Monopoly - Lakehead Universityflash.lakeheadu.ca/~mshannon/micro17b.docx · Web viewPrice Discrimination: Monopolist’s Charging More than One Price - Single-price monopoly: monopolist

Price Discrimination: Monopolist’s Charging More than One Price

- Single-price monopoly: monopolist is constrained to charge the same price to all buyers.

- Price discrimination usually allows the monopolist to do better.

(turn some consumer surplus into profit)

i.e. push the price closer to consumers’ willingness-to-pay (WTP)

WTP? height of the demand curve: maximum a consumer would pay for a particular unit of the good.

In a single price monopoly, Price (Pmon)<WTP on all units of output from 0 to Qmon:

1

Why not price discriminate all the time?

Two problems need to be dealt with:

(a) information problem: can the monopolist identify those willing to pay a high price?

- those willing to pay most have no incentive to reveal this.

- can a monopolist find some way to identify them? if so price discrimination becomes more likely.

(b) resale problem: those who buy at a low price might resell to those who are charged a high price

- resale undercuts the monopolists ability to charge some a high price.

2

Types of price discrimination:

Perfect price discrimination: charge a different price for each (first-degree price discrim.) unit sold.

Second degree price discrimination: different price for different units bought by the same

customer.

Third-degree price discrimination: different price for different groups of customers.

(we will model each of these and give examples below)

3

Another Distinction: Direct and Indirect Price Discrimination

Direct price discrimination: different pricing on the basis of observable characteristics of the buyer e.g. age of buyer, location.

Indirect price discrimination:

- price based on behaviour or choices of buyers that allow sellers to infer something about WTP.

- sellers might be able to induce buyers reveal that they have high or low WTP.

- Variation in product attributes:

- can you add characteristics that appeal to higher WTP people?

e.g. fancy coffee, “luxury” versions of everyday goods; are green or fair-trade goods examples of this?

i.e. appeal to people who are less price sensitive due to high income or due to concern about other attributes of the good.

4

Hurdles:

- Hurdle is a “trick” that overcomes the information problem: gets customers to reveal if they have higher or lower WTP.

- A “hurdle” is placed in the buyers way.

- those most price sensitive will overcome the hurdle and pay less;

- those least sensitive to price will not overcome the hurdle and will pay a higher price.

- typical price discrimination result.

- the hurdle is an example of “screening”: uncovers info about buyer characteristics (WTP)

- Hurdle examples:

coupons and rebates (cost of time and who uses them);

sale pricing (who will wait for bargains?);

penalizing the impatient:hardcover vs. paperback versions of a book (release time who

will wait? video game prices (on release vs. later);

quality differences: have “high quality- high price” and “lower quality – low price version” of the good.

- This could raise profits if those with high WTP are also more likely to prefer high quality.

e.g. IBM laser printer example (added chip to slow down inferior model)

- Practical difficulty? How to identify true price discrimination from price differences due to real quality differences?

5

Modelling Price Discrimination: Perfect Price Discrimination

- Perfect or First-degree price discrimination)

- Say the monopolist knows the maximum that each buyer is willing-to-pay (WTP) for each unit of the good.

i.e., knows the height of the demand curve at each quantity.

- Assume there is no resale problem.

- The monopolist opts for ‘Perfect price discrimination’: charge different prices for each unit sold.

- charge each consumer the maximum they are willing to pay for each unit of the good bought.

- As before the monopolist will maximize profits by producing up to the point where MR=MC.

- but the MR curve is now the same as the demand curve!

- a different price is charged for each unit sold.

so: MR = Price

- the perfectly price discriminating monopolist need not cut the price charged to “infra-marginal” buyers to sell more output.

6

- So the monopolist produces up to the point where:

MR = MC

Price of the last unit sold = MC (QPPD in diagram)

- monopolist charges each consumer the maximum that they will pay.

- this allows the monopolist to expropriate all of the consumer surplus.(all surplus in this market is producer surplus!)

