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DARTMOUTH COLLEGE, DEPARTMENT OF ECONOMICS ECONOMICS 1

© Andreas Bentz page 1

Dartmouth College, Department of Economics: Economics 1, Fall ‘02Dartmouth College, Department of Economics: Economics 1, Fall ‘02Dartmouth College, Department of Economics: Economics 1, Fall ‘02

Topic 4: Theory of the FirmTopic 4: Theory of the Firm

Economics 1, Fall 2002Andreas Bentz

Based Primarily on Frank Chapters 9 - 12

2

FirmsFirms

demand: supply:

inputs:labor,capital

production output

buy in factormarket

cost revenue

Objective: firms are interested in profit = revenue - cost.

sell in productmarket




ProductionProduction

The Black Box

4

ProductionProduction

Production for a neoclassical economist is a“black box”:

We model production as a function that turns inputsinto output:

q = f(k, l)where:

» q: output

» k: capital input

» l: labor input

» f(·, ·): production function



5

Short Run and Long RunShort Run and Long Run

Firms may not immediately be able to change thequantity of all inputs they use.

Example: buildings, etc.

The long run is defined as the shortest period of timein which a firm can change the quantity of all inputs ituses.

An input whose quantity can be freely adjusted is a variableinput.

The short run is the period of time during which one ormore inputs cannot be varied.

An input whose quantity cannot be freely adjusted is a fixedinput.


Production in the Short RunProduction in the Short Run

When not all inputs can be varied.



7

Short-Run ProductionShort-Run Production

Suppose a firm produces output according tothe production function q = f(k, l).

Suppose that, in the short run, the amount ofcapital cannot be varied (fixed input) - assumeit is fixed at k0.

We can then plot the amount of outputproduced as we vary the amount of labor(variable input).

This gives us the short-run productionfunction.

8

Short-Run Production FunctionShort-Run Production Function

The short-run productionfunction f(k0,l) plots thequantity of output (totalproduct), as one input(labor) is varied (holdingcapital fixed at k0).

q

l

f(k0,l)



9

Marginal and Average ProductMarginal and Average Product

The marginal product (MP) of a variable factormeasures the increase in output from a small increasein the variable factor.

MPl = ∆q / ∆l

MPl is the slope of the short-run production function.

The average product (AP) of a variable factor,measures how much output each unit of input yieldson average.

APl = q / l

APl is the slope of the line from the origin to the correspondingpoint on the production function.

10

Marginal ProductMarginal Product

The “law of diminishingreturns”: after somepoint, marginal productdeclines.

The slope of the short-run production functionis the marginal product(MP) of the variableinput:

as the variable input isincreased by a little, byhow much does outputincrease?

MPl = ∆q / ∆l

Note that this changesalong the productionfunction.

q

l

f(k0,l)

∆l

∆q



11

Average ProductAverage Product

The average product(AP) of some input is thequantity of outputproduced, on average,with each unit of thevariable input:

APl = q / l

graphically, it is the slopeof the line connectingorigin and thecorresponding point onthe production function.

q

l

f(k0,l)

q

I

12

Marginal and Average ProductMarginal and Average Productq

l

f(k0,l)

q

l

f(k0,l)

l

q



13

Buzz GroupBuzz Group

You own two car production sites, and you have a totalworkforce of 100. Each site operates a slightlydifferent production technology, but both sites producethe same product. Currently 50 workers are employedat site A, and 50 are employed at site B.

If you were to add one more worker to site A, she would raiseproduction at site A by 3 cars per day. If you were to add onemore worker to site B, she would raise production at site B by4 cars per day.

At site A, each worker on average produces 10 cars per day.At site B, each worker on average produces 8 cars per day.

Should you reallocate workers between the two sites?

14

Maximizing ProfitMaximizing Profit

A firm’s profit is total revenue less total cost.

In the short run, where capital is fixed at k0, profit is:π = p·q - w·l - r· k0

A small change in labor input (∆l) changes output byMPl, and profit by:

∆π / ∆l = p·MPl - w

If this is positive, employing more labor increasesprofit. If it is negative, decreasing labor input increasesprofit. So, at a profit maximum:

p·MPl - w = 0

MPl = w/p



15

Maximizing ProfitMaximizing Profit

So we know that, in order to maximize profit, afirm employs workers until MPl = w/p.

Comparative statics:as the real wage (w/p) increases, the firm willemploy fewer workers.

Another way of putting this:each worker is paid her marginal productivity.


Production in the Long RunProduction in the Long Run

When all inputs can be varied.



17

Long-Run ProductionLong-Run Production

In the long run, all factors of production can bevaried.

Production function q = f(k, l).How do we represent this graphically?

An isoquant (sometimes called productionisoquant) is the set of all input combinationsthat yield the same level of output.

