# Document

```Chapter 12
The Partial Equilibrium
Competitive Model
Market Demand
• Assume that there are only two goods
(x and y)
– An individual’s demand for x is
Quantity of x demanded = x(px,py,I)
– If we use i to reflect each individual in the
market, then the market demand curve is
n
Market demand for X   xi ( px , py , Ii )
i 1
Market Demand
• To construct the market demand curve,
pX is allowed to vary while py and the
income of each individual are held
constant
• If each individual’s demand for x is
downward sloping, the market demand
curve will also be downward sloping
Market Demand
To derive the market demand curve, we sum the
quantities demanded at every price
px
px
Individual 1’s
demand curve
Individual 2’s
demand curve
px
Market demand
curve
px*
x1
x1*
X
x2
x
x2*
x
X*
x1* + x2* = X*
x
Shifts in the Market Demand Curve
• The market demand summarizes the
ceteris paribus relationship between X
and px
– changes in px result in movements along the
curve (change in quantity demanded)
– changes in other determinants of the
demand for X cause the demand curve to
shift to a new position (change in demand)
Shifts in Market Demand
• Suppose that individual 1’s demand for
oranges is given by
x1 = 10 – 2px + 0.1I1 + 0.5py
and individual 2’s demand is
x2 = 17 – px + 0.05I2 + 0.5py
• The market demand curve is
X = x1 + x2 = 27 – 3px + 0.1I1 + 0.05I2 + py
Shifts in Market Demand
• To graph the demand curve, we must
assume values for py, I1, and I2
• If py = 4, I1 = 40, and I2 = 20, the market
demand curve becomes
X = 27 – 3px + 4 + 1 + 4 = 36 – 3px
Shifts in Market Demand
• If py rises to 6, the market demand curve
shifts outward to
X = 27 – 3px + 4 + 1 + 6 = 38 – 3px
– note that X and Y are substitutes
• If I1 fell to 30 while I2 rose to 30, the
market demand would shift inward to
X = 27 – 3px + 3 + 1.5 + 4 = 35.5 – 3px
– note that X is a normal good for both buyers
Generalizations
• Suppose that there are n goods (xi, i = 1,n)
with prices pi, i = 1,n.
• Assume that there are m individuals in the
economy
• The j th’s demand for the i th good will
depend on all prices and on Ij
xij = xij(p1,…,pn, Ij)
Generalizations
• The market demand function for xi is the
sum of each individual’s demand for that
good
m
X i   xij ( p1,..., pn , I j )
j 1
• The market demand function depends on
the prices of all goods and the incomes
Elasticity of Market Demand
• The price elasticity of market demand is
measured by
eQ,P
QD (P, P ' , I ) P


P
QD
• Market demand is characterized by
whether demand is elastic (eQ,P < -1) or
inelastic (0> eQ,P > -1)
Elasticity of Market Demand
• The cross-price elasticity of market
demand is measured by
eQ,P
QD (P, P ' , I ) P '


P '
QD
• The income elasticity of market demand is
measured by
eQ,I
QD (P, P ' , I ) I


I
QD
Timing of the Supply Response
• In the analysis of competitive pricing, the
time period under consideration is
important
– very short run
• no supply response (quantity supplied is fixed)
– short run
• existing firms can alter their quantity supplied, but
no new firms can enter the industry
– long run
• new firms may enter an industry
Pricing in the Very Short Run
• In the very short run (or the market
period), there is no supply response to
changing market conditions
– price acts only as a device to ration demand
• price will adjust to clear the market
– the supply curve is a vertical line
Pricing in the Very Short Run
Price
S
When quantity is fixed in the
very short run, price will rise
from P1 to P2 when the demand
rises from D to D’
P2
P1
D’
D
Q*
Quantity per period
Short-Run Price Determination
• The number of firms in an industry is
fixed
• These firms are able to adjust the
quantity they are producing
– they can do this by altering the levels of the
variable inputs they employ
Perfect Competition
• A perfectly competitive industry is one
that obeys the following assumptions:
– there are a large number of firms, each
producing the same homogeneous product
