Cost Supply Discrimination

7/27/2019 Cost Supply Discrimination

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Intermediate Microeconomic Theory: ECON 251:21Perfect Competition

1

Firm and Industry Supply under Perfect Competition

We have examined how we can think about a firms profit maximizing decision throughits choice of inputs both in the long and short run. Just as in the consumer theory we canthink of those choices as being derived from either utility maximization, or expenditure

minimization, so to can we think of a firms choice as being derived from either revenuemaximization or cost minimization. Both methods must yield the same supply decision.That is the choice of inputs gives the firms demand for inputs. This in turn defines thesupply decision of the firm, since as its demand for input varies, it ultimately changes thelevel of production it engages in. To see this, let output produced be

( ) 21

2

1

, KLKLFQ == such as in the short run. As the labor choice changes so to does the

output. Yet at the same time labor choiceL as we have found is dependent on the wagerate based on the firms labor demand in the short run. We can think of this as firmsbeing given a level of output, and they having to choose the most optimal level of

production.

The next question then is how do firms decide how to produce in the first place? Youwould recall that in your Introduction to Economics classes, that that choice is madebased on a firms profit maximization choice as well. Specifically, the firm chooses profitbased on maximizing,

=PQ-C(Q)

This would yield you the standard condition within the perfect competitive framework,that price must equate with marginal cost of production, i.e. P=MC(Q). And as you willrecall, the solution to that condition gives you the firms supply curve, which is thatsegment of the marginal cost (MC) curve above the average cost (AC) curve.Diagrammatically,

MC

ATC

Firms Supply

Price, $

Quantity


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You should know, or have asked yourself the question why we only consider the segmentof theMCabove theACorATCline. The principal argument is that when price is equalto marginal cost is occurs below the AC curve, we get the case of the firm makingnegative profits, which hence implies the firms should not and would not produce, andsimply exit the market. This would have been what you learned in your first economics

course, but it pertains to the long run when all inputs are variable, and there is nodifferentiation between fixed and variable cost. However, to be even more precise, wehave to examine when it is better for the firm to exit the market, so as to determine thecorrect supply curve in the short run as well.

Recall that a firm has two types of cost in the short run, fixed and variable cost. In theshort run, the former is not variable, and can thus be considered a constant. The questionnow is when should the firm shutdown? Consider when the profit of the firm is lower

than the fixed cost, ( ) FCQVCPQFC >when . At such a price, and productionchoice, the firm cannot even recoup its fixed cost, which means it will shutdown.Rearranging the inequality, we obtain

( )( )

( ) ( )

( ) ( )QMCQAVC

QMCPQAVCQ

QVCPQQVC

>

=>=

>

Which gives the condition that when the firm faces a higher average variable cost thanmarginal cost, it will shutdown. Put another way, the relevant segment in the short run forthe firms supply is that portion of marginal costMC(Q) above theAVC(Q).

To obtain the industrys supply (long and short run), as you would and should recall isjust through horizontal summation of the individual firms supply curves. The principal

assumptions that underlie the perfect competitive outcome is that this market structurehas1. Large number of firms (maybe infinite),2. the size of the industry, in terms of the number of firms is that there is no

barriers to entry,3. all firms produces the same good with the same cost structure.

There is essentially no way we can discern one firm from the other, which means whenone firm shutdown, all should shutdown. No one can outdo the other say because of alower cost structure, then by being able to undercut the other. However, should there bean exogenous increase in demand we should see an increase in the number of firmsthrough entry by new firms. And if instead the demand falls, we can imagine a fall in the

number of firms, but not necessarily everyone would leave. We can think about this casewhen the number of firms falling through some random process. The crux of the matter isthat the market size dictates that there can be only a smaller number of firms, unless atthe same time, firms are able to reduce their cost.

The close of this segment, we now note the relationship between profits, and producersurplus. Profit is the revenue in excess of all cost (both fixed and variable cost) bydefinition, while producer/firm surplus is the portion of revenue above the variable cost.


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This measure is derived from the above idea that supply is the portion ofMC that isabove the AVC, and not just the AC. Recall from your demand and supply framework,that producer surplus is the segment between the price line, and the supply curve. Thismeans diagrammatically,

And lastly, the differential between the long and short run supply as derived from themarginal cost differs in slope, with the latter being steeper than the other. The reasonbeing in the long run, with all factor inputs being variable, the elasticity of supply ishigher, consequently the long run supply is gentler.

