Partial equilibrium analysis:
Competitive markets
Lectures in Microeconomic Theory
Fall 2009, Part 16
02.09.2009
G.B. Asheim, ECON4230-35, #16
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Partial vs. general equilibrium analysis

In a partial equilibrium model, all prices other than
the price of the good studied are assumed to remain
Price
fixed.
Aggregate supply
given factor prices.
Equilibrium
price.
Aggregate demand
given prices of other
goods and given income.
Equilibrium quantity.

Quantity
In a general equilibrium model, all prices are
variable. A general equilibrium requires that all
markets clear.
02.09.2009
G.B. Asheim, ECON4230-35, #16
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1
Overview of lectures on partial equilibrium

22 Oct: Competitive markets
Quasi-linear utility functions. Welfare analysis.

29 Oct: Monopoly
Price discrimination.

5 Nov: Oligopoly and game theory
Cournot competition. Nash equilibrium

(12 & 19 Nov: Repetition of the theory of the firm,
consumer theory, and general equilibrium analysis)
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G.B. Asheim, ECON4230-35, #16
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A competitive market is characterized by

Sellers and buyers take the market price as given and
determine their supply and demand accordingly.

The market price is determined so that
market supply = market demand.

A good is transferred if and only if the price is paid.

Sellers and buyers have the same information about
the transferred good.
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2
Demand facing each competitive firm
if p  p
0

D ( p )  any amount if p  p

if p  p

p
p
D( p)
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G.B. Asheim, ECON4230-35, #16
Supply of a competitive profit maximizing firm, if convex costs
 ( p )  max py  c ( y )
c( y )
y( p)
p
y
y ( p )  arg max py  c ( y )p
y
If interior solution:
FOC : p  c ( y ( p ))
SOC : c ( y ( p ))  0
p
y( p)
How does a competitive
firm respond to a change in
the price of output?
02.09.2009
y
By differentiating the FOC:
1  c ( y ( p )) y ( p )
c ( y )  0  y ( p )  0
G.B. Asheim, ECON4230-35, #16
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3
Supply of a competitive
profit maximizing firm,
if non-convex costs
(1, p)
(1, p)
OutputOutput
Cost
Cost at profit-maximizing output
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Profit-max.
output
Profit in
terms of
output
Interior solution
if price exceeds
minimal average
variable cost.
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G.B. Asheim, ECON4230-35, #16
Supply of a competitive profit maximizing firm, if
non-convex costs (cont.)
Price
y ( p)
AC
AVC
p
Min.
AVC
p
MC
Output
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4
Further analysis of the profit function
 ( p )  py ( p )  c ( y ( p ))
 ( p )  y ( p ) 
Hotelling’s lemma
y ( p)
p
 p  c ( y ( p ))  y ( p )
p  p
 y ( p ) if
p
 ( p)   (0)
p

 ( p )  0  y ( p )
if
p p
y

 ( p)
 ( p )   ( 0 )


p 
0
 ( p ) dp 
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
p 
0
y ( p ) dp
p
p

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G.B. Asheim, ECON4230-35, #16
Firm 2
Price
Firm 1
The industry supply function with a given
number of firms
Market
supply
m
S ( p)   y j ( p)
j 1
Output
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5
Market equilibrium
Price
Market
supply
Equil.
price
n
m
 x ( p)   y ( p)
i 1
i
j 1
j
Market
demand
Output
Equil. output
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G.B. Asheim, ECON4230-35, #16
Entry with non-convex costs
Price
Long-run
market supply
Long-run
equil. price
Market demand
Long-run
equil. output
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G.B. Asheim, ECON4230-35, #16
Output
12
6
Welfare economics

Assume that lump-sum transfers are available, and
that the distribution is optimal. This allows us to
adopt the representative consumer approach.