- profit is as large as it can possibly be in this market.

- output is higher than in single-price monopoly:

- no reason to restrict output

- selling more does not require price cuts for anyone other than the marginal buyer.

- Outcome is efficient! -- achieves maximum surplus- same output level as in perfect competition.

- But all surplus goes to the monopolist as producer surplus. (distribution a concern)

7

- Hard to perfectly price discriminate in practice:

- monopolist needs a lot of information.

- Any possibilities which might come close?

- One-on-one bargaining: bargain over price, can a skilled seller extract the maximum possible price?

e.g. used cars, street vendors.

- Top US universities? - Charge students tuition minus financial assistance.- Financial assistance tailoring assistance to individual

circumstances.

- Is information technology pushing us in the direction of perfect price discrimination?

- Information on WTP is easier/cheaper to obtain. - Internet retailers: gather information on past purchasing

behaviour and tailor the price offered to past behaviour.

- Grocery store discount cards: collect information on buying patterns (tailor prices to customers via coupons sent out).

- Google ad auctions -- is it close to this?

- But consumer reaction: unfair! (early Amazon book pricing case).

(US report from 2015: ‘Big Data and Differential Pricing’ https://www.whitehouse.gov/sites/default/files/docs/Big_Data_Report_Nonembargo_v2.pdf )

8

Third-Degree Price Discrimination: A Monopolist with Multiple Markets

- Monopolist price discriminates between consumers but not between units of a good bought by a particular consumer.

- We will do a case where consumers are divided into two markets: similar reasoning applies to case of three or more markets.

- Say the monopolist can separate customers into two markets with different demand curves, i.e. groups with differences in WTP:

- so: has partly overcome the information problem;

- assume that customers cannot resell between the two markets.

- The firm faces two demand curves (D1 and D2) and two marginal revenue curves (MR1 and MR2).

- As before one set of cost curves: it is the same firm producing output for both markets.

i.e. the level of MC, ATC depends on total output produced and sold.

- Firm must decide how much to sell and what price to charge in each market.

- Consider the first unit of output the firm might produce:

- Say MC1 is the marginal cost of producing the first unit.

- Profitable to produce it as long as MR > MC1 in at least one market.

- If MR>MC1 in both markets: sell it in the market with the highest MR.

9

- Similar decision for all subsequent units:

- Produce more as long as MR in one of the markets >MC.

- then sell the unit in the market with the highest MR.

- This creates a tendency to keep MR1 = MR2 if selling in both markets.

(always sell each extra unit in the high MR market, as you do this MR falls in that market toward the level of MR in the other market – following his strategy keeps MR1 and MR2 roughly equal)

- Since MC depends on Q1+Q2 (combined output)it is useful to construct a combined MR curve that is also defined over Q1+Q2.

- How? Use the logic just above. On each extra unit sold ask which market gives the highest MR.

- Doing this gives the combined MR curve as the horizontal sum (sum over quantities) of MR1 and MR2.

10

- Monopolist’s best choice?

- produce more as long as MR>MC in the combined market diagram.

i.e. produce total output at the point where the horizontal sum of MR1 and MR2 equals MC.

- output in market 1 is where:

MR1 = MC (MC determined where the combined MR curve =MC)

- output in market 2 is where:

MR2 = MC (MC determined where the combined MR curve =MC)

(Combined MR = MC at Q1*+Q2* prices will be P1* and P2*)

(see another version: text Fig. 12-13)

- Notice that if MC intersected MR1+MR2 on its first segment (so output below Q11) -- the monopolist would only sell in market 1.

- Market 2 would never generate revenues sufficient to cover MC.

11

(ASIDE: Calculus version for those interested

Profit = P1∙Q1 + P2∙Q2 – TC(Q1+Q2) with P1=P1(Q1), P2=P2(Q2)

where: P1 and P2 are prices in markets 1 and 2 and these depend on Q1 and Q2 (quantities sold in each market) respectively, TC() is the level of total cost which depends on total output produced: Q1 +Q2.