– each firm attempts to maximize profits
– each firm is a price taker
• its actions have no effect on the market price
– information is perfect
– transactions are costless
Short-Run Market Supply
• The quantity of output supplied to the
entire market in the short run is the sum
of the quantities supplied by each firm
– the amount supplied by each firm depends
on price
• The short-run market supply curve will
be upward-sloping because each firm’s
short-run supply curve has a positive
slope
Short-Run Market Supply Curve
To derive the market supply curve, we sum the
quantities supplied at every price
P
Firm A’s
supply curve
sA
P
P
sB
Firm B’s
supply curve
Market supply
curve
S
P1
q1A
quantity
q1B
quantity
Q1
Quantity
q1A + q1B = Q1
Short-Run Market Supply Function
• The short-run market supply function
shows total quantity supplied by each
firm to a market
n
Qs (P,v ,w )   qi (P,v ,w )
i 1
• Firms are assumed to face the same
market price and the same prices for
inputs
Short-Run Supply Elasticity
• The short-run supply elasticity describes
the responsiveness of quantity supplied
to changes in market price
eS,P
% change in Q supplied QS P



% change in P
P QS
• Because price and quantity supplied are
positively related, eS,P > 0
A Short-Run Supply Function
• Suppose that there are 100 identical
firms each with the following short-run
supply curve
qi (P,v,w) = 10P/3
(i = 1,2,…,100)
• This means that the market supply
function is given by
100
100
10P 1000P
Qs   qi  

3
i 1
i 1 3
A Short-Run Supply Function
• In this case, computation of the
elasticity of supply shows that it is unit
elastic
eS,P
QS (P,v ,w ) P 1000
P




1
P
QS
3 1000P / 3
Equilibrium Price Determination
• An equilibrium price is one at which
quantity demanded is equal to quantity
supplied
– neither suppliers nor demanders have an
incentive to alter their economic decisions
• An equilibrium price (P*) solves the
equation:
QD( P *,P ' , I )  QS( P *,v ,w )
Equilibrium Price Determination
• The equilibrium price depends on many
exogenous factors
– changes in any of these factors will likely
result in a new equilibrium price
Equilibrium Price Determination
The interaction between
market demand and market
supply determines the
equilibrium price
Price
S
P1
D
Q1
Total output per period
Market Reaction to a Shift in Demand
an increase in their demands,
the market demand curve
will shift to the right
Price
S
P2
P1
D’
Equilibrium price and
equilibrium quantity will
both rise
D
Q1
Q2
Total output per period
Market Reaction to a Shift in Demand
If the market price rises,
firms will increase their
level of output
Price
SMC
SAC
This is the short-run
supply response to an
increase in market price
P2
P1
q1
q2
Output per period
Shifts in Supply and Demand Curves
• Demand curves shift because
– incomes change
– prices of substitutes or complements change
– preferences change
• Supply curves shift because
– input prices change
– technology changes
– number of producers change
Shifts in Supply and Demand Curves
• When either a supply curve or a
demand curve shift, equilibrium price
and quantity will change
• The relative magnitudes of these
changes depends on the shapes of the
supply and demand curves
Shifts in Supply
Small increase in price,
large drop in quantity
Price
Large increase in price,
small drop in quantity
Price
S’
S’
S
S
P’
P
P’
P
D
D
Q’
Q
Elastic Demand
Q per
period
Q’ Q
Inelastic Demand
Q per
period
Shifts in Demand
Small increase in price,
large rise in quantity
Large increase in price,
small rise in quantity
Price
S
Price
S
P’
P’
P
P
D’
D’
D
Q
Q’
Elastic Supply
D
Q per
period
Q
Q’
Inelastic Supply
Q per
period
Mathematical Model of Supply and Demand
• Suppose that the demand function is
represented by
QD = D(P,)
–  is a parameter that shifts the demand curve
• D/ = D can have any sign
– D/P = DP < 0
Mathematical Model of Supply and Demand
• The supply relationship can be shown as
QS = S(P,)
–  is a parameter that shifts the supply curve
• S/ = S can have any sign