Example: q = 2kl. What is the isoquant for q = 16?» 16 = 2kl

» k = 8 / l

» … and similarly for other levels of output.

18

IsoquantsIsoquants

Isoquants for the production function q = 2kl.

k

lq = 16

q = 32

q = 16

q = 64



19

MRTSMRTS

Note the similarity withthe MRS in consumertheory!

The (absolute value ofthe) slope of an isoquantis the marginal rate oftechnical substitution(sometimes referred toas the technical rate ofsubstitution):

It is the rate at which, in agiven production process,the firm can substitute alittle more of one input fora little less of the otherinput.

k

l

∆k

∆l

20

MRTS, cont’dMRTS, cont’d

There is a relationship between MRTS andMP:

By how much is output reduced if you reducecapital by ∆k?

» output reduction: MPk ∆k (1)

By how much is output increased if you increaselabor by ∆l?

» output increase: MPl ∆l (2)

Along an isoquant, output is constant, so (1) and(2) are equal:

» MPk ∆k = MPl ∆l, or: = MRTSl

k

MP

MP

k

l

∆∆=



21

Returns to ScaleReturns to Scale

In the long run, all inputs can be varied.

Suppose all inputs were doubled. Wouldoutput:

double?

more than double?

less than double?

This is a question of returns to scale: if we“scale up” production, does output increasemore or less than proportionately?

Returns to scale is a long-run concept.

22

Returns to Scale, cont’dReturns to Scale, cont’d

Definition: If a proportional change in all inputs leadsto a more than proportional change in output, theproduction process exhibits increasing returns toscale.

Definition: If a proportional change in all inputs leadsto a less than proportional change in output, theproduction process exhibits decreasing returns toscale.

Definition: If a proportional change in all inputs leadsto a proportional change in output, the productionprocess exhibits constant returns to scale.




CostsCosts

Fixed, Variable, Total;Average, Marginal.

And what to do with them.


Costs in the Short RunCosts in the Short Run




25

Fixed and Variable CostsFixed and Variable Costs

Fixed cost (FC): the cost of fixed inputs.Example: Capital is fixed at k0. The rental rate forcapital (the opportunity cost, if capital is owned) is r.

» What is the fixed cost?

» FC = k0r

Variable cost (VC): the cost of variable inputs.Example: A firm currently uses an amount l of laborinput (hrs). The wage rate is w.

» What is the variable cost?

» VC = wl

Total cost (TC): the sum of FC and VC.

26

Short-Run Prod. & Variable CostShort-Run Prod. & Variable Cost

l

q

f(k0, l)

q

p

VC

TC

FC



27

Average and Marginal CostsAverage and Marginal Costs

q

p

VC

TC

FC

q

p

AFC

AVC

ATC

MC

AFC Average Fixed Cost; AVC Average Variable Cost; ATCAverage Total Cost; MC Marginal (Total and Variable) Cost.

28

Production and CostsProduction and Costs

There is a simplerelationship betweenmarginal product andmarginal cost:

MC =

= ∆VC / ∆q

= ∆(w · l) / ∆q

= (w · ∆l) / ∆q

= w / (∆q / ∆l)

= w / MPl

Similarly, there is asimple relationshipbetween averageproduct and averagecost:

AVC =

= VC / q

= (w · l) / q

= w / (q / l)

= w / APl



29

Production and Costs, cont’dProduction and Costs, cont’d

MC = w / MPl, AVC = w / APl:

l

q

l (which isproportional to q)

p MP

AP

MC

AVC


Application: Predatory PricingApplication: Predatory Pricing

Shut-Down ConditionAreeda-Turner Rule



31

Predatory PricingPredatory Pricing

What is predatory pricing?One firm lowers its price so far that it drives other firms out ofthe market (“dumping”).

Once the other firms have exited from the market, the firm isthen free to raise its prices, recover the losses from dumping,and make supernormal profits.

This is generally viewed as bad for consumers.

Predatory pricing is anti-competitive (Sherman Act).Competition authorities are responsible for antitrust legislationenforcement (Clayton Act):

» Department of Justice (criminal action)

» Federal Trade Commission (civil action)

32

Predatory Pricing, cont’dPredatory Pricing, cont’d

What constitutes predatory pricing?When is a price anti-competitively low?

A price is “too low” if, from charging such aprice, the firm’s profit is so low that it would bebetter to shut down, even in the short run.

When would it be best for a firm to shut down, evenin the short run?

The condition is known as the “shut-downcondition.”



33

Shut-Down ConditionShut-Down Condition

A firm should shut down in the short run if:profit from producing < profit from shutting down (short-run)

revenue - TC < 0 - FC

revenue - (VC + FC) < - FC

revenue - VC < 0

revenue < VC

p · q < VC

p < VC / q

p < AVC

This just says that the price does not evencover variable costs per unit.

