Competition and Market Equilibrium

Perfect Competition• Defining Characteristic is lack of market power

– Price Takers• How do we get there?

– Homogeneous output (or homogeneous enough)– Enough buyers and sellers that no one (or group

thereof acting together) can effect demand or supply enough to affect market price

– Perfect information (all participants know the market price)

– Free entry and exit in the long run (to ensure price = MC)

Supply and Demand

• The workhorse model of economics assumes perfectly competitive markets.

• Seems odd since so few markets satisfy all conditions, but predictive power holds for markets that are less competitive.

Why do economists like them so much

• With competitive markets, when all goods are private, there are no externalities and we don’t worry about income distribution…

• Markets– Produce goods at the lowest possible cost (technical

efficiency)– Commit all resources to their highest use (we produce

the mix of goods people want as cheaply as possible)– Goods and services are consumed by those who value

them most (maximize economic surplus, but not utility)

Technical Efficiency:Two Apple Growers of Many

q qq*q*

• Both farmers are producing at q* to start. Total cost of production can be lowered if Farmer Blue produces one fewer apple and Farmer Red produces one more.

• To minimize total cost of producing apples, the SMC of the last apple produced by every farmer must be the same.

• Perfectly competitive industries get this result.

Allocative EfficiencyRatio of market price = ratio of MC

Apples

Oranges

MC pSlope MRT

Wow!• Any and all units of a good or service that can be

produced at an opportunity cost below the value of the good to consumers will be produced (and should be produced).

• What coordinates all this magic? Price.• Price

– signals opportunity cost of resources to producers so they can minimize cost and know how much to produce and when to enter or exit production.

– Signals to consumers the value of the resources in production so that goods and services are consumed only by those whose value exceeds cost.

This IS the Invisible Hand

• Adam Smith:– Efficient Resource Allocation: Markets minimize the cost

of production (only the lowest cost producers produce)– Consumer Surplus Maximization: Markets maximize the

consumer surplus in consumption (highest value consumers consume)

– All and only units where benefit > cost will be produced– And not only in one market for one good, but for all

markets and all goods** except for those pesky market failures

Competition vs Non-competitive Markets

• While prices create technical efficiency and promote efficient rationing in less than competitive situations, allocative efficiency is lacking (monopolists underproduce)

• Only in perfect competition is economic surplus maximized.

• MB=MC for last unit produced, no deadweight loss.

Demand

• Demand is simply the horizontal sum of individual demand curves

• No short vs long run… although…• Demand becomes more elastic over time as

time allows individuals to find substitutes.

Market Demand

• Assume a market with 3 individuals:x1 = 25 – 2px

x2 = 45 – 1.5px

x3 = 50 – 2.5px • The market demand curve is the horizontal sum

X = 120 – 6px (P = 20-.143X)

• Except for the kinks. This equation is for this line

Firm and Market Supply

• Very Short Run: Quantities of all inputs are fixed.

• Short Run: At least one input, but not all, are fixed.

• Long Run: Quantities of all inputs used are variable.

Market Adjustment in the Very Short Run

When quantity is fixed in the very short run and demand increases, price will rise but quantity will not change as firms cannot increase production.

Demand for plywood increases as a hurricane approaches.

P Similarly, there can be a supply shock(e.g. hurricane) that shifts supply back

P Gasoline: Price rises with supply shift.Assume an excise tax on gasoline.Politicians call for suspending the tax, but in the short run price will be unaffected as neither supply or demand would shift as a result.

Short Run/Long Run Model• The more usual analysis.• Short Run

– Firms produce where MR = SMC– Firms may shut down in the short run– Market supply is the horizontal sum of all firms in the

industry (no entry or exit in the short run)• Long Run

– Price driven to the break-even price as firms enter/exit to seek profits and avoid losses

– Profits = 0– Firm on expansion path– Capital at the level that minimizes SAC

Long and Short Run Cost Curves• Assume we start here.

Short Run• Short Run supply is SMC at P > min(AVC)

– Yes, firms will produce at lower prices in SR than LR.