First order conditions for a profit maximum are then:

∂(Profit)

∂ Q1 = P1 + Q1∙

∂ P1

∂Q 1 -

∂TC∂Q1

= 0 i.e. MR1 – MC = 0

∂(Profit)

∂ Q2 = P2 + Q2∙

∂ P2

∂Q 2 -

∂TC∂Q2

= 0 i.e. MR2 – MC = 0

so: MR1 = MR2 = MC when profits are maximized)

- Possible outcomes in the two market model:

- Sell in both markets (as in the example)

- Sell to only one market (possible if MC is always above MR in one of the markets)

- Don’t produce at all (e.g. always have MC>40 in the example below).

12

An Algebraic Example: Two Markets with Different Demand Curves Market 1 demand: P1= 27.5-2.5Q1 so MR1=27.5 - 5Q1

Market 2 demand: P2= 40- 5Q2so MR2=40 - 10Q2

Marginal cost: MC = 1∙ (Q1+Q2) note: it depends on total output.

Algebraic solution?

Assuming it is worthwhile to produce in both markets the discussion above tells you that: MR1 = MR2 = MC when the monopolist is maximizing profits.

So you could set: MR1= MR2 :27.5 - 5Q1 =40 - 10Q2 (or 4Q2-2Q1 = 5)

Then use either MR1=MC or MR2=MC, lets use the latter:40 - 10Q2 = (Q1 +Q2) (or 40-11Q2 = Q1)

Now you have 2 linear eqns in two unknowns Q1 and Q2. Solve!

e.g. use the last condition to replace Q1 in: 4Q2-2Q1 = 5 then solve for Q2. (Q2=3.27)

now find Q1 by substituting Q2=3.27 into:27.5 - 5Q1 =40 - 10Q2 you get Q1=4.04

Now that you have Q1 and Q2 you can find P1 and P2 (just substitute the solutions to the quantities into the appropriate demand curves).

This gives: P1 = 27.5-2.5 (4.04) = 17.4P2 = 40 -2.5 (3.27) = 23.65

Combined output (Q1+Q2)=7.31

13

- An alternative way to solve the problem? (have a look on your own) find the combined MR curve in the above example then set combined MR=MC. Then solve for Q1+Q2, once this is known you can calculate MR1 and MR2 and then Q1, Q2 then P1, P2.

e.g. Combined MR is discontinuous: as long as MR>27.5 sells only in

Market 2. - initially combined MR = 40-10Q

- When selling in both markets must sum MR1 and MR2 over quantities to get the combined MR curve.

How? Solve MR1 = 27.5 -5Q1 for Q1= (27.5-MR1)/5

Solve MR2 = 40-10Q2 for Q2= (40-MR2)/10

Now: MR1=MR2=MR along this segment. So add Q1+Q2:

Q1+Q2= ( 95-3 MR) /10

Solve for MR to get combined MR: MR = [95-10 (Q1+Q2)]/3

(combined D-curve can be found the same way: sum across quantities at a given P)

then when maximizing profit: MR=MC[95-10 (Q1+Q2)]/3 = Q1+Q2 so Q1+Q2=7.31

(as above)

(now you can find combined MR=MR1+MR2, and use the result to find Q1 and Q2, etc.)

14

Pricing and Elasticity:

- Notice that the price charged will be higher in the market with least elastic demand.

define: P1 as price in market 1 and P2 as price in market 2 1 as the price elasticity of demand in market 1 2 as the price elasticity of demand in market 2.

when producing for both markets:

MR1 = MR2 on the last unit produced

but we know:

P1 ( 1 + 1/ 1 ) = P2 ( 1 + 1/ 2 )

P1 = ( 1 + 1/ 2 )P2 ( 1 + 1/ 1 )

e.g. if 2 =-2 and 1 =-3 then

P1/P2 = .5 / .67 < 1 so P1 < P2

(makes intuitive sense: those who are most price sensitive pay less)

15

- Some examples of Third-Degree price discrimination:

- Student discounts (students have lower income and lower WTP on average).

