.
3. Finally, pick out the new long-run equilibrium where D 2 (orange) intersects the
long-run supply curve (blue). The price goes down to 40 because firms have more
time to expand output.
2.5. And from students buying textbooks to other consumers?
There are many examples of “unit demand” besides student buying textbooks. Most
household buy only one refrigerator; most people have one Facebook account; most
people get only one gym membership.
In other cases, buyers can flexibly choose how much to consume of a good—such as
how much electricity to use in a month, how many gallons of gasoline to buy each week.
This extension is outlined in Ch. 2B of the FPM lecture notes. However, we deliberately
did not cover this in class; instead, we dwelled on the mirror image for sellers. The
important takeway is that Figure 1, and everything we do with it, works whether buyers
have unit demand or have multi-unit demand.
We merely have different interpretations of the points on the aggregate demand
curve. With unit demand, each point is the valuation of one buyer; this interpretation
is useful when we want to highlight the differences among consumers. With multi-unit
demand, the valuations of the buyers are blended in the aggregate demand curve, so
we cannot easily visualize the individual buyers. Yet the aggregate demand curve still
measures the aggregate marginal valuation.
Otherwise, the complications we have brought up for firms are less important for
consumers. Yes, regulation directly restricts consumers purchases, though not in the
heavy-handed way that regulation affects firms. Yes, consumers can have “adoption”
costs that are analogous to the entry costs of firms, but the adoption decision of one
consumer is not the significant market event that the entry of a firm can be. Yes, buyers
can have market power, particilarly if the buyer is another firm (B2B), but not so com-
Prices & Markets • Overview of perfect competition: Sessions 1–6
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monly or significantly. Yes, it also takes time for consumers to adjust the consumption
in response to changing market prices; yet such adjustment delays and costs are small
compared to those of, for example, the construction of new factories or ships.
Due to (a) the lower importance of these complications for consumers, (b) that studying them would be the mirror image of our treatment for firms, and (c) that our focus is
on the managerial decisions of firms, we do not take up any of these complications on
the buyer side of the market.
3. Entry and exit in isolation
3.1. Model: a reinterpretation of the textbook market
We can isolate Vesta’s entry decision by fixing the size of the windfarm that it must enter
with, such as at 100MW (megawatts). We can isolate entry and exit in equilibrium by
fixing each potential firm’s level of production when in the market. Each firm’s sole
decision is whether to be in the market.
Our model of supply is then the same as in Sessions 1 & 2, but the sell decision is
reinterpreted as an entry decision. The price above which a firm would want to enter—
the analog of the seller’s cost in the textbook market—is the firm’s break-even price or
per-unit cost. The picture of aggregate supply and aggregate MC remains the same, as
in Figure 6, except that the magnitude of each unit on the horizontal axis is the fixed
quantity of each firm.
Figure 6
$
45
40
MC↔supply
35
30
25
20
15
10
5
5
10
15
20
25
30
Q (100MW)
The curve shows the potential firms’ break-even prices, from lowest to highest. Supply expands as the price goes above the break-even price of a larger number of firms, and
thus as more firms enter the market. The supply curve also measures aggregate marginal
cost. For example, the per-MW social cost of expanding output from 1500 to 1600 MW
is the break-even price $17/MWh of the 16th most efficient entrant—this is the entrant
whose production should be brought on line in order to expand output.
Prices & Markets • Overview of perfect competition: Sessions 1–6
We can then add in a demand curve, obtaining a graph like that of Figure 1. We can,
for example, illustrate the impact of a tax on electricity or an increase in production costs
by shifting the MC and hence supply curve.
Only two things remain to be done: (a) probe the meaning of the break-even price;
(b) see what the model tells us about entry and exit.
3.2. Understanding the break-even price
The break-even price could also be called the “willingness-to-sell”: the price above
which the firm prefers to be in the market and produce and below which the firm prefers
to stay out. We call it also the per-unit economic cost. These three terms are synonyms.
What exactly does it represent? For sellers of textbooks, it was a subjective measure
of how much the seller valued the book, taking into account also the possible opportunity
to resell the book outside the market. The cost for a firm might seem more tangible and
easy to measure, but we have to be careful not to confuse it with the accounting cost that
appears in a profit-and-loss statement.