– S/P = SP > 0
• Equilibrium requires that QD = QS
Mathematical Model of Supply and Demand
• To analyze the comparative statics of this
model, we need to use the total
differentials of the supply and demand
functions:
dQD = DPdP + Dd
dQS = SPdP + Sd
• Maintenance of equilibrium requires that
dQD = dQS
Mathematical Model of Supply and Demand
• Suppose that the demand parameter ()
changed while  remains constant
• The equilibrium condition requires that
DPdP + Dd = SPdP
D
P

 SP  DP
• Because SP - DP > 0, P/ will have the
same sign as D
Mathematical Model of Supply and Demand
• We can convert our analysis to elasticities
eP ,
e P ,
D
P 


 

 P SP  DP P
eQ ,
D   Q 


( S P  DP )  P Q eS ,P  eQ ,P
Equilibria with Constant Elasticity Functions
• Suppose the demand for automobiles is
given by
QD( P , I )  0.1P
1.2 3
I
• The supply for automobiles is
QS( P ,w )  6,400Pw
0.5
Equilibria with Constant Elasticity Functions
• If I = \$20,000 and w = \$25
11
QD( P , I ) ( 8  10 )P
1.2
QS( P ,w )  1,280P
• Equilibrium occurs where P* = 9,957 and
Q* = 12,745,000
Equilibria with Constant Elasticity Functions
• If I increases by 10 percent
12
QD( P , I ) ( 1.06  10 )P
1.2
QS( P ,w )  1,280P
• Equilibrium occurs where P* = 11,339 and
Q* = 14,514,000
Equilibria with Constant Elasticity Functions
• If instead w increases to \$30 per hour
11
QD( P , I ) ( 8  10 )P
1.2
QS( P ,w )  1,2168P
• Equilibrium occurs where P* = 10,381
and Q* = 12,125,000
Long-Run Analysis
• In the long run, a firm may adapt all of its
inputs to fit market conditions
– profit-maximization for a price-taking firm
implies that price is equal to long-run MC
• Firms can also enter and exit an industry
– perfect competition assumes that there are
no special costs of entering or exiting an
industry
Long-Run Analysis
• New firms will be lured into any market
where economic profits are greater than
zero
– the short-run industry supply curve will shift
outward
– market price and profits will fall
– the process will continue until economic
profits are zero
Long-Run Analysis
• Existing firms will leave any industry
where economic profits are negative
– the short-run industry supply curve will shift
inward
– market price will rise and losses will fall
– the process will continue until economic
profits are zero
Long-Run Competitive Equilibrium
• A perfectly competitive industry is in
long-run equilibrium if there are no
incentives for profit-maximizing firms to
enter or to leave the industry
– this will occur when the number of firms is
such that P = MC = AC and each firm
operates at minimum AC
Long-Run Competitive Equilibrium
• We will assume that all firms in an
industry have identical cost curves
– no firm controls any special resources or
technology
• The equilibrium long-run position
requires that each firm earn zero
economic profit
Long-Run Equilibrium: Constant-Cost Case
• Assume that the entry of new firms in an
industry has no effect on the cost of
inputs
– no matter how many firms enter or leave
an industry, a firm’s cost curves will remain
unchanged
• This is referred to as a constant-cost
industry
Long-Run Equilibrium: Constant-Cost Case
This is a long-run equilibrium for this industry
P = MC = AC
Price
SMC
Price
MC
S
AC
P1
D
q1
A Typical Firm
Quantity
per period
Q1
Total Market
Quantity
per period
Long-Run Equilibrium: Constant-Cost Case
Suppose that market demand rises to D’
Price
SMC
Price
MC
Market price rises to P2
S
AC
P2
P1
D’
D
q1
A Typical Firm
Quantity
per period
Q1
Q2
Total Market
Quantity
per period
Long-Run Equilibrium: Constant-Cost Case
In the short run, each firm increases output to q2
Price
SMC
Price
MC
Economic profit > 0
S
AC
P2
P1
D’
D
q1
q2
A Typical Firm
Quantity
per period
Q1 Q2
Total Market
Quantity
per period
Long-Run Equilibrium: Constant-Cost Case
In the long run, new firms will enter the industry
Price
SMC
MC
Price
S
S’
AC
P1
D’
D
q1
A Typical Firm
Quantity
per period
Q1
Q3
Total Market
Quantity
per period
Long-Run Equilibrium: Constant-Cost Case