ACMCSMC

Short Run Firm Supply (Algebra)SMC Above AVC

Shutdown priceQuantity where slope of AVC = 0

1 1VC q , AVC q6 6

dAVC 1 q 0 where q = 0dq 3

Or at q where AVC SMC1 1q q6 21 q 0 where q = 03

Supply = Marginal Cost1SC FC q6

SMC .5qFirm supply, SMC P

Short Run Market Supply (Algebra)

Supply = Marginal Cost (above AVC)Firm supply:

q 2pMarket supply with N firms:

Q=N* 2p

Short Run, Firm and Market• Assume we start here for short run.

Q=N* 2Pq 2P

Long Run

• Assume IRS and then DRS (no CRS)$

Firm Long Run Supply

• q where P = MC so long as π ≥0 (P> PBE)$

Firm LRS

Long Run Firm Supply (Algebra)MC above AC

Break-even price1 1 1C q , AC q, MC q8 8 4

Quantity where slope of AC = 0dAC 1 0, at any qdq 8

Or at the quantity where AC MC1 1q q8 41 q 0 where q = 04

Supply = Marginal Cost1C q8

MC .25qFirm supply, MC PP .25qq 4p

Long Run Market Supply

• Long run firm supply: q=4P• So long run market supply: Q=N(4P)?• NO!!!

Long Run Firms Enter and Exit until profit = 0 and market price = PBE

• In long run: P →PBE and π →0$

Long Run Market Supply• Firms enter and exit so that in the long run,

LRS = the quantity demanded at the pBE

Assumes constant

cost industry, more to

come on that!

Shocks

• Change in demand• Change in FC• Change in VC

Change in Demand• Short Run: price up, Δ Q is n*Δq, π > 0

q1 q2 Q1 Q2

Change in Demand• Long run: Firms enter, π > 0

q1 q2 Q3Q2

Change in Demand• Long Run Supply: If the PBE does not change, the

market will always supply the Qd at PBE . $

Comparative Statics Analysis

• In the long run, the number of firms in the industry will vary from one long-run equilibrium to another

• 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 N1 = Q1/q1*

Comparative Statics Analysis• A shift in demand that changes the

equilibrium industry output to Q3 will change the equilibrium number of firms to

N3 = Q3/q1*

• The change in the number of firms is

• In a constant cost industry q*will not change, so only the size of the shift in demand will affect the change in n.

3 13 1

Q QN N

Change in FC• Short Run: MC is unaffected, so qs is unaffected,

so PM is unaffected. But firms suffer losses.$

Change in FC• Long run: Firms exit until the PM = the new PBE . • With higher price of K, firms use less.• Change in firm level of output is unknown.

SMC’ATC’

AVC’

Change in FC• Long run: Firms exit until the PM = the new PBE.

SMC’

SAC’

AVC’

LRS2PBE2

Change in VC• Short Run: MC is affected, so qs is affected, as is

PM . Firms suffer losses, as the higher price does not cover the higher cost.

If AVC > P, firms will shut down.

Change in VC• While firm supply decreases, qs is unknown as

we don’t know the change in price. However, change in MC > change in P.

If AVC > P, firms will shut down.

Change in VC• Again, with higher costs, and PBE, the LRS curve

will shift upwards. The new q* (and optimal K) could be higher or lower.

AVCPBE2

Comparative Statics Analysis

• The effect of a change in input prices – 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

Comparative Statics Analysis• The optimal level of output for each firm may

also be affected• Therefore, the change in the number of firms

becomes

• And the relative changes in Q and q* will determine the change in N.

3 13 1

3 1* *

Q QN Nq q

Comparative Statics, change in q*

t q*, where AC(v,w,q*(v,w,p)) MC(v,w,q*(v,w,p))the change in AC = the change in MC, that is:

AC q* MC MC q*w w w q* w

And at q* where AC=MC,

AC MCq* w w ,

q*AC 0q

, 0, depending MCwq

AC MCon , ,w w

If AC rises more than MC, q* will rise and vice versa.