Remember that a firm wants to enter as long as it can cover its economic cost; it
wants to exit if it could save its economic cost. Zero profit on a P&L statement would
not make the stakeholders happy about having entered the market. The owners of the
firm put in equity and perhaps their own time and other resources. The return required
on each of these resources so that the owner is happy to use it in the firm rather than
in some other way is called the opportunity cost of the resource. The accounting profit
must cover the total opportunity costs in order for entry to be worthwhile. Put another
way, the true break-even price or per-unit economic cost is the sum of the accounting
cost and the opportunity cost of assets and other resources owned by the firm.
This concept of opportunity cost is covered in FPM §3.3. Furthermore, at the beginning of Session 4, I worked through an example based on an entrepreneurial activity (past
or planned) of one of your classmates. Opportunity costs are explored further in your
managerial accounting course in P2, one theme of which is how to measure costs in order
to guide decisions. The bottom line for this course? You should understand that “cost” always means “economic cost”, including opportunity cost; hence “zero economic profit”
means, for example, that the equity holders are getting the same (risk-adjusted) return
on their investment that they could have obtained elsewhere. They are neither thrilled
nor regretful about their investment.
When a firm exits a market, some expenses that loomed large when entering the
market cannot be recovered: they are sunk. These sunk costs do not form part of the
economic cost (the savings from exit) when a firm chooses to exit a market. This may
create an asymmtry between entry and exit. At the moment of entry, no costs are sunk.
At the moment of exit, some costs that were important in the entry decision may now
be sunk. As a consequence, the break-even price above which a firm outside the market
wants to enter may be higher than the break-even price below which that same firm would
choose to exit once in the market. Getting caught between these prices is the familiar
dilemma of the entrepreneur when things do not go well: “I wish I hadn’t entered, but
there is no point in exiting now.”
Sunk costs are reviewed in FPM §3.3 and I used your classmates’ entrepreneurial example in Session 4 to illustrate which costs might be sunk at the moment of exiting the
market. Sunk costs are studied further in managerial accounting. The resulting asym-
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Prices & Markets • Overview of perfect competition: Sessions 1–6
12
metry between entry and exit is an important theme in some of your competitive strategy
courses—along with the associated concept of irreversible investments, the implication
for the value of flexibility in the face of uncertainty, and the effects on market dynamics.
We do not have the time to do much with this asymmetry—at best, it lurks in the background. The bottom line for this course? Any time we are considering a firm’s decision,
the economic cost that guides this decision does not include costs that are already sunk.
3.3. Economic profit and competitive advantage
From here to the end of Section 3, I will explore various ways in which this model helps
us understand entry and exit. Everything I show here will remain true when we intergrate
the entry/exit and quantity decisions, it is just clearer and simpler to see because we have
isolated entry and exit. In particular, Sections 3.3–3.5 are an isolation of ideas about
entry and exit and competitive advantage that appear in FPM Ch. 4.
First, this simple model of entry and exit provides insights into market composition,
the entrepreneurial decision to enter or exit a market, and economic profit—all coming
from the idea of competitive advantage, which here means having a lower cost than other
firms.
The jaggedness of the supply curve in Figure 6 helps us see that each point is the
break-even price or entry decision of another firm, but it can otherwise muddle the picture. So let’s smooth out the diagram, without forgetting that each point is a distinct
firm. Let’s add in a demand curve and visualize equilibrium. This gets us back to Figure 1, which I reproduce it here for your convenience. I have reduced the scale on the
horizontal axis so that each firm does not seem so insignificant (one out of 50 rather than
one out of 500).
Figure 7
$
Consumer surplus
MC ↔ Supply
P ∗ → 35
Producer
surplus
MV ↔ Demand
Q∗ →50
Q
In class, we made these observations:
1. Which firms are in the market? Those with the lowest costs, that is, those with a
competitive advantage over other firms.
2. How much is a firm’s producer surplus? Per unit, it is the gap between the market
price P ∗ and its own cost Ci . The market price is also approximately the cost of
the marginal firm in the market (the last firm to enter or the next firm that would
Prices & Markets • Overview of perfect competition: Sessions 1–6
13
enter). Thus, the magnitude of a firm’s surplus is the magnitude of its competitive
advantage over the marginal firm.