- Senior discounts (more time on average to shop for bargains? Maybe lower income on average: lower WTP)

- Airfares “Saturday-night stayover” rates and business travellers.

- Price differences by location: could reflect costs but in some casesmay largely be price discrimination.

- Price of same pharmaceuticals in poor and rich countries.

(see also Harford chapter on the Assignment 2 for examples)

16

Second-Degree Price Discrimination:

- The monopolist charges a schedule of prices with the price on extra units declining as the consumer buys more.

e.g. charge $5 for each of the first two units bought, $3 for each of the next two and $1 for each purchase over five units.

- price discrimination on the units bought by a given consumer but not across consumers.

- This can allow the monopolist to take advantage of differences in willingness to pay for various units of the good,

i.e., take advantage of demand curves for individual buyers that are downward sloping (high WTP for first few units, lower WTP for additional units consumed)

- Allows the monopolist to capture more consumer surplus than the single price case but not as much as the perfectly discriminating monopolist.

- An example in diagrams:

- Start with demand curve for a typical buyer (say market consists of many identical buyers?)

- Single-price monopoly solution: MR=MC say gives P1, Q1.

- Would the monopolist be willing to sell more units (given it has charged P1 and sold Q1)?

- Treat like a single-price monopoly problem with new demand curve equal to old minus Q1. Set MR2=MC.

- Generally can raise profits by selling additional units at a lower price (P2): see diagram.

17

- Can do even better than this if you recognize interdependence of first stage and second stage.

i.e. set P1 recognizing that it affects size of left-over market at the second stage.

- Could imagine extending this: charge a third, fourth, fifth etc. price

for still more units.

- how many prices in the schedule? if complex pricing is costless to administer then move toward perfect price discrimination!

In practice complexity is not costless.

- Notice: need to prevent people buying additional units at lower prices from reselling to those buying initial units at high prices if this is to work.

18

Two-Part Tariff or Two-Part Pricing: an Example of Non-linear pricing

- “Disneyland Dilemma”! W. Oi Quarterly Journal of Economics 1971.

- Text discussion of this type of scheme: pp. 164-65 (older edition: 135-136)

- Key aspect: two-part pricing(1) Fixed charge; and (2) marginal charge.

- Imagine an amusement park operator facing a typical downward sloping demand curve for rides.

- say like the usual single-price monopolist it sets price and output of rides so that MR = MC (call the price P*)

- Say that at the single-price monopoly outcome a typical consumer has a typical demand curve for rides (downward-sloping).

- indicate consumer surplus when price is P* as area “A+B”. (next page)

- The operator can do still better by also charging an admission fee in addition to its per ride price.

i.e., this is “two-part pricing” or a “two-part tariff”.

- How much would the admission fee be?

- given the price per ride of P* the maximum entrance fee is area A+B.

- notice that the monopolist gets all the surplus: fee turns consumer surplus into producer surplus.

19

- Model above assumed that P* was set as if a single-price monopolist.

- If the firm knows that it will also charge an entry fee at what level will it set the price P*?

- The firm will want the efficient outcome (P**=MC) as this maximizes total surplus (the fee allows it to take all surplus).

- Disneyland? P**=0 (roughly the MC of a ride), entry fee only.

- Other examples of this type of arrangement?

- Cell phone packages: often a fixed fee plus charges based on usage.

- Electricity pricing: often a fixed fee plus charges per KwH.

- Club pricing (text example: tennis club with membership and court fees)

20

Efficiency and Monopoly:

- Single-price Monopolist (see above):

- at profit maximizing outcome: Price > MC

- what someone will pay for one more unit of the good is greater than the extra resource cost: some extra consumer and producer surplus could be created by raising output.