Supply and Demand• Basis is the competitive model

– Usually, competitive market in the short run.– Sometimes used to depict competitive market in the

long run with increasing cost industry assumption.• Treatment

– Algebra (to get equilibrium)– Calculus (comparative statics)

• Demand shifters• Supply shifters• Sales and Excise taxes

As in Intermediate Micro• Inverse Demand: P = 1,500 - .5Qd• Inverse Supply: P = 600 + Qs• Solution is Q = 600, P = 1,200

Sales Tax, Comparative Statics• Intermediate

– Add Sales Tax = $150• Inverse Demand: P = 1500 - tax - .5Qd• Inverse Supply: P = 600 + Qs• Solution is Q = 500, P = 1100 (consumer cost = P + t = $1250)• Just by comparing outcomes,

0 0dP* dQ *, dt dt

MarketPrice

P*=1,100

PD=1,250

Excise Tax, Comparative Statics• Intermediate

– Add Excise Tax = $150• Inverse Demand: P = 1500 - .5Qd• Inverse Supply: P = 600 + tax + Qs• Solution is Q = 500, P = 1250 (producer keeps = P – t = $1100)• Just by comparing outcomes, dP* dQ *0, 0

MarketPrice

PS=1,100

P*=1,250

Linear Supply and Demand, Equilibrium• General linear functions specified

– Inverse Demand: P = a – bQd (a > 0, b > 0)

– Inverse Supply: P = c + dQs (c > 0, d > 0)

– Equilibrium condition: Qs = Qd (and Ps = Pd)

• Reduced form solution (only in terms of a, b, c, d) ad bcP*b da cQ*b d

cslope = -b

slope = d

Shifts in Supply or Demand, Comparative Statics

• Solution

• Comparative Statics

dP* d dQ * 10, 0da b d da b d

d c a c adP* dQ *0, 0db dbb d b d

dP* b dQ * 10, 0dc b d dc b d

a c c adP* dQ *0, 0dd ddb d b d

ad bc a cP* , Q*b d b d

So long as a>c

slope = -b

slope = d

Note, “b” rising means demand must be getting steeper.

Sales Tax• Market Model (sales tax)

– Inverse Demand: P = a - t – bQd (a > 0, b > 0)

– Inverse Supply: P = c + dQs (c > 0, d > 0)

– Equilibrium condition: Qs = Qd

• Reduced form solution (only in terms of a, b, c, d, t)

* *D t

ad td bcPb d

a t cQb d

QQt* Q*

Sales Tax, Comparative Statics• Solution

• Comparative Statics

dP d 0dt b d

dQ 1 0dt b d

dP d d1 0 as 1 0dt b d b d

* * * *tt D t

ad td bc a t cP , Q , P P tb d b d

QQt* Q*

Supply and Demand with General Form Equations

• All we assume is:

• And that at equilibrium (Q*, P*):

• First assume only a is changing and then only b.

dQD(P;a) Q , 0 and "a" is a parameter that shifts demand

S(P;b) Q , 0 and "b" is a parameter that shifts supplydp

D(P*;a) Q*, or D(P*;a) Q* 0S(P*;b) Q*, or S(P*;b) Q* 0

• Start withFD = D(P*, a) – Q* = 0FS = S(P*) – Q* = 0

• Substitute in:P*=P*(a), and Q*=Q*(a)

• To getFD = D(P*(a), a) – Q* (a)= 0FS = S(P*(a)) – Q*(a) = 0

• Take the total derivative with respect to a:

Comparative Statics of a Demand Shift

(see 8.41 in Chiang)

*dP dQda da

dQda d

(see 8.40 in Chiang), Implicit function theorem tells us equations P* and Q* must exist to solve these equations simultaneously.

• From above

• Matrix Notation

Demand Shifting

D DP a

*dP dQda dadP dQda d

Slope of demand curveso dQd/dP

Slope of supply curvedQs/dP

Change in equilibrium quantity when a changes

Change in demand when a changes(Holding P constant, how does Qd change with a).

Change in equilibrium price when a changes

• Cramer’s Rule

• If a is income and the good is normal, then Da > 0 and equilibrium price will rise with a.

• If a is price of a complimentary good, then Da < 0 and equilibrium price will fall with a.

