Perfect Competition
ECON 212 Lecture 13
Tianyi Wang
Queen’s Univeristy
Winter 2013
Tianyi Wang (Queen’s Univeristy)
ECON 212 Lecture 13
Winter 2013
1 / 12
Intro
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We can analyze …rm’s supply decision.
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Firm faces two constraints: technology and market.
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Market constraint is summarized by the demand curve.
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Demand curve facing the …rm di¤ers from market demand curve.
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one …rm, two …rms, ...
see graphs later.
We start with the simplest market enviroment: perfect competition.
Tianyi Wang (Queen’s Univeristy)
ECON 212 Lecture 13
Winter 2013
2 / 12
Perfect Competittion
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Market is perfectly competititve if there are large number of …rms so
that each one is too small to in‡uence market price.
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Firm’s problem: how much to produce taken price as given.
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Strong assumption, works well.
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See class notes for graph of Deman facing a Competitive …rm.
Tianyi Wang (Queen’s Univeristy)
ECON 212 Lecture 13
Winter 2013
3 / 12
Supply Decision of a Competitive Firm
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Here we take the cost sturcture as given.
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Competitve …rm’s problem is
max pq
q
Tianyi Wang (Queen’s Univeristy)
c (q )
ECON 212 Lecture 13
Winter 2013
4 / 12
Supply Decision of a Competitive Firm
I
Here we take the cost sturcture as given.
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Competitve …rm’s problem is
max pq
q
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c (q )
Note we can backup input demands after solving for q.
Tianyi Wang (Queen’s Univeristy)
ECON 212 Lecture 13
Winter 2013
4 / 12
Supply Decision of a Competitive Firm
I
Here we take the cost sturcture as given.
I
Competitve …rm’s problem is
max pq
q
I
I
c (q )
Note we can backup input demands after solving for q.
FOC is
p c 0 (q ) = 0
Tianyi Wang (Queen’s Univeristy)
ECON 212 Lecture 13
Winter 2013
4 / 12
Supply Decision of a Competitive Firm
I
Here we take the cost sturcture as given.
I
Competitve …rm’s problem is
max pq
q
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c (q )
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Note we can backup input demands after solving for q.
FOC is
p c 0 (q ) = 0
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or
p = MC (q )
MR (q ) = MC (q )
Tianyi Wang (Queen’s Univeristy)
ECON 212 Lecture 13
Winter 2013
4 / 12
Supply Decision of a Competitive Firm
I
Here we take the cost sturcture as given.
I
Competitve …rm’s problem is
max pq
q
I
c (q )
I
Note we can backup input demands after solving for q.
FOC is
p c 0 (q ) = 0
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or
p = MC (q )
MR (q ) = MC (q )
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Competitive …rm’s supply curve is its MC curve.
Tianyi Wang (Queen’s Univeristy)
ECON 212 Lecture 13
Winter 2013
4 / 12
Supply Decision of a Competitive Firm
I
Here we take the cost sturcture as given.
I
Competitve …rm’s problem is
max pq
q
I
c (q )
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Note we can backup input demands after solving for q.
FOC is
p c 0 (q ) = 0
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or
p = MC (q )
MR (q ) = MC (q )
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Competitive …rm’s supply curve is its MC curve.
However there are two issues.
Tianyi Wang (Queen’s Univeristy)
ECON 212 Lecture 13
Winter 2013
4 / 12
Competitive Firm’s Supply Curve
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We derived supply curve from FOC. It could either be a max or a min.
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See class notes graph where two output levels satisfy FOC.
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Note we can avoid q1 by checking SOC.
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Graphically this happens on declining portion of MC.
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So …rm’s supply curve is only the upward sloping portion of MC.
Tianyi Wang (Queen’s Univeristy)
ECON 212 Lecture 13
Winter 2013
5 / 12
Competitive Firm’s Supply Curve (Con’t)
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Second issue is if price is so low that not pro…table to produce.
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See class notes for shutdown condtion.
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Note: shutdown is di¤erent from exit.
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So only upward sloping portion of MC above AVC is competitve
…rm’s supply curve.
Tianyi Wang (Queen’s Univeristy)
ECON 212 Lecture 13
Winter 2013
6 / 12
Long-run Supply of Competitive Firm
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Long-run curve intersects shrot-run curve at output q where …xed
factor is optimal.
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See class notes for graph.
Tianyi Wang (Queen’s Univeristy)
ECON 212 Lecture 13
Winter 2013
7 / 12
Long-run Supply of Competitive Firm
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Long-run curve intersects shrot-run curve at output q where …xed
factor is optimal.
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See class notes for graph.
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LR curve is more responsive to price.
Tianyi Wang (Queen’s Univeristy)
ECON 212 Lecture 13
Winter 2013
7 / 12
Long-run Supply of Competitive Firm
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Long-run curve intersects shrot-run curve at output q where …xed
factor is optimal.
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See class notes for graph.
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LR curve is more responsive to price.