- the monopoly outcome is inefficient.

- size of efficiency loss (deadweight loss, excess burden):

- area between height of demand curve and MC curve from output where MR=MC to where MC intersects demand curve.

- from an efficiency sense price is too high and output too low.

21

- The efficiency loss gives an economic justification for policies limiting monopoly power (anti-trust legislation: Canada: Competition Act ).

- The political reason for regulation likely has more to do with the distributional consequences of monopoly.

i.e., higher monopoly price transfers consumer surplus to producers.

- Perfect price discrimination:

- no efficiency loss: monopolist produces up to where P = MC .

- distribution: All the surplus goes to the monopolist!

- Imperfect price discrimination:

- typically between the two extremes: smaller efficiency loss than single-price monopoly, larger than perfect discrimination case.

- Efficiency vs. equity: two criteria for policy

- price discrimination enhances efficiency but seems inequitable.

i.e. different prices for different people.

22

Policy Response to Monopoly:

- A standard policy response to monopoly is to break it up, prevent it or penalize the exercise of monopoly power.

- Canada: Competition Bureau.

e.g. Bureau is opposing the proposed acquisition of Office Depot (Grand and Toy) by Staples (December 2015)

(http://www.competitionbureau.gc.ca/eic/site/cb-bc.nsf/eng/04012.html)

Bureau penalized Toyo Tire and others for bid-rigging (acting like a cartel) when selling anti-vibration parts to Toyota.

(http://www.competitionbureau.gc.ca/eic/site/cb-bc.nsf/eng/04013.html )

(policies to move things toward competition)

Some examples of legal penalities: (http://www.competitionbureau.gc.ca/eic/site/cb-bc.nsf/eng/01863.html )

- Another policy: regulate the monopoly

e.g. impose a price ceiling at the efficient price level (P=MC). - regulating prices in monopoly industries not unusual.

- What if it is a natural monopoly?

- with large economies of scale the market will always tend toward monopoly.

- the monopolist will produce where MR=MC

- there will be an efficiency loss.

- but given cost structure: competitive market impossible.

23

- Efficiency requires setting Price = MC.

- with a natural monopoly this will often involve making a loss.

e.g. consider cost structure:

Fixed cost and constant marginal cost:

TC = F + m Q F = fixed cost Q= output m = marginal cost

P = m then P < AC = (F/Q) + m (loss)

- with flat or falling MC setting price = MC (efficient outcome) will result in the firm making a loss.

24

- Some possible Policy Solutions when faced with natural monopoly?

- Public enterprise:

- government run monopolist.

- efficiency requires making a loss.

- how to cover this (taxes will create their own efficiency losses).

- incentive issues: will public enterprises be more badly run than private firms?

e.g. cost curves may be higher for public enterprises if they are less well run (another source of efficiency loss)

- see text discussion: pp. 421-423.

- Regulation:

- government regulates the private monopolist.

e.g., could control price: price ceiling could give efficiency could regulate rates of return (incentives here to

inflate costs of investment)

- Contracting out:

- government specifies in detail what it wants provided and accepts bids from private firms to provide the good or service.

- Could avoid some of the problems of the public enterprise.

25

- “Detail”Monopoly and Innovation: Some Considerations

- Questions and concerns about what monopoly does in the long run.

- Does lack of competitive pressure discourage innovation?

(model of firm behaviour and this: if above is true the firm is not a profit maximizer)

- Does the existence of monopoly profits provide finance for innovation?

(role of financial markets: statement may be true if financial marketsare inefficient and firm’s must finance expansion with own profits)

- Do monopoly profits provide other firms with an incentive to create alternatives to the monopoly good/service?

Should we care about monopoly?

- Concerns:

- Distribution and efficiency issues.

- Equity (fairness) issues and price discrimination.

- Possible innovation problems.

- Question of whether the government can do better?

- regulation, public enterprise: better or not?

26