How about the industrys long and short run supply? Essentially, the shape of the supplytakes on that of the firms since the industry supply is obtained through horizontalsummation of the firms supply. Recall also that another key characteristic of perfectcompetition is that it has a large number of firms. Recall from your earlier classes that asthe number of firms increases, and you keep performing horizontal summation, the slopeof the industry supply falls. Well, on the limit, when there is a large number of firms, theslope of the industry supply would tend to zero, i.e. a flat horizontal line. This is why inyour first year, whenever we talk about perfect competition, we simply draw a flatP=MCline, and have the demand determine the level of production for the industry, andconsequently the firms.

MC

ATC

Firms Supply

Price, $

Quantity

AVC

Producer Surplus


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Intermediate Microeconomic Theory: ECON 251:21Monopoly

4

Monopoly

We have completed the study of a competitive firms behavior where the firm operateswithin a market structure with a lot of other similar firms, producing and selling the sameproduct. This assumption prevents any of the competitors from attaining any form of

market power. In fact, in the long run, none of the firms would be able to earn anypositive profit. We will now examine the other extreme where the firm operates within amarket where it is totally unique, and where no other firm sells a product that directlycompetes with it, i.e. a monopoly.

Principally, the manner in which a firm chooses between its optimal technology, or modeof production is as we have examined earlier, using the isoprofit line for the short runanalysis, and the isoquant and isocost curves in the long run. This then allows us to focuson the key differential between a perfectly competitive firm, and that of a monopoly, theirequilibrium choice of optimal level of output. As we noted above, because the perfectlycompetitive firm is a price taker, its optimal choice is to produce up to the point where its

price of output is equal to the cost of producing its output. What is the choice for amonopoly then? Let us assume a simple and general representation, and let R be themonopolys revenue function, and C be its cost function, both dependent on the quantityof output it chooses;

( ) ( )( ) ( )

( ) ( )

( ) ( )QMCQMR

QMCQMRQ

QC

Q

QR

QCQR

=

==

=

0

Which gives the marginal revenue equal to marginal cost condition you had learnedbefore in your first year. More specifically, we can write the revenue function as theproduct of price and output, noting that the price that the monopoly chooses is dependenton its level of output it chooses, since it is a price setter.

( )( ) ( )( )

( )( )

( ) ( )

( )( )

( )( )

( )( )

( )

( )( )

( )( )

( )

( )

( )

( )

=

=

=

+

=

+=

+

==

+

=

Q

Q

QC

QP

Q

QC

QQP

QQP

Q

QC

QQP

Q

QC

QP

Q

Q

QPQP

QMCQMRQ

QCQPQ

Q

QP

QCQQP

11

111

1

011

1

0


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Let us examine the denominator of the final equality condition we derive from above,

( )

Q

11 . First note that the monopoly would never choose to operate where the

elasticity of demand is less than 1, i.e. where the demand is inelastic, since when

elasticity is less than 1, the term above is less than 1, which turn would mean themonopoly charges a price of less than 0, which is not possible. Secondly, since themonopoly produces at the point where the demand is elastic, i.e. greater than one, thebracketed term is less than 1, and consequently implies charges a price that is greater thanthe marginal cost, and we call this the markup of monopoly above the perfectly

competitive outcome,

( )

Q11

1. When we have a constant elasticity of demand

(examine your earlier work in the first three chapters where we did have an example of a

constant elasticity demand), this markup is just

11

1, which means the price is

always set at a constant markup above the marginal cost.

We will now examine how we should depict the diagrams for a monopoly. Let usexamine a simple example when the monopolys demand is a straight line as like ourearlier discussions.

