Perfectly Competitive Markets

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Lecture 14 Perfectly Competitive
Markets Lecturer Martin Paredes
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Outline

• Perfect Competition Defined
• Profit Maximisation
• Short Run Equilibrium
• Supply curve for the firm and market
• Equilibrium
• Producer surplus
• Long Run Equilibrium
• Equilibrium Conditions
• Supply Curve

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Perfectly Competitive Markets

• Definition A perfectly competitive market
  consists of firms that produce identical products
  that sell at the same price.
• Each firms 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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Perfectly Competitive Markets

• Assumptions
• Firms produce undifferentiated products, in the
  sense that consumers perceive them to be
  identical.
• Consumers have perfect information about the
  prices all sellers in the market charge
• All firms (industry participants and new
  entrants) have equal access to resources
  (technology, inputs).

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Perfectly Competitive Markets

• Assumptions (cont.)
• Each buyers purchases are so small that he/she
  has an imperceptible effect on market price.
• Each sellers sales are so small that he/she has
  an imperceptible effect on market price.
• Each sellers input purchases are so small that
  he/she perceives no effect on input prices

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Perfectly Competitive Markets

• 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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Perfectly Competitive Markets

• 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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Perfectly Competitive Markets

• 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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Profit Maximisation

• Definition The Economic Profit is the difference
  between total sales revenues and the economic
  cost (including opportunity costs).
• Then, the firms objective is to choose the
  amount of output to maximise profits
• Max ?(q) TR TC P q C(q) q

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Profit Maximisation

• Example
• Suppose Total Revenues 10 M Costs of
  supplies and labor 9 M Owners opportunity
  cost 2 M
• Accounting Profit 10M 9M 1M
• Economic Profit 10M 9M 2M 1M
• Business destroys 1M of wealth of owner

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Profit Maximisation

• Since the firms objective is
• Max ?(q) TR TC P q C(q) q
• then the first order condition is
• d?(q) 0 or dTR dTC dq
  dq dq
• The last term states that marginal revenue equals
  marginal cost.

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Profit Maximisation

• Notes Recall that
• If MR gt MC then profit rises if output is
  increased gt Increase output.
• If MR lt MC then profit falls if output is
  increased gt Decrease output.
• Therefore, the profit maximization condition for
  any firm is MR MC.

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Profit Maximisation

• Definition A firms marginal revenue is the rate
  at which total revenue changes with respect to
  output.
• MR dTR(q) dP(q) q dq
  dq
• In perfect competition, P(q) P. As a result, MR
  P.

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Profit Maximisation

• Note
• Since MR P under perfect competition, then the
  profit maximization condition for a price-taking
  firm is P MC.

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Profit Maximisation

• Example
• Suppose
• The market price is P 15
• Each firm has the cost function
• TC(q) 24q 0.9q2 0.0167q3
• gt MC(q) 24 1.8q 0.05q2

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/yr
Example Profit Maximization Condition
Total revenue pq
15
q (units per year)
17
/yr
Example Profit Maximization Condition
Total cost
Total revenue pq
q (units per year)
18
/yr
Example Profit Maximization Condition
Total cost
Total revenue pq
Total profit
q (units per year)
19
/yr
Example Profit Maximization Condition
Total cost
Total revenue pq
Total profit
q (units per year)
30
6
20
/yr
Total revenue pq
Example Profit Maximization Condition
q (units per year)
P, MR
15
q (units per year)
21
/yr
Total revenue pq
Total Cost
Example Profit Maximization Condition
q (units per year)
MC
P, MR
15
q (units per year)
22
/yr
Total revenue pq
Total Cost
Example Profit Maximization Condition
q (units per year)
MC
P, MR
15
q (units per year)
6
30
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Profit Maximisation

• Notes
• At profit maximizing point
• P MC
• MC is non-decreasing

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Profit Maximisation

• Notes
• What is the firms demand curve?
• The firm can sell as much as it likes at price P,
  so the firms demand curve is a straight line at
  P
• What is the firms supply curve?
• It is defined by the MC curve, but not in its
  entirety.

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Short Run Equilibrium

• Definition The short run is the period of time
  in which the firms 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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Short Run Equilibrium

• Recall that the short run total cost function can
  be decomposed into two elements
• Total variable cost TVC(q)
• Total fixed cost TFC
• In turn, the fixed cost can be divided into
• Sunk fixed costs SFC
• Non-sunk fixed costs NSFC

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Short Run Equilibrium

• Then
• TVC(q) SFC NSFC when q gt 0
• TC(q)
• SFC when q 0
• Obviously TFC SFC NSFC

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Firm's Supply Curve in Short Run
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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Firm's Supply Curve in Short Run

• General Idea
• If the firm chooses to produce q gt 0, then
  condition P SMC defines short run supply curve
  of the firm.
• The firm produces q gt 0 as long as
• ?(q) ? ?(0)
• If ?(q) lt ?(0), then the firm shuts down.