Furthermore, we observed in class that a firm’s surplus equals its contribution to the
market, as follows. Suppose a firm i in the market with cost Ci were to disappear. Either
the amount consumed by the buyers must fall or this firm must be replaced by a firm not
in the market.
• In the first case, the loss on the margin to the buyers is P ∗ because this is the marginal
value on the demand side: either the valuation of the lowest-valuation buyer who is
getting the good or the marginal valuation of each buyer in the case of multi-unit
demand. Thus, buyers lose P ∗ per unit but the firm’s cost Ci per unit also disappears:
the net decline in gains from trade is P ∗ −Ci per unit. This is precisely the economic
profit earned by the firm.
• If instead firm i is replaced, the next firm brought into the market has a per-unit cost
of approximately P ∗ . The production cost thus increases from Ci to P per unit that
i was producing. In other words, the presence of firm i reduces production costs by
P − Ci per unit, and this is also precisely firm i’s economic profit.
The magnitude of firm i’s economic profit (and thus its contribution to the market) is
small when its cost is similar to that of the marginal firm. This is necessarily true for all
firms active in the market if all potential entrants have very similar costs, as illustrated
in Figure 8.
Figure 8
$
MC ↔ Supply
P ∗ → 35
Producer
surplus
MV ↔ Demand
Q∗ →50
Q
Each firm gets very little profit because it is replaceable. It is in the red ocean of
a mature industry in which imitation is easy. No firm contributes much to the market
because it can be replaced by another firm with similar cost. From the outside, it would
be hard to identify which firms have a competitive advantage and hence should be in the
market.
Figure 7 shows, in contrast, a blue-ocean industry in which successful firms have
unique capabilities that cannot be imitated by other firms.
Prices & Markets • Overview of perfect competition: Sessions 1–6
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Figure 9
$
MC ↔ Supply
P2∗ → 40
P1∗ → 35
D2
D1
50 57
Q
Figure 10
$
MC ↔ Supply
P2∗ ≈ P1∗ → 35
D2
D1
50
63
Q
3.4. Long-run market dynamics and the elasticity of supply
The similarity of the firms’ costs in Figure 8 means also that the supply curve is flat and
hence very elastic. That is, small changes in the price lead to large changes in supply,
due to the entry and exit of similar firms. How much the market price changes when the
demand curve shifts depends on the elasticity of supply.
Figures 9 and 10 show the supply curves in Figures 7 and 8, along with the demand
curve in those figures (labeled D 1 ) and the same demand curve shifted up by $10 (D 2 ).
The price is initially $35 for both supply curves. After the shift in demand, the price
increases significantly in Figure 9. Yet the price hardly moves in Figure 10 because
supply is so elastic: the narrow range of break-even prices nearly pins down the market
price, whatever is the demand curve. An increase in demand merely leads to the entry
of new firms into the market until the price is close to where it was before.
Prices & Markets • Overview of perfect competition: Sessions 1–6
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3.5. Taking firm similarity to an extreme: free entry
In a red ocean in which firms have similar costs because they lack unique capabilities
and imitation is easy, we have observed the following:
1. The market price is nearly pinned down by the similar costs of the firms; an increase
in demand leads to new entry until the price settles to nearly where it was before.
2. Each firm earns very little economic profit, because each is nearly replaceable.
3. Differences between firms are so small that it may be difficult from the outside to
see which firms should/would be in the market.
Let’s take this scenario to the extreme: all firms, including a large pool of potential entrants, have the exact same cost structures. This idealization is called free entry.
Figure 8 becomes Figure 11 if the common break-even price is $35.
Figure 11
$
MC ↔ Supply
P ∗ → 35
Demand
∗
Q →50
Q
It is important to understand that free entry is an assumption about the similarity of
firms, not about whether firms are “allowed” to enter a market or not. We had been doing
quite fine studying entry and exit by firms that could freely choose whether to be in or
out. However, previously we had taken in account firm differences—which in reality
exist whether minor or significant. In contrast, the idealization called free entry means
that all firms are identical.