34

Shut-Down Condition, cont’dShut-Down Condition, cont’d

q

p

AVC

ATC

If the firm sells output ata price above averagevariable cost, but belowaverage total cost, it willstill make negativeprofits:

each unit sold contributesto revenue (its price) lessthan it costs in total toproduce that unit.

But by shutting down,the firm would makeeven greater losses.



35

AreedaAreeda-Turner Rule-Turner Rule

So a firm should shut down, even in the shortrun, if the price it charges is below its AVC.

As a rule to judge predatory pricing, this wasfirst argued by:

Areeda P & D F Turner (1975) “Predatory Pricingand Related Practices Under Section 2 of theSherman Act” Harvard Law Review 88

Hence: “Areeda-Turner Rule.”


Costs in the Long RunCosts in the Long Run




37

Long-Run CostLong-Run Cost

In the long run, all inputs can be varied.

We already have a tool for representing long-run output.

We want cost in the same “space”.

l

k

isoquants

38

Total CostTotal Cost

(Long-run) total cost is: LTC = r·k + w·l

LTC - w·l = r·k

LTC/r - (w/r) l = k

l

k

slope: -(w/r)

LTC/r

The isocost line plots allcombinations of inputsthat have the same totalcost (at given factorprices).



39

Minimizing CostMinimizing Cost

The firm wants to produce a given level ofoutput at minimum cost.

This is one step to profit maximization:» (i) What is the minimum cost at which some output can be

produced?

» (ii) What is the optimum output?

This fits a “delegation” story:» The manager has established the quantity that some

division needs to produce.

» Now she asks the division to produce this quantity at thelowest cost.

» How much of each factor should the division use?

40

Minimizing Cost, cont’dMinimizing Cost, cont’d

Implication: at theoptimal choice, we have:

If the firm wants toproduce the “requiredoutput level,” and it hasa production technologywith given marginalproducts for labor andcapital, and faces inputprices w and r ...

… it should use l* unitsof labor and k* units ofcapital.

l

krequiredoutput level

slope: -(w/r)

LTC/risoquantslope: -

MPMP

k

l

rw

MPMP

k

l =

k*

l*



41

Factor DemandFactor Demand

If a firm is profit maximizing (i.e. costminimizing), it should employ inputs in itsproduction process such that:

r

MP

w

MP

:or

r

w

MP

MP

kl

k

l

=

=… that is, it should use inputssuch that the marginal productper dollar spent on each inputis the same.

The “law of the equal bang forthe buck”.

42

Long-Run Output Expansion PathLong-Run Output Expansion Path

The output expansionpath contains the long-run total cost curve,which plots outputagainst (minimum) cost.

As required output rises,the firm chooses itsoptimal inputcombination. This giveus the long-run outputexpansion path.

Each point on the outputpath is a

specific quantity of output(which isoquant is it on?)

specific cost (whichcombination of inputs, atgiven factor prices?)

l

koutput expansionpath



43

Long-Run Total CostLong-Run Total Cost

The long-run total cost curve traces the least cost ofproducing given output levels.

It always passes through the origin: In the long run, afirm can avoid all costs by not producing.

44

LMC, LACLMC, LAC

From long-run total cost (LTC), we can derivelong-run marginal cost (LMC) and long-runaverage cost (LAC) in the usual way:

q

LTCLAC =

q

LTCLMC

∆∆=



45

LMC, LAC, cont’dLMC, LAC, cont’d

q

p

LTC

q

p

LAC

LMC

46


You are in charge of Bell Atlantic’s directoryassistance.

Currently every call is taken by an operator, wholooks up the name of the person whose number isrequested and then tells the caller that number.

Voice recognition software has become muchcheaper in recent years, and the price of computershas fallen. Wages have remained the same.

What long term decisions should you make toensure Bell Atlantic’s survival in the newmillennium?



47

LTC and Returns to ScaleLTC and Returns to Scale

There is a simple connection between long-run totalcost and returns to scale:

If a production function exhibits constant returns toscale, a doubling of all inputs results in a doubling ofoutput.

If you double all inputs, long-run total cost doubles:LTC = r · k + w · l;

r·2k + w·2l = 2LTC

So: a production process exhibits constant returns toscale if a doubling of output results in a doubling ofcost, that is, if the LTC curve is a straight line.

48

LTC and Returns to Scale, cont’dLTC and Returns to Scale, cont’d

Constant returns to scale:

q

p

LTC



49


If a production function exhibits increasing returns toscale, a proportional change in all inputs results inmore than a proportional change in output.

If you change all inputs by a factor of t, long-run totalcost changes by a factor of t:

LTC = r · k + w · l;

r·tk + w·tl = tLTC

So: a production process exhibits increasing returns toscale if a change in output (by a factor of t) results in achange in long-run total cost of less than a factor t;that is, the LTC curve is concave.