The long-run supply curve will be a horizontal line
(infinitely elastic) at p1
Price
SMC
Price
MC
S
S’
AC
LS
P1
D’
D
q1
A Typical Firm
Quantity
per period
Q1
Q3
Total Market
Quantity
per period
Infinitely Elastic Long-Run Supply
• Suppose that the total cost curve for a
typical firm in the bicycle industry is
C(q) = q3 – 20q2 + 100q + 8,000
• Demand for bicycles is given by
QD = 2,500 – 3P
Infinitely Elastic Long-Run Supply
• To find long-run equilibrium, we must find
the minimum point on the typical firm’s
average cost curve
– where AC = MC
AC = q2 – 20q + 100 + 8,000/q
MC = 3q2 – 40q + 100
– this occurs where q = 20
• If q = 20, AC = MC = \$500
– this will be the long-run equilibrium price
Shape of the Long-Run Supply Curve
• The zero-profit condition is the factor that
determines the shape of the long-run cost
curve
– if average costs are constant as firms enter,
long-run supply will be horizontal
– if average costs rise as firms enter, long-run
supply will have an upward slope
– if average costs fall as firms enter, long-run
supply will be negatively sloped
Long-Run Equilibrium: Increasing-Cost Industry
• The entry of new firms may cause the
average costs of all firms to rise
– prices of scarce inputs may rise
– new firms may impose “external” costs on
existing firms
– new firms may increase the demand for
tax-financed services
Long-Run Equilibrium: Increasing-Cost Industry
Suppose that we are in long-run equilibrium in this industry
Price
SMC
P = MC = AC
MC
Price
S
AC
P1
D
q1
A Typical Firm (before entry)
Quantity
per period
Q1
Total Market
Quantity
per period
Long-Run Equilibrium: Increasing-Cost Industry
Suppose that market demand rises to D’
Market price rises to P2 and firms increase output to q2
Price
SMC
MC
Price
S
AC
P2
P1
D’
D
q1
q2
Quantity
A Typical Firm (before entry) per period
Q1 Q2
Total Market
Quantity
per period
Long-Run Equilibrium: Increasing-Cost Industry
Positive profits attract new firms and supply shifts out
Entry of firms causes costs for each firm to rise
SMC’
Price
MC’
Price
S
AC’
S’
P3
P1
D’
D
q3
A Typical Firm (after entry)
Quantity
per period
Q1
Q3
Total Market
Quantity
per period
Long-Run Equilibrium: Increasing-Cost Industry
The long-run supply curve will be upward-sloping
SMC’
Price
MC’
Price
S
AC’
S’
LS
p3
p1
D’
D
q3
Quantity
A Typical Firm (after entry) per period
Q1
Q3
Total Market
Quantity
per period
Long-Run Equilibrium: Decreasing-Cost Industry
• The entry of new firms may cause the
average costs of all firms to fall
– new firms may attract a larger pool of
trained labor
– entry of new firms may provide a “critical
mass” of industrialization
• permits the development of more efficient
transportation and communications networks
Long-Run Equilibrium: Decreasing-Cost Case
Suppose that we are in long-run equilibrium in this industry
Price
SMC
P = MC = AC
Price
MC
S
AC
P1
D
q1
Quantity
A Typical Firm (before entry) per period
Q1
Total Market
Quantity
per period
Long-Run Equilibrium: Decreasing-Cost Industry
Suppose that market demand rises to D’
Market price rises to P2 and firms increase output to q2
Price
SMC
MC
Price
S
AC
P2
P1
D
q1
q2
Quantity
A Typical Firm (before entry) per period
Q1 Q2
Total Market
D’
Quantity
per period
Long-Run Equilibrium: Decreasing-Cost Industry
Positive profits attract new firms and supply shifts out
Entry of firms causes costs for each firm to fall
Price
SMC’
Price
MC’
S
S’
AC’
P1
P3
D’
D
q1 q3
A Typical Firm (before entry)
Quantity
per period
Q1
Total Market
Q3
Quantity
per period
Long-Run Equilibrium: Decreasing-Cost Industry
The long-run industry supply curve will be downward-sloping
Price
Price
SMC’
S
MC’
S’
AC’
P1
P3
D
q1 q3
Quantity
A Typical Firm (before entry) per period
Q1
Total Market
D’
Q3
LS
Quantity
per period
Classification of Long-Run Supply Curves
• Constant Cost
– entry does not affect input costs
– the long-run supply curve is horizontal at
the long-run equilibrium price
• Increasing Cost