Our observations about the red ocean of firms with similar costs become absolute
statements when the firms have identical costs:
1. The market price must equal the common break-even price of the firms; an increase
in demand leads to new entry until the price settles to exactly where it was before.
2. Each firm earns no economic profit, because each is replaceable.
3. Because firms are identical, the model does not pin down which firms end up in the
market.
Although we lose any ability to identify who is in the market, the assumption of free
entry allows us to quickly see the essential features of a market in which firms are highly
similar. It immediately pins down the market price and then, with access to demand data,
the number of firms in the market.
Prices & Markets • Overview of perfect competition: Sessions 1–6
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For example, consider the wholesale market for cut roses. Colombia and Ecuador
are the world’s largest producers. Colombia has about 215 exporters of flowers, many of
whom grow roses. Let the unit for measuring output be one million roses. For example,
the United States imports about 2 billion roses per year, or 2000 of our one-million-rose
units. The wholesale price for one unit could be, for example, $250K. (These numbers
provide some context but I will not try to precisely calibrate my numerical example.)
To isolate entry and exit, we assume that each grower must have production of exactly 8 units per year. To make this a model of free entry, we assume that each grower
has the exact same production cost of $250K per unit. Thus, without yet any information
about demand, we know that the market price must be $250K and that each grower just
breaks even.
We cannot determine which firms are in the market, but we can figure out how many.
For this, we need information about demand. Given the market price, the demand curve
tells us total demand. Then, since supply=demand, this is also the total supply. We
divide by the size of each firm (8 units) to get the number of firms in the market.
For example, suppose that the demand curve (here measuring prices in $1,000) is
Q = 1060 − 2P.
Thus, at the market price of P ∗ = 250, total demand is
Q∗ = 1060 − 2 × 250 = 560.
This number must also be the total supply. Since each firm supplies 8 units, the number
of firms is N∗ = 560 ÷ 8 = 70.
In summary, we have these simple calculations in this model of free entry:
Symbol
Q∗i
P∗
Q∗
N∗
Measuring …
Comes from …
Output per firm
Market price
Total output
Number of firms
Fixed in order to isolate entry/exit
The firms’ common break-even price
Demand d(P ∗ ) at the market price
Q∗ ÷ Q∗i
Here
8
$250K
560
70
3.6. Market dynamics based on entry and exit
We can use this model of entry and exit for our first concrete story about the difference
between the short run and the long run. For our short run, we assume that firms cannot
exit or enter. Since we have suppressed quantity decisions, this means that supply cannot
adjust at all: it is perfectly inelastic, as drawn in Figure 12.
Prices & Markets • Overview of perfect competition: Sessions 1–6
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Figure 12
$
Sshort
Slong
Pshort → 45
P2∗ → 40
P1∗ → 35
D2
D1
50
57
Q
The story is interesting. When the demand shifts, the price jumps up to 45. Then it
begins to fall as one firm after another enters the market, until the number of firms grows
from 50 to 57.
Something not evident until now is that firms have to really understand the world
to make their decisions: they cannot simply respond myopically to market prices. The
total number of firms with break-even prices below 45 is about 65 in Figure 12. Thus,
when the price first jumps to 45, there are 15 firms not in the market who would find
it profitable to enter. Yet in the long-run equilibrium, only 7 of these firms end up in
the market. Remember, entry takes time, so firms have to decide now whether to enter,
before seeing the long-run price. Each firm has to forecast that price in order to determine
whether to enter. Firms do this by having either hard data or intuition about demand and
hard data or intuition about where they stand (in terms of cost) relative to other potential
entrants. The latter is particularly challenging—one has to have insights about firms that
do not even exist. Especially when the data are poor, understanding the forces driving
market dynamics is better than naively responding to market prices and being buffeted
about by the market winds.
4. Quantity decisions in isolation
Next we consider the quantity (that is, scale or volume) decision of a firm given that it
is in the market, and the resulting market equilibrium given a fixed set of firms in the
market. We covered this, including a full numerical example, in Session 3. The best
summary is the blackboard write-up that I sent by email and posted on the course web
page. (A more complicated numerical example is our perfect competition simulation, in
which 39 firms competed in a market and made quantity but not entry or exit decsions.)