( )

( )( ) bQaQMR

bQaQQQP

bQaQP

2

2

=

=

=

Comparing the inverse demand, the first equation, and the last equation, which gives themarginal revenue line, note that both are straight lines, with the sole exception that the


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latter has a slope that is twice as steep as the inverse demand. Diagrammatically,

Adopting the usual shape ofMCandAC, and combining the above diagram we get;

Q

P

Demand,AR=P=a-bQ,R,P=a-2bQ

C

Q*

P*

ATC

Profit

Markup

Intercept of a

Demand,P=a-bQMR,P=a-2bQ

Slope of -b

Slope of -2b

Q

P


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We next ask ourselves, is the perfectly competitive output more efficient in its choice,than say the monopolistic choice. For that we refer to the following diagram,

1. Because of market power, the monopolist captures the portion of consumersurplus, A, that would have accrued to consumers under perfect competition.

2. Because of the fact that a monopolists MR is less than price, they chooses toproduce less than the competitive level, and hence creates deadweight loss, B+C.This is commonly noted as welfare loss, since society would have benefited fromthis had production been increased to the competitive level.

3. Because of their choice, resources that could have been used to produce moregoods are diverted to other uses in the form of D. This is not a loss to the societyin general, unless the resources diverted are used for evil, and goods produced bythe monopolist potentially benefits human kind!

But none of these arguments relate to efficiency. In examining efficiency, we are askingourselves whether by changing the level of output, would that choice make everyonebetter of, or at least one person better of without making another worse off, be it inpecuniary or non-pecuniary ways (when we think about utility, it measure is non-pecuniary). Lets begin at the monopoly output choice, suppose the monopoly chooses toraise that output by an additional unit, based on the above diagram, since the willingnessof the consumer to pay, which gives the price the monopoly would receive from the

additional sale is greater than the marginal cost, the monopoly benefits, and yet at thesame time, the consumer who otherwise wouldnt have gotten the good would benefitfrom consuming the good. This means that everyone is better or at least as well off. Thisthen means that the monopoly choice is inefficient.

Based on the above argument, if by raising production by an additional unit, everyone isbetter off, why doesnt it do it. The principal reason is that in selling the additional unit ata lower price based on the demand (reflecting the consumers willingness to pay), all its

Q

P


C

Q*

P*

PPC

QPC

AB

C

D


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other clients would also be eligible for that price. That is the monopoly has to contendwith the inframarginaleffects!

It would seem based on the above analysis, Monopolies are by necessity a bad and shouldthen be subject to regulation, forcing them to either breakup into smaller separate entities

such as in the case of AT&T, and Microsoft, or by forcing them to produce at the level ofP=MC. The latter however does not always work. Consider the example below of anatural monopoly, which arises due to large fixed cost of operation, and small marginalcosts;

Based on the above scenario, by forcing the natural monopoly to operate at the pointwhere MC and demand intersect would be about its demise since the firm would bemaking a lost.

In such a scenario, what governments has done is through one of the following,1. Regulation to produce at point where demand equals to ATC, thereby having the

firm just breaks even. The idea is for the natural monopoly to just breakeven.2. Have the Natural Monopoly be operated by the Government, which would attain

theP=MClevel through direct subsidy. Is this really efficient? Is the point whereP=MCreally efficient, when say the effective supply, segment of MC above AVCis above the demand. That is the demand is in fact to inelastic! Put another way,

what if the supply and demand never intersect?!

What causes Monopolies?

The formation of monopolies is dependent on the idea ofMinimum Efficient Scale(MES), the level of output that minimizes average cost, relative to demand. Consider twoextreme examples below, the first should result in a competitive market, and in the latter,a monopoly may result.

Q

P


C

Q*

P*

ATC

PC


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Under the latter scenario, and assuming there is no way to enlarge the market, it becomes

a candidate for regulation. However, even regulation entails cost through governmentaloversight. If these costs are more substantial then the deadweight loss induced by themonopoly, the market might best be left to operate on its own, unless there are othernational agenda that needs to be fulfilled through the provision of the good.

Another reason for the formation of monopolies is through Cartel formation which is theformation of a pseudo monopoly through collusion between firms to raise prices abovethe competitive level. This practice is illegal, but because it is often not overt, its

Q

P

Demand

ES

P*

ATC

Q

P

Demand

ES

P*

ATC


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detection is not possible, and evidence is not verifiable, i.e. without hard evidence, it isdifficult to incriminate the culprits. Examples: De Beers, and OPEC.