– entry increases inputs costs
– the long-run supply curve is positively
sloped
Classification of Long-Run Supply Curves
• Decreasing Cost
– entry reduces input costs
– the long-run supply curve is negatively
sloped
Long-Run Elasticity of Supply
• The long-run elasticity of supply (eLS,P)
records the proportionate change in longrun industry output to a proportionate
change in price
eLS ,P
% change in Q QLS P



% change in P
P QLS
• eLS,P can be positive or negative
– the sign depends on whether the industry
exhibits increasing or decreasing costs
Comparative Statics Analysis
• Comparative statics analysis of long-run
equilibria can be conducted using
estimates of long-run elasticities of
supply and demand
• In the long run, the number of firms in
the industry will vary from one long-run
equilibrium to another
Comparative Statics Analysis
• Assume that we are examining a
constant-cost industry
• Suppose that the initial long-run
equilibrium industry output is Q0 and the
typical firm’s output is q* (where AC is
minimized)
• The equilibrium number of firms in the
industry (n0) is Q0/q*
Comparative Statics Analysis
• A shift in demand that changes the
equilibrium industry output to Q1 will
change the equilibrium number of firms to
n1 = Q1/q*
• The change in the number of firms is
Q1  Q0
n1  n0 
q*
– determined by demand shift and the optimal
output level for the typical firm
Comparative Statics Analysis
• The effect of a change in input prices is
more complicated
– we need to know how much minimum
average cost is affected
– we need to know how an increase in longrun equilibrium price will affect quantity
demanded
Comparative Statics Analysis
• The optimal level of output for each firm
may also be affected
• Therefore, the change in the number of
firms becomes
Q1
Q0
n1  n0  *  *
q1 q0
Rising Input Costs and Industry Structure
• Suppose that the total cost curve for a
typical firm in the bicycle industry is
C(q) = q3 – 20q2 + 100q + 8,000
and then rises to
C(q) = q3 – 20q2 + 100q + 11,616
• The optimal scale of each firm rises
from 20 to 22 (where MC = AC)
Rising Input Costs and Industry Structure
• At q = 22, MC = AC = \$672 so the longrun equilibrium price will be \$672
• If demand can be represented by
QD = 2,500 – 3P
then QD = 484
• This means that the industry will have
22 firms (484  22)
Producer Surplus in the Long Run
• Short-run producer surplus represents
of what would be earned if output was
zero
– the sum of short-run profits and fixed costs
Producer Surplus in the Long Run
• In the long-run, all profits are zero and
there are no fixed costs
– owners are indifferent about whether they
are in a particular market
• they could earn identical returns on their
investments elsewhere
• Suppliers of inputs may not be indifferent
about the level of production in an
industry
Producer Surplus in the Long Run
• In the constant-cost case, input prices
are assumed to be independent of the
level of production
– inputs can earn the same amount in
alternative occupations
• In the increasing-cost case, entry will bid
up some input prices
– suppliers of these inputs will be made better
off
Producer Surplus in the Long Run
• Long-run producer surplus is the extra
return that producers make by making
transactions at the market price over and
above what they would earn if nothing
were produced
– the area above the long-run supply curve
and below the market price
Ricardian Rent
• Assume that there are many parcels of
land on which a particular crop may be
grown
– the land ranges from very fertile land (low
costs of production) to very poor, dry land
(high costs of production)
Ricardian Rent
• At low prices only the best land is used
• Higher prices lead to an increase in
output through the use of higher-cost
land
– the long-run supply curve is upward-sloping
because of the increased costs of using less
fertile land
Ricardian Rent
The owners of low-cost firms will earn positive profits
Price
MC
Price
AC
S
P*
D
q*
Low-Cost Firm
Quantity