50


Increasing returns to scale:

q

p

LTC



51


If a production function exhibits decreasing returns toscale, a proportional change in all inputs results in lessthan a proportional change in output.

If you change all inputs by a factor of t, long-run totalcost changes by a factor of t:

LTC = r · k + w · l;

r·tk + w·tl = tLTC

So: a production process exhibits decreasing returnsto scale if a change in output (by a factor of t) resultsin a change in long-run total cost of more than a factort; that is, the LTC curve is convex.

52


Decreasing returns to scale:

q

p

LTC



53


You are a management consultant working fora company that hopes to offer telephoneservice on cable in Hanover. Your job is to findthe company’s Long Run Average Cost curve.

The way the company operates is this: First, itbuilds a cable network that passes every house inHanover. Then, every time a consumer makes acall, the company incurs a very low cost related tothe wear in its main switching facility.

Hint: it may help if you draw the Long Run TotalCost curve first.

54


In almost all industries, decreasing returns toscale set in eventually (i.e. for high enough q).

This explains the shape of the long-run total costcurves we have drawn so far.

If an industry exhibits increasing returns toscale throughout, we refer to it as a naturalmonopoly:

it is socially better to have one firm exploit thereturns to scale, than to have more than one firmproduce (at a higher cost).



55

Natural MonopoliesNatural Monopolies

Every additional unit produced in the firmlowers long-run average cost: it is better (lesscostly) to have one firm than two (or more).

q

p

LAC

LMC

56

Natural Monopolies, cont’dNatural Monopolies, cont’d

Examples of natural monopolies (?):electricity distribution (though not generation)

water supply

railroads: tracks, signals

mail delivery

telephone network (but: cellular networks, cable)

Dartmouth Bookstore (but: amazon.com)



57

Minimum Efficient ScaleMinimum Efficient Scale

q

p

LAC

q*

q* is the minimumefficient scale: if a firmproduces below q*, itcould lower its per-unitcost by producing more.

If q* is large (relative toindustry output), weshould expect themarket to be dominatedby a few firms.

(conversely for q* small)


Costs in the LongCosts in the Longand the Short Runand the Short Run

The Envelope Theorem



59

Long-Run and Short-Run CostsLong-Run and Short-Run Costs

In the short run, a firm’s capital input is fixed:If it wants to produce more or less, it can only varylabor (the variable input): (ATC is short-run ATC)

q

p

ATC (k=k’’)

60

L-R and S-R Costs, cont’dL-R and S-R Costs, cont’d

In the long run, the firm can choose capitalinput.

Suppose it can choose between levels k’, k’’, k’’’.

q

p

ATC (k=k’’)

ATC (k=k’)

ATC (k=k’’’)



61


In the long run, the firm can choose capitalinput.

Suppose it can choose any level of k.

q

p

62


Each average cost curve has a marginal costcurve, that intersects it at its lowest point:

q

p

ATC (k=k’’)

ATC (k=k’)

ATC (k=k’’’)

MC (k=k’)

MC (k=k’)MC (k=k’)

LMC

LAC



63


LTC

TC(k=k)

In the short run, not all factors are variable.Suppose capital is fixed at k.

How does short run cost compare to long run cost?

64

Production, Cost & Production, Cost & MktMkt. Structure. Structure

The term “market structure” refers to the environmenta firm operates in:

Does the firm operate in a competitive market?

… in a market where it is the only supplier (monopoly)?

What we have so far covered in this topic (production,costs) does not depend on market structure:

Production function and (by implication) costs areindependent of market structure.

But a firm’s behavior does depend on marketstructure: monopolists act differently from competitivefirms.

We now turn to our study of market structure and firmbehavior.




Perfect CompetitionPerfect Competition

ex pluribus unum

66

Four ConditionsFour Conditions

Perfectly competitive markets have fourproperties:

homogeneous product;» all goods sold in this market are “the same” (standardized)

firms are price takers;» firms treat the market price as given: each firm is small

relative to the size of the market

» free entry or exit

» (excludes monopoly, etc.)

perfect factor mobility;» firms can expand/contract/cease production

perfect information.



67

Firm Objective: ProfitFirm Objective: Profit

What is a firm’s objective?Firms aim to maximize profit.

Profit is revenue minus cost:

π = p · q - TC

Distinguish economic profit and accounting profit:» Economic profit includes opportunity cost (e.g. for capital

that is owned rather than rented)

» Accounting profit does not include opportunity cost.


Profit MaximizationProfit Maximizationin the Short Run,in the Short Run,

under Perfect Competitionunder Perfect Competition

… when firms cannot enteror leave the market



69

Profit & Profit Maximization (S-R)Profit & Profit Maximization (S-R)

q

p

q

p

TC

π

The slope of thetotal revenue (TR)curve is marginalrevenue (MR), orjust the price p.