Demand Shifting and Change in P*

0 DaS D

1dD 1PS 1

• Cramer’s Rule

• If a is income and the good is normal, then Da > 0 and equilibrium quantity will rise with a.

• If a is price of a complimentary good, then Da < 0 and equilibrium price will fall with a.

* * a P

P P* *

D 1PS 1

D S0 D Sa PS

dQda D S D

Demand Shifting and Change in Q*

• Start withFD = D(P*) – Q* = 0FS = S(P*, b) – Q* = 0

• Substitute in:P*=P*(b), and Q*=Q*(b)

• To getFD = D(P*(b)) – Q* (b)= 0FS = S(P*(b), b) – Q*(b) = 0

• Take the total derivative with respect to b:

Supply Shifting

(see 8.41 in Chiang)

(see 8.40 in Chiang), Implicit function theorem tells us equations P* and Q* must exist to solve these equations simultaneously.

dP dQdb dbdP dQdb db

• From above

• Matrix Notation

Supply Shifting

dP dQd

Slope of demand curveso dQd/dP

Slope of supply curveso dQs/dP Change in

equilibrium price when b changes

Change in equilibrium quantity when b changes

Change in supply when b changes (holding P constant, how does Qs change with a).

• Cramer’s Rule

• If b is technology, then Sb > 0 and equilibrium price will fall with b.

• If b is wages, then Sb < 0 and equilibrium price will rise with b.

Supply Shifting and the Change in P*

S D DP

• Cramer’s Rule

• If b is technology, then Sb > 0 and equilibrium quantity will rise with b.

• If b is wages, then Sb < 0 and equilibrium quantity will fall with b.

* * * *

*P* b P* b

P P P P*

S D SD S D Sb P b

dQdb D

S D D SP P

Supply Shifting and the Change in P*

• We can convert our analysis to elasticities

SdP b bdb P S D P

b S,bbP,b

P P Q ,P Q ,PP P

b(S )(S ) b Q Q(S D ) P P PS DQ QQ

Results in Elasticities

DdP a ada P S D P

a D,aaP,a

P P Q ,P Q ,PP P

a(D )(D ) a Q Q(S D ) P P PS DQ QQ

• Assume D,M = .5, S,p = .75, D,p = -1.25

D,MP,M

Q ,P Q ,P

.5.75 1.25

D’.25%

.1875%

1% increase in income .5% inc. in demand.5% increase in

demand .25% inc. in price

.25 increase in price .1875% inc. in quantity:

%ΔQs/%ΔP =.75 %ΔQs/.25 =.75 %ΔQs =.1875

Effect of a 1% increase in income on demand for a normal good

• Assume S,w = -.60, Qs,p = .80, Qd,p = -.70

1% increase in income for a .6% dec. in supply.6% decrease in

supply .40% inc. in price

.40% increase in price .28% dec. in quantity:%ΔQd/%ΔP =-.70 %ΔQd/.40 =-.70

%ΔQs =-.28

S,wP,w

Q ,P Q ,P

.60.80 .70

Effect of a 1% increase in wages

• Start withFD = D(P*+t) – Q* = 0FS = S(P*) – Q* = 0

• Substitute in:P*=P*(t), and Q*=Q*(t)

• To getFD = D(P*(t) + t) – Q*(t)= 0FS = S(P*(t)) – Q*(t) = 0

• Take the total derivative with respect to t:

Supply and Demand (Sales Tax)

dP dQdt dt

dP dQd

D dP dQ D1 0P dt dt P

P* is the market price, but the buyer pays PD = P*+t

• From above

• Matrix Notation

Supply and Demand (Sales Tax)

D 1PS 1P

dP dQdt dt

dP dQdt

Change in P* when t rises

P P* *

S DP P

*S D SD D

S D S D S D

D0 P 0 , S D S DP P

PD Q 0

1D 1PS

dP 1 1 0dtdt

Original Tax

Change in Q* when t rises

S D* **

PD0QP 0

S D PP P

P PD 1PS 1

Original Tax

D 1PS 1P

• Start withFD = D(P*) – Q* = 0FS = S(P*-t) – Q* = 0

• Substitute in:P*=P*(t), and Q*=Q*(t)

