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Lecture # 14
Perfectly Competitive Markets
Lecturer: Martin Paredes
1. Perfect Competition Defined
2. Profit Maximisation
3. Short Run Equilibrium
 Supply curve for the firm and market
 Equilibrium
 Producer surplus
4. Long Run Equilibrium
 Equilibrium Conditions
 Supply Curve
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Definition: A perfectly competitive market
consists of firms that produce identical
products that sell at the same price.
 Each firm’s volume of output is so small in
comparison to the overall market demand that
no single firm has an impact on the market
price.
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Assumptions:
1. Firms produce undifferentiated products, in
the sense that consumers perceive them to be
identical.
2. Consumers have perfect information about the
prices all sellers in the market charge
3. All firms (industry participants and new
entrants) have equal access to resources
(technology, inputs).
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Assumptions (cont.):
4. Each buyer’s purchases are so small that
he/she has an imperceptible effect on market
price.
5. Each seller’s sales are so small that he/she has
an imperceptible effect on market price.
6. Each seller’s input purchases are so small that
he/she perceives no effect on input prices
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Implications of Assumptions:
 The Law of One Price:
Conditions (1) and (2) imply that there is a
unique, single price at which all transactions
occur.
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Implications of Assumptions:
 Price Takers:
Conditions (3) and (4) imply that buyers and
sellers take the price of the product as given
when making their purchase and output
decisions.
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Implications of Assumptions:
 Free Entry:
Condition (5) and (6) implies that all firms have
identical long run cost functions.
 We need also need to assume that setup costs
are easily achievable.
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Definition: The Economic Profit is the difference
between total sales revenues and the economic
cost (including opportunity costs).
 Then, the firm’s objective is to choose the
amount of output to maximise profits:
Max (q) = TR – TC = P· q – C(q)
q
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Example:
Suppose:
Total Revenues
Costs of supplies and labor
Owner’s opportunity cost
€ 10 M
€9M
€2M

Accounting Profit:
€ 10M – € 9M = € 1M

Economic Profit:
€ 10M – € 9M – € 2M = – € 1M
 Business “destroys” € 1M of wealth of owner
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 Since the firm’s objective is:
Max (q) = TR – TC = P· q – C(q)
q
…then the first order condition is:
d(q) = 0
dq
…or…
dTR = dTC
dq
dq
 The last term states that marginal revenue
equals marginal cost.
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Notes: Recall that:
 If MR > MC then profit rises if output is
increased => Increase output.
 If MR < MC then profit falls if output is
increased => Decrease output.
 Therefore, the profit maximization condition
for any firm is MR = MC.
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Definition: A firm’s marginal revenue is the rate at
which total revenue changes with respect to
output.
MR = dTR(q) = d[P(q)· q]
dq
dq
 In perfect competition, P(q) = P. As a result,
MR = P.
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Note:
 Since MR = P under perfect competition, then
the profit maximization condition for a pricetaking firm is P = MC.
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Example:
Suppose:
 The market price is P = 15
 Each firm has the cost function:
TC(q) = 24q – 0.9q2 + 0.0167q3
=> MC(q) = 24 – 1.8q + 0.05q2
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€/yr
Example: Profit Maximization Condition
Total revenue = pq
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q (units per year)
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€/yr
Example: Profit Maximization Condition
Total cost
Total revenue = pq
q (units per year)
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€/yr
Example: Profit Maximization Condition
Total cost
Total revenue = pq
Total profit
q (units per year)
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€/yr
Example: Profit Maximization Condition
Total cost
Total revenue = pq
Total profit
6
30
q (units per year)
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€/yr
Total revenue = pq
Example: Profit Maximization Condition
q (units per year)
15
P, MR
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q (units per year)
€/yr
Total revenue = pq
Total Cost
Example: Profit Maximization Condition
q (units per year)
MC
15
P, MR
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q (units per year)
€/yr
Total revenue = pq
Total Cost
Example: Profit Maximization Condition
q (units per year)
MC
P, MR
15
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6
30
q (units per year)
Notes:
 At profit maximizing point:
 P = MC
 MC is non-decreasing
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Notes:
 What is the firm’s demand curve?
 The firm can sell as much as it likes at price
P, so the firm’s demand curve is a straight
line at P
 What is the firm’s supply curve?