At the profit-maximizing outputlevel, the slopesof TR and TC arethe same, or …

MR = p = MCq*

TRTR = p·q

70

Profit-Maximization (S-R)Profit-Maximization (S-R)

Profit-maximizing condition: p = MC

q

p

MR = p

MC

q*

AVC

MC = MR is the profit-maximizing condition if itis above AVC (recall the shut-down condition!)



71

MC

Short-Run Firm SupplyShort-Run Firm Supply

The MC curve (above AVC) tells us how mucha firm produces for each given price.

It is the firm’s supply curve.

q

p

AVC

72

Short-Run Industry SupplyShort-Run Industry Supply

The supply curve of a competitive industry is just thehorizontal sum of the supply curves of the firms in themarket.

Recall how market demand was made up of the (horizontal)sum of all individual demand curves.

qA

p p

q

p

MC MC

qB



73

Short-Run Competitive EquilibriumShort-Run Competitive Equilibrium

Remember one of the conditions for competitiveequilibrium: firms are price-takers:

Each firm is “small”: it cannot raise price, and there is no pointin lowering price. Demand facing a firm is horizontal.

q

p

qf

p

D

MC

qf*

AVCATC

S

p* = MR

market firm

74

Producer SurplusProducer Surplus

How much better off is a firm as a result of producingsome quantity q*?

In the short run, if the firm produces nothing, it still has to payfixed cost. So producer surplus is the difference betweenrevenue and variable cost.

q

p

MC

q*

AVC

p*

q

p

q*

p*

MC



75

Producer Surplus, cont’dProducer Surplus, cont’d

Producer surplus is the area between MC and themarket price.

The MC curve is the firm’s supply curve.

So: aggregate producer surplus in a market is the areabetween the supply curve and the market price.

q

p

q*

p*

MC

PS

q

p

D

S

marketfirm

aggregate PS


Profit MaximizationProfit Maximizationin the Long Run,in the Long Run,

under Perfect Competitionunder Perfect Competition

… when entry and exit is possible



77

Not a Long-Run EquilibriumNot a Long-Run Equilibrium

Suppose p* were the market price.In the long run, firms can vary all inputs, so the firm wouldchoose to produce where its LMC = p* (with the given short-run curves, MC and ATC). This firm makes positive profits.

π

MC

ATC

q

p

qf

p

D

qf*

S

p* = MR

market firm

LAC

LMC

78

Not a Long-Run Equilibrium, cont’dNot a Long-Run Equilibrium, cont’d

This cannot be a long-run equilibrium:A firm makes positive profits

Since other firms are perfectly informed about profitopportunities (perfect information assumption!),other firms would enter this market.

The supply curve shifts to the right.



79

Toward Long-Run EquilibriumToward Long-Run Equilibrium

Entry shifts the market supply curve to the right.Entry into the market reduces profits.

q

p

qf

p

D

SMC

ATC

qf*

p* = MR

market firm

LAC

LMC

80

Long-Run EquilibriumLong-Run Equilibrium

In long-run equilibrium, all profit has been eliminatedthrough entry into the market:

each firm in this industry produces at the lowest point of itslong-run average cost curve.

q

p

qf

p

D

S

market firm

LAC

LMC

qf*

S’

p* = MR

MC

ATC



81

Long-Run Equilibrium, cont’dLong-Run Equilibrium, cont’d

What is good about equilibrium?All firms earn normal (zero) profits.

Goods are produced at the lowest possible cost(production at the minimum point on long-run AC).

Price is equal to marginal cost:» This is allocatively efficient: all gains from trade are

realized (no room for private side-trades):

• Consumers would buy more if the price were lower;but at p = MC, the cost required to produce one moreunit is just p, and at that price, consumers do not wantto consume more.

• Producer would supply more at a higher price; butconsumers do not wish to buy more at that price.

82

Long-Run Industry SupplyLong-Run Industry Supply

The long-run industry supply curve ishorizontal, at minimum average cost.

q

p

qf

p

D

S

qf*

p* = MR

market firm

LAC

LMC

qf*

p* = MR

MC

ATC

market

D’

S’

long-run supply



83

Long-Run Industry Supply, cont’dLong-Run Industry Supply, cont’d

There is an exception to horizontal long-run supply:We have assumed that input prices (and therefore long-runcost) are constant.

If input prices rise with expanding production, long-run supplyis upward-sloping (“pecuniary diseconomy”)

q

p

qf

p

D

market firm

LAC

qf*market

D’

LAC

LAC

D’’

LS


MonopolyMonopoly

The power to set price.



85

Perfect Competition and MonopolyPerfect Competition and Monopoly

We have just studied firm behavior in perfectlycompetitive markets.