Monopoly Behavior

We have thus far considered Monopoly behavior in a single market. However, the reachof these large firms are typically quite wide in terms of geographic range of its market,and the size of its product range. What kind of behavior can they engage in to capture thehighest level of profit? We will now consider these possibilities.

We have rationalized that monopolies do not wish to sell at the competitive price levelbecause of its inframarginal concerns. However, if the monopolist could sell differentunits of output at different prices then it would sell up to the point whereP=MC. We callthis practicePrice Discrimination.

First Degree Price Discrimination means the monopolist sells different unit at different

prices, and this could differ for every individual. This is sometimes referred to asPerfectPrice Discrimination. In this scenario, the Monopolist captures the entire consumersurplus (Area A) since it charges each an every consumer its willingness to pay.

Second Degree Price Discrimination mans that the monopolist sells different units of

output for different prices, but every individual who buys the same amount of the goodspays the same price. An example of this is bulk discounts, and the price schedule ofpublic utilities. To see how this works, consider two types of individuals with twodifferent demand, and the monopolist know the demand function, hence it can potentiallyas in First Degree Price Discrimination obtain the full surplus. The problem however isthat the monopolist does not know who has which demand, and hence has to rely on selfselection, i.e. trickery to induce the consumer to reveal her own type of demand. Letsassume that the monopoly does not have any cost to speak of, so that we can isolate the

P

Q

C

Demand

Surplus CapturedA


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crux of the argument. And let demand for type 1 consumer be uniformly greater than type2, that is type 1 has a higher willingness to pay, such as below.

Ideally, the monopolist if he knew the consumers type would charge type 1 consumers aprice of A+B+C for quantity Q1, and type 2 consumers a price of A for Q2. However,consumer 1 knows that by pretending to be type 1, and buying Q2 at A, she gains B insurplus, which is greater than 0 should she reveal her true type. Note that with thisstrategy, the monopolist gains 2A in profit.

The question now is how to induce the type 1 consumer to reveal herself. Of course themonopolist could charge type 1 consumer A+C, and thereby induce type 1 consume Q1.This gives a profit of 2A+C. But it is possible to raise profit to the monopolist byreducing output to type 1 consumer. Here is how it can work.

The monopolist could sell instead now Q3 to type 2 consumers at D, but Q1 to type 1consumers at D+G+F+H. At this price, type 2 consumers would consume Q3 at the said

P

Quantity

D

E

H

Q2 Q1

G

F

Q3

P

Quantity

A

B

C

Type 1 Consumer

Type 2 Consumer

Q2 Q1


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price of D. Following our consumer theory assumption that if the consumer can consumemore it would consume more, we have the type 1 consumer revealing herself byconsuming Q1 and paying D+G+F+H, but gaining E in surplus, which is lower than B ofbefore, while the monopolists profit is 2D+F+H>2A. In fact, the monopolist using thisrationale would continue squeezing for additional profit until it just equal the additional

cost of profit lost from type 2 consumers, that is until 2G=F.

This type second degree price discrimination however typically is on the qualitydimension, but the crux of the argument is that you need at least two types of consumers,of whose demand you know are different, and of what form, and magnitude.

The final type of price discrimination is Third Degree Price Discrimination where themonopolist sells output to different people for different prices, but every individual who

buys the same amount of the goods pays the same price. Here the monopolist knows thedemand of the different groups (markets) of consumers but cannot fully extract the fullsurplus buy selling different units at different price. In this case, the problem of themonopolist is to maximize profit by choosing two quantities,

( )( ) ( )( ) ( )212211,, 2121 maxmax QQCQQPQQPQQQQ ++= This then gives two equilibrium conditions

( )( )

( )

( )

( )

( )MC

Q

QQCMR

Q

QP

MCQ

QQCMR

QQP

=

+==

=

+==

212

2

2

211

1

1

11

11

This means that as usual, the monopolist would charge up to the point where theindividual marginal revenue for each market is equal to its marginal cost. It also has aninteresting point, suppose the market 1 has a higher elasticity of demand. Then themarkup term for market 1 is smaller, and consequently the price charged to them for theoutput is smaller than that of the less elastic market which is a very intuitive outcome.

P

Quantity

D

E

H

Q2 Q1

G

F

Q3

Cost Supply Discrimination

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