 It is defined by the MC curve, but not in its
entirety.
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Definition: The short run is the period of time in
which the firm’s plant size is fixed and the
number of firms in the industry is also fixed.
 Firms need to take into account their respective
short run total cost.
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 Recall that the short run total cost function can
be decomposed into two elements:
1. Total variable cost:
TVC(q)
2. Total fixed cost:
TFC
 In turn, the fixed cost can be divided into:
a. Sunk fixed costs
SFC
b. Non-sunk fixed costs
NSFC
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 Then:
TVC(q) + SFC + NSFC
when q > 0
SFC
when q = 0
TC(q) =
 Obviously
TFC = SFC + NSFC
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Definition: The short run supply curve for a firm
tells us how the profit-maximizing output
changes as the market price changes.
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General Idea:
 If the firm chooses to produce q > 0, then
condition P = SMC defines short run supply
curve of the firm.
 The firm produces q > 0 as long as:
(q)  (0)
 If (q) < (0), then the firm shuts down.
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Definition: The shut-down price, Ps, is the price
below which the firm would opt to produce
zero.
 The firm’s short run supply function is defined
by:
SMC
when P  PS
s(P) =
0
when P < PS
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 The value of Ps depends on the structure of the
fixed costs. In particular, whether there are
sunk costs or not.
 Let’s look at two cases:
1. All fixed costs are sunk
NSFC = 0 and SFC > 0 ==> (0) = SFC
2. All fixed costs are non-sunk
NSFC > 0 and SFC = 0 ==> (0) = 0
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Case 1: NSFC = 0 and SFC > 0
 Hence, TFC = SFC (fixed costs are all sunk)
 The firm will choose to produce a positive
output only if:
(q)  (0) …or…
P· q – TVC(q) – TFC  – TFC = – SFC
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Case 1: NSFC = 0 and SFC > 0
 In other words:
P· q – TVC(q)  0
…which can be re-written as:
P  AVC(q)
 Therefore, the shut-down price, Ps, is the
minimum point on the AVC curve.
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€/yr
Example: Short Run Supply Curve of the Firm
NSFC = 0 and SFC > 0
SMC
SAC
AVC
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Quantity (units/yr)
€/yr
Example: Short Run Supply Curve of the Firm
NSFC = 0 and SFC > 0
SMC
SAC
AVC
Ps
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Quantity (units/yr)
€/yr
Example: Short Run Supply Curve of the Firm
NSFC = 0 and SFC > 0
SMC
SAC
AVC
Ps
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Quantity (units/yr)
Case 1: NSFC = 0 and SFC > 0
 A perfectly competitive firm may operate in
short run even if economic profit is negative.
 At prices below SAC but above AVC, profits
are negative if the firm produces…but the firm
loses less by producing than by shutting down
because of sunk costs.
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Case 2: NSFC > 0 and SFC = 0
 The firm will choose to produce a positive
output only if:
(q)  (0) …or…
P· q – TVC(q) – TFC  0
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Case 2: NSFC = 0 and SFC > 0
 In other words:
P  AVC(q) + AFC = SAC
 Therefore, the shut-down price, Ps, is the
minimum point on the SAC curve.
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Example: Short Run Supply Curve of the Firm
NSFC = 0 and SFC > 0
SMC
SAC
AVC
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Quantity (units/yr)
€/yr
Example: Short Run Supply Curve of the Firm
NSFC = 0 and SFC > 0
SMC
SAC
Ps
AVC
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Quantity (units/yr)
€/yr
Example: Short Run Supply Curve of the Firm
NSFC = 0 and SFC > 0
SMC
SAC
Ps
AVC
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Quantity (units/yr)
Definition:
 The market supply at any price is the sum of
the quantities each firm supplies at that price.
 The short run market supply curve is the
horizontal sum of the individual firm supply
curves.
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Example: From Short Run Firm Supply Curve to
Short Run Market Supply Curve
Firm Type 1
P
Firm Type 2
SMC1
P
SMC2
Market supply
P
30
20
Q
Q
Q
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Definition: A short run perfectly competitive
equilibrium occurs when the market quantity
demanded equals the market quantity
supplied:
ni=1 qs(P) = Qd(P)
where qs(P) is determined by the firm's
individual profit maximization condition.