In competitive markets, firms are price takers.

We will now study firm behavior in a market inwhich the firm is the only supplier.

This means the firm can choose the price itcharges.

86

P. C. and Monopoly, cont’dP. C. and Monopoly, cont’d

Why these two limiting cases?They are “easy”:

» In perfectly competitive markets, each firm is so small thatit has a negligible effect on total output. If a firm reducesits output, this has no effect on the price in the market, andtherefore no effect on other firms.

» A monopolist is the only firm in the market, so if it reducesoutput, it will raise price; but it is the only player in themarket, so we need not consider issues of interaction.

Interaction is difficult to model:» If there are few firms in a market, the decision of each

influences the decision of all the others which influencesthe decision of all the others which … (and so on).



87

P. C. and Monopoly, cont’dP. C. and Monopoly, cont’d

The difference between perfect competition andmonopoly is this:

Each firm in a perfectly competitive market faces a demandcurve that is horizontal: the price elasticity of demand isinfinite.

» If a firm chooses to raise price, it will sell nothing.

The demand curve the monopolist faces is the marketdemand curve. For the reasons we have discussed in Topic 3,the market demand curve is downward sloping: the priceelasticity of demand is finite.

» If the monopolist raises price, it will sell less, but will notlose all its customers.

88

Total RevenueTotal Revenue

Recall: TR = p·q

For a firm in a perfectlycompetitive market,price is fixed:

If a monopolist wants toincreases output, shehas to lower price:

q

TRTR

q

TR q

p

D




The Monopolist’s Short-RunThe Monopolist’s Short-RunProfit MaximizationProfit Maximization


90

Profit MaximizationProfit Maximization

The slope of thetotal revenue(TR) curve ismarginalrevenue (MR).

At the profit-maximizingoutput level, theslopes of TRand TC are thesame, or …

MR = MC

q

p

q

p

TC

q*

TR

π



91

Optimality and Marginal RevenueOptimality and Marginal Revenue

The profit-maximizing condition for amonopolist is, as for a perfectly competitivefirm, MR = MC.

For a competitive firm, MR = p:» if it expands output by one unit, revenue increases by p.

But for a monopolist, MR is not equal to price:» if a monopolist wants to increases output, she has to lower

price (because she faces a downward sloping demandcurve), and she has to lower the price for all (not just thelast) units she sells; therefore:

» if monopolist expands output by one unit, revenueincreases by less than p: MR < p.

92

q

p

p’

p’’

p’’’

D

Marginal RevenueMarginal Revenue

For small changes inoutput, this approximatesthe solid-line MR curve.

Suppose the monopolistcurrently charges price p’(so that she sells nothing),and considers selling onemore unit of output.

To sell one more unit, she hasto lower the price to p’’.

Starting from p’’:To sell one more unit, she hasto lower the price to p’’’ for thesecond and the first unit sold.So her marginal revenue is notp’’’, but p’’’ - (p’’ - p’’’) … (etc.)

MR



93

Marginal Revenue and ElasticityMarginal Revenue and Elasticity

A producer currently charges price p and sellsq units of output:

her total revenue is p·q

To expand output by ∆q (to q + ∆q), she has tolower price to p + ∆p (where ∆p is negativeand small):

her total revenue is (p + ∆p)·(q + ∆q) =

= p·q + p·∆q + ∆p·q + ∆p∆q

94

MR and Elasticity, cont’dMR and Elasticity, cont’d

Her marginal revenue is the change in totalrevenue, divided by ∆q (i.e. for a small change∆q in output):

(This is clearly less than price since demand isdownward-sloping, i.e. ∆p/∆q < 0.)

qq

pp

pqq

pp

q/)qpqpqpqpqp(MR

∆∆+≈

∆+∆∆+=

∆⋅−∆⋅∆+⋅∆+∆⋅+⋅=



95


What is the definition of price elasticity ofdemand?

Draw a linear (straight line) demand curve.What is the price elasticity of demand at the pointwhere q=0?

What is the price elasticity of demand at the pointwhere p=0?

Where is the price elasticity of demand -1?

96


Recall the definition of price elasticity ofdemand:

And we have just derived:

So we have

(Recall that η is negative: MR < p)

q

p

p

q∆∆=η

∆∆+=

∆∆+=

p

q

q

p1pq

q

ppMR

η

+= 11pMR



97


The elasticity relationship we have derived helps usgraph the MR curve:

Recall that

And: for a linear demandcurve (p = a - bq) theelasticity at q is: 1 - (a/bq).

So elasticity is -1 just whereq = (1/2)(a/b), i.e. halfwayalong the demand curve.

η

+= 11pMR

q

p

D

η = -1

1/2 1/2MR

98


A monopolist would therefore never produce on theinelastic part of the demand curve:

on that portion, each additional unit contributes negatively torevenue and increases total cost.