per period
Q*
Total Market
Quantity
per period
Ricardian Rent
The owners of the marginal firm will earn zero profit
Price
Price
MC
AC
S
P*
D
q*
Marginal Firm
Quantity
per period
Q*
Total Market
Quantity
per period
Ricardian Rent
• Firms with higher costs (than the
marginal firm) will stay out of the market
– would incur losses at a price of P*
• Profits earned by intramarginal firms
can persist in the long run
• The sum of these long-run profits
constitutes long-run producer surplus
Ricardian Rent
Each point on the supply curve represents minimum
average cost for some firm
Price
For each firm, P – AC represents
profit per unit of output
Total long-run profits can be
computed by summing over all
units of output
S
P*
D
Q*
Total Market
Quantity
Ricardian Rent
• The long-run profits for the low-cost firms
may be reflected in the prices of the
unique resources owned by those firms
– the more fertile the land is, the higher its
price
• Thus, profits are said to be capitalized
into inputs’ prices
– reflect the present value of all future profits
Ricardian Rent
• It is the scarcity of low-cost inputs that
creates the possibility of Ricardian rent
• In industries with upward-sloping longrun supply curves, increases in output
not only raise firms’ costs but also
generate factor rents for inputs
Economic Efficiency and Welfare Analysis
• The area between the demand and the
supply curve represents the sum of
consumer and producer surplus
– measures the total additional value
obtained by market participants by being
able to make market transactions
• This area is maximized at the
competitive market equilibrium
Economic Efficiency and Welfare Analysis
Price
S
Consumer surplus is the
area above price and below
demand
P*
Producer surplus is the
area below price and
above supply
D
Quantity per period
Q*
Economic Efficiency and Welfare Analysis
Price
S
At output Q1, total surplus
will be smaller
At outputs between Q1 and
Q*, demanders would value
it would cost suppliers to
produce
P*
D
Quantity per period
Q1
Q*
Economic Efficiency and Welfare Analysis
• Mathematically, we wish to maximize
consumer surplus + producer surplus =
Q
Q
0
0
[U (Q )  PQ]  [PQ   P (Q )dQ]  U (Q )   P (Q )dQ
• In long-run equilibria along the long-run
supply curve, P(Q) = AC = MC
Economic Efficiency and Welfare Analysis
• Maximizing total surplus with respect to
Q yields
U’(Q) = P(Q) = AC = MC
– maximization occurs where the marginal
value of Q to the representative consumer
is equal to market price
• the market equilibrium
Welfare Loss Computations
• Use of consumer and producer surplus
makes it possible to calculate welfare
losses caused by restrictions on
voluntary transactions
– in the case of linear demand and supply
curves, the calculation is simple because
the areas of loss are often triangular
Welfare Loss Computations
• Suppose that the demand is given by
QD = 10 - P
and supply is given by
QS = P - 2
• Market equilibrium occurs where P* = 6
and Q* = 4
Welfare Loss Computations
• Restriction of output to Q0 = 3 would
create a gap between what demanders
are willing to pay (PD) and what
suppliers require (PS)
PD = 10 - 3 = 7
PS = 2 + 3 = 5
Welfare Loss Computations
The welfare loss from restricting output
to 3 is the area of a triangle
Price
S
7
The loss = (0.5)(2)(1) = 1
6
5
D
3
4
Quantity per period
Welfare Loss Computations
• The welfare loss will be shared by
producers and consumers
– it will depend on the price elasticity of
demand and the price elasticity of supply to
determine who bears the larger portion of
the loss
• the side of the market with the smallest price
elasticity (in absolute value)
Price Controls and Shortages
• Sometimes governments may seek to
control prices at below equilibrium
levels
– this will lead to a shortage
• The changes in producer and consumer
surplus from this policy show its impact
on welfare
Price Controls and Shortages
Price
Initially, the market is
in long-run equilibrium
at P1, Q1
SS
LS
P1
Demand increases to D’