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Example: Short Run Perfectly Competitive Equilibrium
€/unit
Market:
Supply
P*
Demand
Q*
m. units/yr
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Example: Short Run Perfectly Competitive Equilibrium
€/unit
€/unit
Market:
Typical firm:
Supply
SMC
SAC
P*
Demand
Q*
P*=MR
AVC
Ps
m. units/yr
q*
Units/yr
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Definition:
The Producer Surplus is the area above the
market supply curve and below the market
price.
It is a monetary measure of the benefit that
producers derive from producing a good at a
particular price.
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P
Example: Producer Surplus
Market Supply Curve
Q
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P
Example: Producer Surplus
Market Supply Curve
P*
Q
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P
Example: Producer Surplus
Market Supply Curve
P*
Producer Surplus
Q
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Notes:
 The producer earns the price for every unit
sold, but only incurs the (short run) marginal
cost for each unit.
 The distance between P and SMC curve
measures the total benefit derived from
production.
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Notes:
 Since the market supply curve equals the sum
of the individual supply curves, then the
difference between price and the market supply
curve measures the surplus of ALL producers
in the market.
 The producer’s surplus does not deduct fixed
costs, so it does NOT equal profit!
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Definition: The long run supply curve for a firm
tells us how the profit-maximizing output
changes as the market price changes.
MC
when P  min(AC) = PS
0
when P < min(AC) = PS
s(P) =
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Definition: A long run perfectly competitive
equilibrium occurs at a market price, P*, a
number of firms, n*, and an output per firm, q*
that satisfies the following conditions:
1. Long run profit maximization with respect to
output and plant size:
P* = MC(q*)
2. Zero economic profit:
P* = AC(q*)
3. Demand equals supply:
Qd(P*) = n*q*
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Example: Long Run Perfectly Competitive Equilibrium
$/unit
$/unit
Typical Firm
n* = 10,000/50=200
MC
SAC
Market
AC
P*
Market demand
SMC
q*=50
q
Q*=10,000
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Q
 Summarizing long run equilibrium:
If the firm’s strategy is based on:
 Skills that can be easily imitated
 Resources that can be easily acquired
Then, in the long run its economic profit will be
zero.
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Definition: The Long Run Market Supply Curve
tells us the total quantity of output that will be
supplied at various market prices, assuming
that all long-run adjustments (plant, entry) take
place.
Note: Since new entry can occur in the long run, we
cannot obtain the long run market supply
curve by summing the long run firms’ supply
curves.
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Definition: A constant-cost industry is one in
which a change in industry output does NOT
affect input prices.
 In a constant-cost industry, output changes in
the long run occur along a horizontal line
corresponding to the minimum level of long
run average cost.
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 In a constant-cost industry:
 If P > min(AC), entry would occur, driving
price back to min(AC)
 If P < min(AC), firms would earn negative
profits and would supply nothing
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Example: Long Run Market Supply Curve
Typical Firm
Market
$/unit
$/unit
SS0
MC
SAC
D0
AC
LS
15
SMC
50
q (000s)
10
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Q (M.)
Example: Long Run Market Supply Curve
Typical Firm
Market
$/unit
$/unit
SS0
D1
MC
23
15
SAC
D0
AC
LS
SMC
50 52
q (000s)
10
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Q (M.)
Example: Long Run Market Supply Curve
Typical Firm
Market
$/unit
$/unit
SS0
SS1
D1
MC
23
15
SAC
D0
AC
LS
SMC
50 52
q (000s)
10
18
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Q (M.)
Example: Long Run Market Supply Curve
Typical Firm
Market
$/unit
$/unit
n** = 18,000/50 = 360
SS0
SS1
D1
MC
23
15
SAC
D0
AC
LS
SMC
50 52
q (000s)
10
18
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Q (M.)
1. Perfectly Competitive markets have the
following characteristics:
a. Homogeneous products
b. Perfect information
c. Atomicity or fragmentation (small buyers and
sellers)
d. Equal access to resources
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2. A price taking firm maximizes profit by
producing at an output level at which (rising)
marginal cost equals the market price (which is
the marginal revenue for a price-taking firm).
3. If all fixed costs are sunk, a perfectly
competitive firm will produce positive output in
the short run only if market price exceeds AVC.
4. The short run market supply is the horizontal
sum of the short run supplies of individual
firms.
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