Recall:

So: the elastic part of alinear demand curve isto the left of the pointwhere η = -1. Theinelastic part is to theright.q

p

D

η = -1

1/2 1/2MR

q

p

p

q∆∆=η



99

MaximizationMaximization

To maximize profit, themonopolist producesoutput q* such thatMR=MC.

In order to sell q* unitsof output, she needs toprice output at p*.

Her profit is π, thedifference between totalrevenue and total cost.q

p

D

MR

MC

q*

p*ATC

100

Maximization and ElasticityMaximization and Elasticity

We know that:

We also know that a monopolist optimally choosesoutput so that MC = MR:

η

+= 11pMR

MC1

1

1p

11pMC

η

+=

η

+=

The fraction (1/(1+1/ η)) is themonopolist’s markup:

it is the fraction by which amonopolist “marks up” price overmarginal cost.



101

Shutdown ConditionShutdown Condition

If she shuts down, she will still incur fixed costs, butthat loss is less than producing any positive amount.

A monopolist shouldshut down, even in theshort run, when there isno quantity she couldsell at which revenuecovers variable cost:

She should shut down ifaverage variable cost iseverywhere above thedemand curve.q

p

D

MR

AVC

102

Monopoly SupplyMonopoly Supply

q

p

D

MR

There is no well-defined(unique) relationshipbetween price and MRwhen demand shifts:

A monopolist mayproduce differentquantities at the sameprice when demand shifts.

A monopolist has nosupply curve.

Instead, she has a supplyrule, viz. to set MR=MC.

MR’

D’

MC




The Monopolist’s Long-RunThe Monopolist’s Long-RunProfit MaximizationProfit Maximization


104

Long-Run ProfitsLong-Run Profits

This monopolist hasincreasing returns toscale (declining LACcurve throughout), i.e. itis a natural monopoly.This means that long-run profits may persist.

The optimal level ofcapital (or, the fixedfactor) is such that it givesrise to the short-runcurves MC and ATC).

q

p

D

MRq*

p*

LMC

LAC

MC

ATC




Monopoly and EfficiencyMonopoly and Efficiency

Dead-Weight Loss

106

Monopoly and EfficiencyMonopoly and Efficiency

In the long run, competitive markets operate efficiently:production takes place at minimum average cost, andthere are no unexploited gains from trade.

Monopolistic markets (even in the long-run) will notgenerally be efficient:

The monopolist restricts output so as to charge a higher price.This should make you suspicious:

If the monopolist could make one more trade (at a slightlylower price, but without having to reduce the price on theoutput she already sells), she would want to do it; similarly,there are consumers who would be willing to buy at a slightlylower price.



107

Inefficiency of MonopolyInefficiency of Monopoly

The efficiency loss is theloss in surplus: area D(deadweight loss).

In the long-run, thismonopolist would makepositive profits.

Her producer surplus isarea A, and consumersurplus is area B.

In a competitive market,profits would encourageentry, to the point whereevery firm only makesnormal profits: outputwould rise until P = LMC:Consumer surplus is areaC.

q

p

D

MRq*

p*

LMC=LAC

108

Inefficiency of Monopoly, cont’dInefficiency of Monopoly, cont’d

We have just compared a monopolist to aperfectly competitive market ...

… because the cost-structure would have allowed acompetitive market.

» Why is there monopoly in this case? Maybe because thefirm has a patent. Even in this case, does the deadweightloss measure the loss in welfare accurately? Notnecessarily: without the promise of monopoly profits thepatented product might never have been developed.

This comparison does not always make sense:when the industry is a natural monopoly, what isthe alternative to monopoly, for purposes of welfarecomparisons?



109

D

Natural MonopolyNatural Monopoly

If an industry has thecost structure of anatural monopoly, it issocially efficient (leastcostly) to have one firmproduce all the output.

The problem is a pricingissue: A monopolistalways has the incentiveto restrict output andincrease the price, belowthe competitive level.

q

p

D

MRq*

p*

LMCLAC

110

Policy toward Natural MonopolyPolicy toward Natural Monopoly

Do nothing (“laissez-faire”).Efficiency? Fairness?

State ownership.Example: Postal Service

Private ownership, state regulation of prices.Example: Telecommunications

Competitive tendering/bidding.Example: PCS auction




Price DiscriminationPrice Discrimination

… when a monopolist can chargedifferent prices

112

Single-Price MonopolySingle-Price Monopoly

Why does the inefficiency of monopoly arise?The monopolist restricts output so that she cancharge a high price:

The single-price monopolist (i.e. a monopolist whohas to charge the same price for all units she sells)does not increase output because she would haveto reduce price on all output she sells.

» This is just the old story that MR < P.