D’
D
Q1
Quantity per period
Price Controls and Shortages
Price
SS
In the short run, price
rises to P2
P2
LS
P3
Firms would begin to
enter the industry
P1
D’
The price would end
up at P3
D
Q1
Quantity per period
Price Controls and Shortages
Price
Suppose that the
government imposes
a price ceiling at P1
SS
LS
P3
P1
D’
There will be a
shortage equal to
Q2 - Q1
D
Q1
Q2
Quantity
Price Controls and Shortages
Price
because they can
purchase the good for
a lower price
SS
LS
P3
P1
D’
This gain in consumer
rectangle
D
Q1
Q2
Quantity per period
Price Controls and Shortages
Price
The gain to consumers
is also a loss to
producers who now
SS
LS
P3
P1
D’
D
Q1
Q2
therefore represents a
pure transfer from
producers to consumers
No welfare loss there
Quantity per period
Price Controls and Shortages
Price
SS
LS
P3
P1
D’
represents the value
consumer surplus
that would have
been attained
without the price
control
D
Q1
Q2
Quantity per period
Price Controls and Shortages
Price
SS
LS
P3
P1
D’
represents the value
producer surplus
that would have
been attained
without the price
control
D
Q1
Q2
Quantity
Price Controls and Shortages
Price
SS
LS
P3
represents the total
value of mutually
beneficial transactions
that are prevented by
the government
P1
D’
D
Q1
Q2
This is a measure of
the pure welfare
costs of this policy
Quantity
Disequilibrium Behavior
• Assuming that observed market
outcomes are generated by
Q(P1) = min [QD(P1),QS(P1)],
suppliers will be content with the
outcome but demanders will not
• This could lead to a black market
Tax Incidence
• To discuss the effects of a per-unit tax
(t), we need to make a distinction
between the price paid by buyers (PD)
and the price received by sellers (PS)
PD - PS = t
• In terms of small price changes, we
wish to examine
dPD - dPS = dt
Tax Incidence
• Maintenance of equilibrium in the
market requires
dQD = dQS
or
DPdPD = SPdPS
• Substituting, we get
DPdPD = SPdPS = SP(dPD - dt)
Tax Incidence
• We can now solve for the effect of the
tax on PD:
eS
dPD
SP


dt
SP  DP eS  eD
• Similarly,
dPS
DP
eD


dt
SP  DP eS  eD
Tax Incidence
• Because eD  0 and eS  0, dPD /dt  0
and dPS /dt  0
• If demand is perfectly inelastic (eD = 0),
the per-unit tax is completely paid by
demanders
• If demand is perfectly elastic (eD = ), the
per-unit tax is completely paid by
suppliers
Tax Incidence
• In general, the actor with the less elastic
responses will experience most of the
price change caused by the tax
dPS / dt
eD


dPD / dt
eS
Tax Incidence
Price
S
A per-unit tax creates a
wedge between the price
the price that sellers
PD
P*
t
PS
D
Q**
Q*
Quantity per period
Tax Incidence
Price
S
PD
P*
But some of this loss goes
to the government in the
form of tax revenue
PS
D
Q**
Q*
Quantity per period
Tax Incidence
Price
S
Sellers also incur a welfare
loss equal to the shaded area
PD
But some of this loss goes
to the government in the
form of tax revenue
P*
PS
D
Q**
Q*
Quantity per period
Tax Incidence
Price
S
PD
Therefore, this is the deadweight loss from the tax
P*
PS
D
Q**
Q*
Quantity per period
• All nonlump-sum taxes involve
– the size of the losses will depend on the
elasticities of supply and demand
• A linear approximation to the deadweight
loss accompanying a small tax, dt, is
given by
DW = -0.5(dt)(dQ)
• From the definition of elasticity, we know
that
dQ = eDdPD  Q0/P0
• This implies that
dQ = eD [eS /(eS - eD)] dt Q0/P0
• Substituting, we get
2
 dt 
DW  0.5  [eD eS /( eS  eD )]P0Q0
 P0 
• Deadweight losses are zero if either eD
or eS are zero
– the tax does not alter the quantity of the
• Deadweight losses are smaller in
situations where eD or eS are small
Transactions Costs
• Transactions costs can also create a
wedge between the price the buyer pays
and the price the seller receives
– real estate agent fees
– broker fees for the sale of stocks
• If the transactions costs are on a per-unit
basis, these costs will be shared by the
– depends on the specific elasticities involved
Price
S
P*
In the absence of
