Download Long Run Market Supply Curve

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   x i ( px , py , Ii )
i 1
• 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*
x
x1* + x2* = 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
Elasticity of Market Demand
• 1) The price elasticity of market demand is
measured by e  QD (P, P ' , I )  P
Q,P
P
QD
• Market demand is characterized as
elastic if (eQ,P < -1) or inelastic (0> eQ,P > -1)
• 2) The cross-price elasticity of market demand is
measured by
QD (P, P ' , I ) P '
eQ,P 
P '

QD
• 3) The income elasticity of market demand is
QD (P, P ' , I ) I
measured by
eQ,I 
I

QD
Timing of the Supply Response
• In the analysis of competitive pricing, the time
period under consideration is important
– 1) Very Short Run
• no supply response (quantity supplied is fixed)
– 2) Short Run
• existing firms can alter their quantity supplied, but
no new firms can enter the industry
– 3) Long Run
• new firms may enter an industry
1) 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
P2
P1
When quantity is fixed in the
very short run, price will rise
from P1 to P2 when the
demand rises from D to D’
D’
D
Q*
Quantity per period
2) 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:
– 1) there are a large number of firms, each
producing the same homogeneous product
– 2) each firm attempts to maximize profits
– 3) each firm is a price taker
• its actions have no effect on the market price
– 4) information is perfect
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
sB
Firm B’s
supply curve
P
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
3
i 1
i 1
A Short-Run Supply Function
• In this case, computation of the elasticity of
supply
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:
Q D( P *,P ' , I )  QS( P *,v ,w )
• 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
Price
S
The interaction between
market demand and market
supply determines the
equilibrium price
P1
D
Q1
Total output per period
Market Reaction to a Shift in Demand
If many buyers experience
an increase in their demands
the market demand curve
will shift to the right
Price
S
P2
P1
D’
D
Q1
Q2
Equilibrium price and
equilibrium quantity will
both rise
Total output per period
Market Reaction to a Shift in Demand
Price
If the market price rises,
firms will increase their
level of output
SMC
SAC
P2
P1
This is the short-run
supply response to an
increase in market price
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
• 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
Large increase in price,
small drop in quantity
Small increase in price,
large drop in quantity
Price
Price
S’
S’
S
S
P’
P
P’
P
D
D
Q per
Elastic Demand period
Q’ Q
Q’Q
Q per
Inelastic Demand period
Shifts in Demand
Small increase in price,
large rise in quantity
Price
Large increase in price,
small rise in quantity
S
Price
S
P’
P’
P
P
D’
D
Q
Q’
Elastic Supply
D
Q per
period
Q
Q’
D’
Q per
period
Inelastic Supply
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
• 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  D P )  P Q eS ,P  eQ ,P
Equilibria with Constant Elasticity Functions
• Suppose the demand for automobiles is given
by
Q D( P , I )  0.1P
1.2
I
3
• 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
Q D( 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
Q D( 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 Market Equilibrium
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:
1) Long run profit maximization with respect to
output and plant size:
P* = MC at an output level q*
2) Zero economic profit
P* = AC at an output level q*
3) Demand equals supply
Qd depending on (P*) = n*q* …or…
n* = {Qd depending on (P*)} / q*
Calculating Long Run Equilibrium
In the market, all firms and potential entrants are
identical. Each has a total cost function given as:
TC(q) = 40q - q2 + .01q3
where q is measured in ‘000 units.
The market demand curve is D(P):
Qd(P) = 25000-1000P
Find the following:
1) Long run equilibrium quantity per firm
2) Long run equilibrium price
3) Number of firms.
Long Run Perfectly Competitive
$/unit
$/unit
n* = 10,000,000/50,000=200
SAC
MC
Market demand
AC
P*
SMC
q*=50,000
q
Q*=10 Million
Q
Long Run Market Supply Curve
• We have calculated a point at which the market
will be in long run equilibrium.
• This is a point on the 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.
Long-Run Competitive Equilibrium:
Derivation of LRIS curve
• 1) Constant cost industry
• 2) Increasing cost industry
• 3) Decreasing cost industry
1) 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 typical 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
Price
SMC
P = MC = AC
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
Economic profit will return to 0
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
Price
The long-run supply curve will be a horizontal line
(infinitely elastic) at p1
SMC
Price
MC
S
S’
AC
LRIS
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
• Calculate
1) Long run equilibrium quantity per firm
2) Long run equilibrium price
3) Number of firms.
• If the demand increases to QD = 3,000 – 3P
2) 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 taxfinanced services
Long-Run Equilibrium:
Increasing-Cost Industry
Suppose that we are in long-run equilibrium in this industry
Price
SMC
MC
P = MC = AC
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
q1
q2
A Typical Firm (before entry)
Quantity
per period
Q1 Q2
Total Market
D’
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
q3
A Typical Firm (after entry)
Quantity
per period
Q1
Q3
Total Market
D’
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’
LRIS
p3
p1
D’
D
q3
A Typical Firm (after entry)
Quantity
per period
Q1
Q3
Total Market
Quantity
per period
Increasing Cost Industry
• Increasing cost Industry: An industry which increases in industry
output increase the price of inputs. Especially if firms use industry
specific inputs i.e. scarce inputs that are used only by firms in a
particular industry and no other industry.
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 Industry
Suppose that we are in long-run equilibrium in this industry
Price
SMC
P = MC = AC
Price
MC
S
AC
P1
D
q1
A Typical Firm (before entry)
Quantity
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
A Typical Firm (before entry)
Quantity
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
SMC’
Price
S
MC’
S’
AC’
P1
P3
D
q1 q3
A Typical Firm (before entry)
Quantity
per period
Q1
Total Market
D’
Q3
LRIS
Quantity
per period
Decreasing Cost Industry
• Decreasing-cost Industry: An industry in which increases in
industry output decrease the prices of some or all inputs.
63
Long-Run Elasticity of Supply
• The long-run elasticity of supply (eLS,P)
records the proportionate change in long-run
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 long-run
equilibrium price will affect quantity demanded
• 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 long-run
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 the return to a
firm’s owners in excess of what would be earned if
output was zero
– the sum of short-run profits and fixed costs
• 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
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
Producer Surplus
P
Market Supply Curve
P*
Producer Surplus
Q
73
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)
• 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
Economic Rent
• Economic Rent: The economics rent that is
attributed to extraordinarily productive inputs
whose supply is scarce.
– Difference between the maximum value is
willing to pay for the services of the input and
input’s reservation value.
• Reservation value: The returns that the owner of
an input could get by deploying the input in its
best alternative use outside the industry.
Economic Rent
• Economic rent is the shaded area
Each point on the supply curve represents
minimum average cost for some firm
For each firm, P – AC
represents profit per unit of
output