She would like to increase output if she could lowerthe price on just the additional unit sold, i.e. if shecould price-discriminate.



113

Price DiscriminationPrice Discrimination

First-degree (perfect) price discrimination:different prices for different units of output, and

different prices for different consumers.

Second-degree price discrimination (non-linearpricing):

different prices for different units of output, and

same prices for similar customers.

Third-degree price discrimination:same prices for different units of output, but

different prices for different customers.

114

First-Degree Price DiscriminationFirst-Degree Price Discrimination

Assumption: The perfectly discriminating monopolistknows each consumer’s demand curve.

The monopolist prices each unit of output at eachconsumer’s marginal willingness to pay.



115

First-Degree Price Disc., cont’dFirst-Degree Price Disc., cont’d

Perfectly discriminating monopolist would like to sell:to consumer 1: q1 at price A + A’; to consumer 2: q2 at B + B’

All consumer surplus is extracted by the monopolist.

First-degree price discrimination is efficient.

But: informationally demanding.

116

First-Degree Price Disc., cont’dFirst-Degree Price Disc., cont’d

What limits first-degree price discrimination:unobservable preferences:

» “informationally demanding”;

competition (or the threat of entry)

arbitrage (resale):» Example: Suppose my marginal willingness to pay is low

(i.e. I pay a low price for the quantity I buy). Since myconsumer surplus is zero, there are gains from trade if Isell to you (your willingness to pay is high);

administrative costs.



117

Two-Part TariffTwo-Part Tariff

The monopolist couldachieve the same outcomeby charging a two-part tariff:

charge a one-off fee of A(consumer surplus), and

charge each unit bought atmarginal cost.

The consumer will then buyx1 units (i.e. up to whereprice = willingness to pay),and all consumer surplus isextracted.

As before, this isefficient, butinformationallydemanding.

118

Two-Part Tariff: ExamplesTwo-Part Tariff: Examples

How does economic theory (the theory of two-part tariffs) explain features of the real world?

Amusement parks:admission fee + marginal cost per ride.

Telephone line:connection charge + marginal cost per call.

Xerox photocopiers:rental fee + marginal cost per copy.



119

Second-Degree Price Disc.Second-Degree Price Disc.

Suppose a monopolist cannot observe eachcustomer’s marginal willingness to pay.

But: she can observe the quantity demanded bycustomers.

She could sell different price-quantity “packages”,aimed at customers with different marginalwillingness to pay: customers will self-select intobuying the “package” designed for them.

This explains “nonlinear” pricing schedules,e.g. different per-unit prices for large and smallusers of electricity.

120

Third-Degree Price DiscriminationThird-Degree Price Discrimination

The monopolist charges different prices todifferent customers (i.e. in different elasticitymarkets).

Examples: private/business telephony, studentdiscounts, business/economy class air travel, …

(The monopolist must be able to observe acustomer’s demand elasticity.)

Marginal cost equals marginal revenue in eachmarket. (Monopoly pricing in each market.)

(argument by contradiction)



121

Third-Degree Price Disc., cont’dThird-Degree Price Disc., cont’d

Example:Low elasticity market: demand D1 (e.g. private telephony)

High elasticity market: demand D2 (e.g. business telephony)

Price where marginal cost = marginal revenue

Price is high in the low elasticity market, and low in thehigh elasticity market.

MC

122

Third-Degree Price Disc.: WelfareThird-Degree Price Disc.: Welfare

The welfare effects of third-degree price discrimination(compared with standard monopoly pricing) areambiguous:

Two inefficiencies:Output is too low:

» The monopolist charges the monopoly price in each market.(She restricts output below the efficient level.)

Misallocation of goods:» Goods are allocated to the wrong individuals.

» Example: I value a theatre ticket at $40, you value it at $20. Youget a student discount (ticket for $15) and buy the ticket. I haveto pay the normal price ($50) so I don’t buy the ticket. But myvaluation is higher than yours, so I should get the ticket!




Monopolistic CompetitionMonopolistic Competition

Differentiated Products and theHotelling Model

124

Product DifferentiationProduct Differentiation

Monopolistic Competition: every firm faces adownward-sloping demand curve (i.e. hassome degree of monopoly power).

In an industry with non-homogeneousproducts, how do firms choose their products’characteristics?

Example: cars, economics courses, …

Imagine one product characteristic that can bechosen continuously: e.g. location of two ice-cream vendors along a beachfront.



125

Product Differentiation: LocationProduct Differentiation: Location

Hotelling’s “principle of minimum differentiation”: bothice-cream vendors locate in the middle of the beach.

This is not welfare maximising (the location choice in the left-hand panel in the diagram is).

More examples: political parties, radio stations, ...

s-04-theory of the firm - dartmouth collegeecon01ab/f02-topic4.pdftopic 4: theory of the firm...

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