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Firm can exit in the long-run. Thus pro…t has to be greater than zero.
pq
c (q )
p
Tianyi Wang (Queen’s Univeristy)
ECON 212 Lecture 13
0
c (q )
q
Winter 2013
7 / 12
Long-run Supply of Competitive Firm
I
Long-run curve intersects shrot-run curve at output q where …xed
factor is optimal.
I
See class notes for graph.
I
LR curve is more responsive to price.
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Firm can exit in the long-run. Thus pro…t has to be greater than zero.
pq
c (q )
p
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0
c (q )
q
Thus long-run supply curve is the upward sloping portion of LRMC
above LRAC.
Tianyi Wang (Queen’s Univeristy)
ECON 212 Lecture 13
Winter 2013
7 / 12
Long-run Supply of Competitive Firm
I
Long-run curve intersects shrot-run curve at output q where …xed
factor is optimal.
I
See class notes for graph.
I
LR curve is more responsive to price.
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Firm can exit in the long-run. Thus pro…t has to be greater than zero.
pq
c (q )
p
0
c (q )
q
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Thus long-run supply curve is the upward sloping portion of LRMC
above LRAC.
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See class notes for constant returns to scale technology.
Tianyi Wang (Queen’s Univeristy)
ECON 212 Lecture 13
Winter 2013
7 / 12
Short-run Industry Supply
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Suppose there are n …rms, let Si (p ) be …rm i’s supply curve. Then
the industry/market supply is
n
S (p ) =
∑ Si ( p )
i =1
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If …rms are identical, S (p ) = nSi (p )
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Market demand and market supply determines equilibrium price and
output level.
Tianyi Wang (Queen’s Univeristy)
ECON 212 Lecture 13
Winter 2013
8 / 12
Long-run Industry Equilibrium
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If no barriers to entry, …rms enter and exit in the long-run.
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Firms entry and exit a¤ect output produced and therefore equilibrium
price.
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We can get market supply by adding up individuals.
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Will get an approximation. See class notes.
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Note LR industry supply looks the same as …rm supply with CRS
technology.
Tianyi Wang (Queen’s Univeristy)
ECON 212 Lecture 13
Winter 2013
9 / 12
Long-run Industry Equilibrium
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In Competitive Equilibrium, we have Demand = Supply and each …rm
max pro…t.
1. Firm max pro…t: p = LMC (q )
2. Perfect competition: p = LAC (q )
3. Market clears: Q D (p ) = Q S (p ) = n q
Tianyi Wang (Queen’s Univeristy)
ECON 212 Lecture 13
Winter 2013
10 / 12
Opportunity Cost and Economic Rent
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Suppost entry is limited in some industries (Agriculture) due to
limited …xed factors (Land).
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It might look like farmer earns positive pro…t π.
Tianyi Wang (Queen’s Univeristy)
ECON 212 Lecture 13
Winter 2013
11 / 12
Opportunity Cost and Economic Rent
I
Suppost entry is limited in some industries (Agriculture) due to
limited …xed factors (Land).
I
It might look like farmer earns positive pro…t π.
I
This not correct, we do not measure opportunity cost of Land.
Tianyi Wang (Queen’s Univeristy)
ECON 212 Lecture 13
Winter 2013
11 / 12
Opportunity Cost and Economic Rent
I
Suppost entry is limited in some industries (Agriculture) due to
limited …xed factors (Land).
I
It might look like farmer earns positive pro…t π.
I
This not correct, we do not measure opportunity cost of Land.
I
Farmer can sell the Land for π.
Tianyi Wang (Queen’s Univeristy)
ECON 212 Lecture 13
Winter 2013
11 / 12
Opportunity Cost and Economic Rent
I
Suppost entry is limited in some industries (Agriculture) due to
limited …xed factors (Land).
I
It might look like farmer earns positive pro…t π.
I
This not correct, we do not measure opportunity cost of Land.
I
Farmer can sell the Land for π.
I
Whenever a …xed factor is preventing entry, a rental rate for that
factor exists.
Tianyi Wang (Queen’s Univeristy)
ECON 212 Lecture 13
Winter 2013
11 / 12
Opportunity Cost and Economic Rent
I
Suppost entry is limited in some industries (Agriculture) due to
limited …xed factors (Land).
I
It might look like farmer earns positive pro…t π.
I
This not correct, we do not measure opportunity cost of Land.
I
Farmer can sell the Land for π.
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Whenever a …xed factor is preventing entry, a rental rate for that
factor exists.
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This is Economic Rent: payments to a factor of production in excess
of the minimum necessary to have that factor supplied.
Tianyi Wang (Queen’s Univeristy)
ECON 212 Lecture 13
Winter 2013
11 / 12
(Optional) Relationship b/w Cost-Min and Pro…t-Max
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Directly write pro…t max problem:
max pq
q
(wL + rK )
s.t. q = Q (L, K )
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How to solve? sub constraint into objective by eliminating q.
max pQ (L, K )
K ,L
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FOC for K and L respectively are
pQk0
pQL0
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(wL + rK )
= r
= w
Take the ratio, we get the optimality cond’t for cost-min.
r
MPK
=
MPL
w
Tianyi Wang (Queen’s Univeristy)
ECON 212 Lecture 13
Winter 2013
12 / 12