For a firm’s quantity decision, only marginal cost matters. Therefore, this topic draws
on the discussion of marginal cost—but nothing else—from FPM Ch. 3. The supply
decision is studied in FPM Ch. 4 on page 98. The bottom line is that a firm’s supply
curve is the inverse of its marginal cost curve.
We then find aggregate supply by summing the individual supply curves. This is
straightforward; I did it in class and you can see also FPM §4.4. In class, I explained
Prices & Markets • Overview of perfect competition: Sessions 1–6
why the aggregate supply curve measures aggregate marginal cost. This is a deeper
concept, but the bottom line is that Figure 1 remains valid.
In this setting, we can revisit short-run vs. long-run dynamics. Here the long run
means that there is a fixed set of firms in the market who have a long time (as long
as they need) to adjust production efficiently. The short run means that firms cannot
change their usage of one or more inputs—that is, some inputs are fixed in the short
run. This is covered in FPM Ch. 5. In class, I only cover it graphically and briefly, in
the debrief of the simulation. Therefore, I will not ask detailed questions on the exam
about short-run costs vs. long-run costs as covered in FPM §5.2–5.4. Nevertheless, you
should understand well the the general picture of short-run vs. long-run market dynamics
in Section 2.4 of these notes. That section subsumes FPM §5.5, and FPM §5.6 and 5.7
are already excluded by the Prep Guide as required reading. Thus, none of FPM Ch. 5
is essential reading for the quiz and exam.
5. Combining entry/exit and quantity decisions
This was covered in the second half of Session 4 and most of Session 5. We went through
a full numerical example.
Conceptually, there is little not already covered in Topic 3 and Topic 4. The main
innovation concerns the individual firm’s AC curve, what it says about economies of
scale (or why its shape comes from economies of scale), and how it characterizes the
firm’s entry decision.
Whereas in Topic 3 we simply assume a scale for each firm, here the reason that
entry is a discrete jump into the market is due to economies of scale: initially decreasing
average cost. Furthermore, the minimum scale at which entry takes place depends on
the magnitude of these economies and is given by the quantity Qu that minimizes the
firm’s average cost. Furthermore, whereas in Topic 3 a firm’s break-even price is simply
given, here we derive it as the firm’s minimum average cost ACu .
Thus, key FPM readings are from Ch. 3 on costs: fixed costs as a source of economies
of scale, and the mathematics of U-shaped average cost (pages 87–89). The other key
reading is pages 105–107 of Ch. 4 on equilibrium with free entry.
In the notes that follow, I give a skeletal summary of the main ideas. See the slides
from Session 5 for numerical examples.
5.1. Costs
The average cost curve becomes important for two interrelated reasons having to do
with entry. First, it captures economies of scale, which is why a firm’s entry is a discrete
decision. That is, a firm jumps into the market with a significant scale rather than sliding
in unnoticeably. Second, the entry decision can be derived entirely form the AC curve.
We assume that the AC curve is U-shaped: there are initially economies of scale and
then, at higher quantities, diseconomies of scale. This is both realistic (even if more
complicated situations could arise) and provides good intuition about entry decisions.
The simplest way to have a U-shaped AC curve is to assume FC > 0 and increasing
MC. This is the only case we consider. Besides being simplest, it provides the best
intuition about entry. The fixed cost can be thought of as an entry cost. The firm enters
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Prices & Markets • Overview of perfect competition: Sessions 1–6
19
if this entry cost is made up for by the variable profit that it earns in the market (where
variable profit is calculated excluding the fixed cost).
5.2. A firm’s quantity
A firm’s optimal quantity or scale, given that it enters, is given entirely by the MC curve,
as illustrated in Figure 13. This is a repeat of the firm’s decision in Topic 4. Fixed cost
and average cost do not matter.
Figure 13
€
MC↔supply
8
7
6
5
4
3
2
1
s(6) = 40
10
20
30
40
50
60
70
Q
5.3. A firm’s entry or exit decision
A firm’s entry or exit decision is given entirely by the minimum point on the AC curve.