the domestic
equilibrium price
would be P* and
the domestic
equilibrium quantity
would be Q*
D
Q*
Quantity per period
Price
S
If the world price (PW)
is less than the domestic
price, the price will fall
to PW
Quantity demanded will
rise to Q1 and quantity
supplied will fall to Q2
P*
PW
D
Q2
Q*
Q1
imports
Imports = Q1 - Q2
Quantity per period
Price
S
Consumer surplus rises
Producer surplus falls
There is an unambiguous
welfare gain
P*
PW
D
Q1
Q*
Q2
Quantity per period
Effects of a Tariff
Price
S
Suppose that the government
creates a tariff that raises
the price to PR
Quantity demanded falls
to Q3 and quantity supplied
rises to Q4
PR
PW
Imports are now Q3 - Q4
D
Q2 Q4 Q3 Q1
imports
Quantity per period
Effects of a Tariff
Price
S
Consumer surplus falls
Producer surplus rises
The government gets
tariff revenue
PR
PW
These two triangles
D
Q2 Q4 Q3 Q1
Quantity per period
• Estimates of the sizes of the welfare
loss triangle can be calculated
• Because PR = (1+t)PW, the proportional
change in quantity demanded is
Q3  Q1 PR  PW

 eD  teD
Q1
PW
Price
S
The areas of these two
triangles are
DW1  0.5(PR  PW )(Q1  Q3 )
DW1  0.5t 2eDPW Q1
PR
PW
DW2  0.5(PR  PW )(Q4  Q2 )
D
Q2 Q4 Q3 Q1
DW2  0.5t 2eS PW Q2
Quantity per period
• A quota that limits imports to Q3 - Q4
would have effects that are similar to
those for the tariff
– same decline in consumer surplus
– same increase in producer surplus
• One big difference is that the quota
does not give the government any tariff
revenue
– the deadweight loss will be larger
• If the market demand curve is
QD = 200P-1.2
and the market supply curve is
QS = 1.3P,
the domestic long-run equilibrium will
occur where P* = 9.87 and Q* = 12.8
• If the world price was PW = 9, QD would
be 14.3 and QS would be 11.7
– imports will be 2.6
• If the government placed a tariff of 0.5
on each unit sold, the world price will be
PW = 9.5
– imports will fall to 1.0
• The welfare effect of the tariff can be
calculated
DW1 = 0.5(0.5)(14.3 - 13.4) = 0.225
DW2 = 0.5(0.5)(12.4 - 11.7) = 0.175
• Thus, total deadweight loss from the
tariff is 0.225 + 0.175 = 0.4
Important Points to Note:
• Short-run equilibrium prices are
determined by the intersection of what
demanders are willing to pay (demand)
and what firms are willing to produce
(supply)
– both demanders and suppliers act as price
takers
Important Points to Note:
• In the long run, the number of firms may
vary in response to profit opportunities
– the assumption of free entry and exit implies
that firms in a competitive industry will earn
zero economic profits in the long run (P = AC)
Important Points to Note:
• The shape of the long-run supply curve
depends on how entry affects input prices
– in the constant-cost case, input prices do not
change and the long-run supply curve is
horizontal
– if entry raises input costs, the long-run supply
curve will have a positive slope
Important Points to Note:
• If shifts in long-run equilibrium affect input
prices, the welfare of the suppliers of
these inputs will be affected
– such changes can be measured by changes
in the value of long-run producer surplus
Important Points to Note:
• The concepts of consumer and producer
surplus provide useful ways of measuring
the welfare impact of economic changes
– changes in consumer surplus represent
changes in utility
– changes in producer surplus represent
changes in the monetary returns that inputs
Important Points to Note:
• The competitive model can be used to
study the impact of various economic
policies
– it can be used to measure the transfers
and welfare losses associated with price
controls
Important Points to Note:
• The competitive model can also be
applied to study taxation
– the model illustrates tax incidence and the
welfare losses associated with taxation
– similar conclusions can be derived by using
the competitive model to study transactions
costs
Important Points to Note:
• A final, important application uses the
competitive model to study international