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Firm's Supply Curve in Short Run

• Definition The shut-down price, Ps, is the price
  below which the firm would opt to produce zero.
• The firms short run supply function is defined
  by
• SMC when P ? PS
• s(P)
• 0 when P lt PS

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Firm's Supply Curve in Short Run

• The value of Ps depends on the structure of the
  fixed costs. In particular, whether there are
  sunk costs or not.
• Lets look at two cases
• All fixed costs are sunk
• NSFC 0 and SFC gt 0 gt ?(0) SFC
• All fixed costs are non-sunk
• NSFC gt 0 and SFC 0 gt ?(0) 0

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Firm's Supply Curve in Short Run

• Case 1 NSFC 0 and SFC gt 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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Firm's Supply Curve in Short Run

• Case 1 NSFC 0 and SFC gt 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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Example Short Run Supply Curve of the Firm
NSFC 0 and SFC gt 0
/yr
SMC
SAC
AVC
Quantity (units/yr)
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Example Short Run Supply Curve of the Firm
NSFC 0 and SFC gt 0
/yr
SMC
SAC
AVC
Ps
Quantity (units/yr)
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Example Short Run Supply Curve of the Firm
NSFC 0 and SFC gt 0
/yr
SMC
SAC
AVC
Ps
Quantity (units/yr)
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Firm's Supply Curve in Short Run

• Case 1 NSFC 0 and SFC gt 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 producesbut the firm loses
  less by producing than by shutting down because
  of sunk costs.

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Firm's Supply Curve in Short Run

• Case 2 NSFC gt 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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Firm's Supply Curve in Short Run

• Case 2 NSFC 0 and SFC gt 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 gt 0
SMC
SAC
AVC
Quantity (units/yr)
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Example Short Run Supply Curve of the Firm
NSFC 0 and SFC gt 0
/yr
SMC
SAC
Ps
AVC
Quantity (units/yr)
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Example Short Run Supply Curve of the Firm
NSFC 0 and SFC gt 0
/yr
SMC
SAC
Ps
AVC
Quantity (units/yr)
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Short Run Market Supply Curve

• 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
Firm Type 2
Market supply
SMC1
SMC2
P
P
P
30
20
Q
Q
Q
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Short Run Perfectly Competitive Equilibrium

• Definition A short run perfectly competitive
  equilibrium occurs when the market quantity
  demanded equals the market quantity supplied
• ?ni1 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
PMR
P
AVC
Demand
Ps
q
Units/yr
Q
m. units/yr
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Producer Surplus
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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Example Producer Surplus
P
Market Supply Curve
Q
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Example Producer Surplus
P
Market Supply Curve
P
Q
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Example Producer Surplus
P
Market Supply Curve
P
Producer Surplus
Q
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Producer Surplus

• 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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Producer Surplus

• 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 producers surplus does not deduct fixed
  costs, so it does NOT equal profit!

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Firm's Supply Curve in LONG Run
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 s(P) 0 when P lt min(AC)
PS
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Long Run Perfectly Competitive Equilibrium

• 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
• Long run profit maximization with respect to
  output and plant size P MC(q)
• Zero economic profit P AC(q)
• Demand equals supply Qd(P) nq

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Example Long Run Perfectly Competitive
Equilibrium
/unit
/unit
Typical Firm Market
n 10,000/50200
MC
AC
SAC
P
Market demand
SMC
q50
Q10,000
q
Q
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Long Run Market Equilibrium

• Summarizing long run equilibrium
• If the firms 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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Long Run Market Supply Curve
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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Long Run Market Supply Curve

• 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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Long Run Market Supply Curve

• In a constant-cost industry
• If P gt min(AC), entry would occur, driving price
  back to min(AC)
• If P lt 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
D0
AC
SAC
LS
15
SMC
50
10
Q (M.)
q (000s)
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Example Long Run Market Supply Curve
Typical Firm Market
/unit
/unit
SS0
D1
MC
D0
AC
SAC
23
LS
15
SMC
50 52
10
Q (M.)
q (000s)
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Example Long Run Market Supply Curve
Typical Firm Market
/unit
/unit
SS0
SS1
D1
MC
D0
AC
SAC
23
LS
15
SMC
50 52
10 18
Q (M.)
q (000s)
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Example Long Run Market Supply Curve
Typical Firm Market
/unit
/unit
n 18,000/50 360
SS0
SS1
D1
MC
D0
AC
SAC
23
LS
15
SMC
50 52
10 18
Q (M.)
q (000s)
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Summary

• Perfectly Competitive markets have the following
  characteristics
• Homogeneous products
• Perfect information
• Atomicity or fragmentation (small buyers and
  sellers)
• Equal access to resources

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Summary

1. 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).
2. If all fixed costs are sunk, a perfectly
   competitive firm will produce positive output in
   the short run only if market price exceeds AVC.
3. The short run market supply is the horizontal sum
   of the short run supplies of individual firms.