• To getFD = D(P*(t)) – Q*(t)= 0FS = S(P*(t) - t) – Q*(t) = 0

• Take the total derivative with respect to t:

Supply and Demand (Excise)

* ** *

S dP dQ S1

dP dQd

0 0P dt dt P

t dtdP dQdt dt

P* is the market price, but the supplier keeps Ps = P*-t

• Matrix Notation

Supply and Demand (Excise Tax)

D 1PS 1P

dP dQdt dt

dP dQd

0Pt dtS

Change in P* when t rises

P P* *

S DP P

*S S S D D

S D S D S D S D

SP P 0 S D S DP P

PS Q 0

dP 1 1 0d

Original Tax

S PD S

DPSPD 1PS 1

P QP P 0S

dP dQdt dt

dP dQd

0Pt dtS

Original Tax

Change in Q* when t rises

And FinallyS D

Note that for Sales tax, P*=P and for excise tax, P*= PFor either tax, the ratio of change in the demander price to the supplier price is as follows:

dPdt dPdt

Absolut

e value of both sides to get:dPdt dPdt

If , suppliers see the bigger change in price

If , demanders see the bigger change in price

S DIf 3 and 1, the price to demanders will rise 3x more than the price for suppliers will fall.That is, for a $4 tax, demanders willsee prices rise $3 and sellers will seetheir price fall $1.

Increasing Cost Industries and Decreasing Cost Industries

• What happens when the market expands or contracts.– For constant cost industries, expansion and

contraction of the market does not affect v and w so the break-even price remains constant.

– For increasing cost industries:• Factor price effect: w, or v rise with Qe• Less efficient firm’s effect

– For decreasing cost industries:• Factor price effect: w, or v fall with Qe

Short Run• Assume we start here.

• Demand Increases

Increasing Cost Industry:Factor Price effect

• Firms increase production in the short run

• If it is w that rises with an increased demand for labor, MC will rise with expansion.

SRS’

• Profits > 0, so firms still enter, but profit returns to zero before the price falls to its previous level.

SRS’’SRS’

• Profits > 0, so firms still enter, but profit returns to zero before the price falls to its previous level.

SRS’ SRS’’

PBE’

SR or LR effects

• Often, costs are assumed stable in SR, but increase only in the long run.

• Same result, easier math.

• Firms increase production in the short run

Increasing Cost Industry:Differential Productivity Effect

• New firms are less efficient, so entry stops before price returns to original level

SRS’

• New firms are less efficient, so entry stops before price returns to original level

SRS’

Why differential in efficiency?

• Better (lower cost) location? Rent should rise to compensate.

• Better managers at some firms? Wages should rise to equilibrate costs.

• Smarter entrepreneur? Should have higher opportunity cost.

• More fertile land (Ricardo’s original example)

Decreasing Cost Industry• As a market expands, economies of scale in

production of inputs causes input prices to fall.• As the market expands, inputs prices fall and

when firms enter, the price falls below its initial level before P = PBE.

• Reverse of factor price effect.• As demand for micro computers rose in the

1980s-90s, chip factories got bigger and prices fell (technological advances exacerbated the issue, but that is separate).

Producer Surplus• Remember the short run

PS=π+FC

Long Run Producer Surplus• Long Run producer surplus is long run π• Zero producer surplus if constant cost industry.

Producer Surplus• In an increasing cost industry, depends on the

source of the upward sloping LRS curve.$

Producer Surplus• Factor price effect, the rising price needed to increase

supply of the input provides a surplus to lower cost suppliers

• However, individual firms have LR π=0 and PS=0.

Factor MarketOutput Market

Producer Surplus• Differential Productivity Effect: if some firms

have a cost advantage, the firm that owns the source will benefit in the long run.

SOutput Market

Long Run Producer Surplus• Farmer with the best land will earn an

increasing producer surplus (long run profit).– The excess future stream of long run profits will be

capitalized into the market price (value) of the land.

• Actors and Athletes who are really good earn a long run profit because there is no substitute. But now we are starting to talk about market power.

excess annual profitextra land value = i

Competition and Market Equilibrium

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