Assume that there are no income effects; i.e., the
Mashallian and Hicksian demand functions coincide.
This means that preferences are represented by a
quasi-linear utility function:
Utility  u ( x )  z
Utility derived from good in question
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
Utility  u ( x )  z
x
Marg. willingness to pay
u (x)
u (x)
dz
 u(x)
dx
x
x
v
MRS is
independent x
of money
spent on
other goods
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G.B. Asheim, ECON4230-35, #16
Quasi-linear utility
u ( x)dx
 dz  0
Money spent
on other goods
Demand fn is
determined by:
p  u ( D( p ))
z
G.B. Asheim, ECON4230-35, #16
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Welfare analysis
p
p
Efficiency gain
c(x)
c(x)
S ( p)
S ( p)
D( p )
D( p )
u(x)
x
u(x)
x
x
x
x
x
x
x
u ( x)  u ( x)   u( x)dx
c( x)  c( x)   c( x)dx
Willingness to pay for
increased quantity
Cost to produce
increased quantity
x
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x
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G.B. Asheim, ECON4230-35, #16
Welfare analysis (cont.)
p
In equilibrium:
u ( D( p ))  p  c( S ( p ))
c( x)
D( p)  S ( p)
S ( p)
1st welfare thm
2nd welfare thm
p̂
D( p )
u( x)
Welfare maximization:
max u ( x)  z s.t. z    c( x)
x
FOC : u ( x)  c( x)
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G.B. Asheim, ECON4230-35, #16
x
x̂
16
8
Welfare analysis (cont.)
Total surplus maximization … p
CS ( xˆ )  u ( xˆ )  pˆ xˆ
c( x)
arg maxCS ( x)  PS ( x)
x
S ( p)
 arg maxu ( x)  px 
x
p̂
D( p )
  px  c( x) 
u( x)
 arg maxu ( x)  c( x)
x
x
x̂
… entails maximization of u(x)c(x), PS ( xˆ )  pˆ xˆ  c( xˆ )
which is achieved in equilibrium.
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G.B. Asheim, ECON4230-35, #16
Taxes and subsidies
Market equilibrium with a tax. p
Tax revenue
D( pˆ d )  S ( pˆ s )
pˆ d  pˆ s t
Alternatively:
D( pˆ s t )  S ( pˆ s )
p̂d
c( x)
S ( p)
t
D( p )
p̂s
u( x)
Or: D( pˆ d )  S ( pˆ d t )
x
x̂
Tax revenue is smaller than
the reduction in total surplus.
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G.B. Asheim, ECON4230-35, #16
Deadweight
loss
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9
Rôle for intervention

Prevent that firms get market
power ― competition policy
A competitive market is characterized by

Sellers and buyers take the market price as given and
determine their supply and demand accordingly.

The market price is determined so that
market supply = market demand.

A good is transferred if and only if the price is paid.

Sellers and buyers have the same information about
the transferred good.

Ensure that markets clear ― labor market policy

Protect private property, create low transaction costs

Ensure that firms pay for external effects (pollution)

Ensure efficient provision of public goods

Address informational problems

Contribute to a just income distrubution
02.09.2009
Fields of microeconomics

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G.B. Asheim, ECON4230-35, #16
Industrialthat
Prevent
organization
firms get market
power ―
(Game
theory)
competition policy
A competitive market is characterized by

Sellers and buyers take the market price as given and
determine their supply and demand accordingly.

The market price is determined so that
market supply = market demand.

A good is transferred if and only if the price is paid.

Sellers and buyers have the same information about
the transferred good.

Ensuremarket
Labor
that markets
economics
clear ― labor market policy

Protect private
Economics
of crime,
property,
transaction
create low
costs
transaction
economics
costs

Ensure that firms
Environmental
economics
pay for external effects (pollution)

Ensureeconomics
Public
efficient provision of public goods

Address informational
Information
economicsproblems
(Game theory)

Contribute
Welfare
economics,
to a just income
public finance
distrubution
02.09.2009
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10