The minimum average cost, denoted ACu , is the firm’s break-even price. The firm enters
if the market price is higher (or expected to be higher) than ACu and it stays out otherwise.
The quantity Qu that minimizes average cost is the firm’s minimum scale of production
if it enters the market.
Figure 14
€
8
7
AC
6
ACu 5
4
3
2
1
10
20
Qu
30
40
50
60
70
Q
Prices & Markets • Overview of perfect competition: Sessions 1–6
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5.4. Combining the two decisions
We can superimpose the AC and MC curves to see the entry/exit and quantity decisions
together. The two curves cross at the minimum point on the AC curve. This is shown in
Figure 15. The firm stays out of the market, and hence supplies 0, until the price reaches
ACu . At that price, the firm would enter the market with quantity Qu . At higher prices,
the firm’s output follows the MC curve. Overall, the firm’s supply curve is the thick light
blue line.
Figure 15
€
MC
8
7
AC
6
u
AC 5
4
3
2
1
10
20
Qu
30
40
50
60
70
Q
5.5. Aggregate supply and equilibrium
As the price rises, aggregate supply increases for two reasons: entry of new firms as
the price crosses their break-even prices (as in Topic 3); and expansion of output by
firms in the market (as in Topic 4). The supply curve could look as shown in Figure 16.
Equilibrium is then found in the usual way by supply=demand.
Figure 16
P
30
25
20
15
10
5
Q
100
200
300
400
Prices & Markets • Overview of perfect competition: Sessions 1–6
5.6. An alternate view of entry/exit and equilibrium
Constructing the aggregate supply curve allows us to see that Figure 1, and everything
we can do with it, remains valid. Furthermore, we understand that we can interpret the
increase in supply in Figure 1 as coming from both entry of new firms and expansion of
output by firms already in the market.
However, there is an alternate two-stage view of equilibrium that is closer to the way
the firms think about entry. In the first stage, firms decide whether to enter or stay in the
market. In the second stage, firms compete—as in the model of fixed firms in the market
from Topic 4.
The individual firms’ decisions and equilibrium are understood by working backwards. In the second stage, the equilibrium price and the variable profit that each firm
earns (disregarding its fixed cost of entry) depends on the set of firms in the market.
The first-stage entry and exit decisions are in equilibrium if the each firm in the
market does not lose money (and hence would not prefer to exit) whereas any firm not
in the market could not make a profit by entering. In terms of break-even prices, this
means that the equilibrium price is not lower than the break-even price of any firm in
the market, whereas if a firm not in the market were to enter then the equilibrium price
would be lower than its break-even price. In terms of fixed costs and variable profits, this
means that each active firm’s variable profit covers its fixed cost of entry, yet if another
firm entered the market then its variable profit would be lower than its fixed cost of entry.
Although the dynamics of market entry and exit can be very complex, the most intuitive story is to suppose that firms enter one at a time, with the most efficient firms
entering first. We can then see how eventually equilibrium must be reached. Each time
another firm enters the market, supply expands, the market prices falls, and the variable
profit of each firm goes down. At the same time, the pool of remaining firms are increasingly inefficient. Hence, eventually the declining market price and declining variable
profit makes subsequent entry unprofitable and the market reaches equilibrium.
This two-stage approach is not outlined in any of the lecture notes except in the form
of Exercise 4.3, which I think most students will find too involved. Furthermore, I have
not found time to discuss it in class, so it does not form part of the our required material
in this part of the course on perfect competition. On the other hand, I will use it for entry
and exit with imperfect competition.
5.7. Free entry
When there is free entry (that is, firms are identical), the main conclusions are the same
as in Topic 3: Firms earn zero profit, the price is pinned down by the common break-even
price of the firms, and supply is perfectly elastic.
The calculations change a bit because each firm’s output Q∗i and the break-even price
P ∗ are derived from the cost curve as the quantity Qu that minimizes average and the
minimum value ACu of the average cost. (A firm’s output and break-even price were
simply given in Topic 3.) Otherwise, the calculations are the same: total output comes
from the demand curve: Q∗ = d(P ∗ ); the number of firms comes from N∗ = Q∗ ÷ Q∗i .
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