econs 305 - pricing and advertising - part 1 · 2017. 10. 18. · price discrimination is a method...

EconS 305 - Pricing and Advertising - Part 1

Eric Dunaway

Washington State University

[email protected]

October 29, 2015

Eric Dunaway (WSU) EconS 305 - Lecture 26 October 29, 2015 1 / 50

Introduction

Our next unit is going to cover price discrimination and advertising.

Price discrimination is a method for a monopolist to charge di¤erentprices to di¤erent people based on their characteristics.

We see it all the time.

Today, we will cover rst and third degree price discrimination.

Dont forget, exam 2 is a week from today.


Price Discrimination

Just what is price discrimination?

It can take two forms: either a temporary sale, or a permanentdiscount on the price of a good.

Up until now, we have been using uniform pricing. This is where arm can only select one price to charge to an entire market.

Now we will consider nonuniform pricing, where a rm can chargedi¤erent prices to di¤erent people.

The key is how the rms di¤erentiate their customers.



Why price discriminate?

To increase prots, of course!

By price discriminating, the rm, acting as a monopolist, can "steal"even more of the consumer surplus from the consumers.

At the same time, the monopolist can also turn some of the deadweight loss back into producer surplus.



A quick example from Perlo¤:

A theater in town is holding a showing of a new movie this weekend.Students will see the movie if the price is 10 dollars or less. SeniorCitizens will see the movie if the price is 5 dollars or less.

We would say that the studentswillingness to pay is $10, whereasthe senior citizenswillingness to pay is $5.

Lets say that there are 10 students and 5 seniors. Depending onwhat price the theater charges, the movie theaters prots look like

Price Student π Senior π Total π$5 50 25 75$10 100 0 100

In this case, the rm would do better by charging a higher price andlosing the senior market.

Could they do better?



Certainly! What if the theater charged $10 to students and $5 toseniors? Its prot would be

Price Student π Senior π Total π$5 50 25 75$10 100 0 100

$10/$5 100 25 125

this way, the rm could increase its prots by charging less to theseniors and getting them to come see the movie, too.

In this case, we would say that the seniors have more elastic demandThey arent willing to pay as much as the students, so a discountedprice is necessary to get them in to the market.



Real world example: Disneyland.

They charge $199 to out of state residents for a 3 day pass.But they only charge $154 to California residents.

Why? People who are travelling from out of state are likely onvacation and are planning on going to Disneyland regardless. Theyare less sensitive to the price than the local residents who havealready been several times.

The locals are likely more sensitive to the price.



How can rms establish price discrimination?

First, the rm has to have market power. If a market were perfectlycompetitive, there would be no room for price discrimination.Second, they need to have ways to di¤erentiate customers. This couldbe by age, occupation, location, etc.

More importantly, these groups need to have di¤erent demand curves,as well.

Lastly, the rm has to have some way to prevent resale (arbitrage). Ifthey cant a person could get a discounted price, then sell it to a higherpriced group for a prot.



Lets talk a little bit about preventing resale.

This is probably the most essential component to price discrimination.If consumers could resale (arbitrage) the market, the people who canget a cheaper price can buy the item, then resell it to people who wouldhave to pay a higher price, stealing the prots from the monopolist.In our theater example, the senior citizens could pay $5 for a ticket,then sell it to a student for less than $10, making both the seniorcitizen and the student better o¤, but the monopolist worse o¤.Practically, the theater can prevent arbitrage by having the ticketholder show proof that they belong to their respective age group to getthe price discount (identication).Likewise, Disneyland checks the identication of those who want alocal discount.


First Degree Price Discrimination

Lets start with rst degree price discrimination.

Also known as perfect price discrimination.

In this case, the rm is able to identify every single customer as anindividual group.

In order to do this, the rm must be able to identify every consumerswillingness to pay, or reservation price.



The reservation price is the highest price a consumer is willing to payfor a good or service.

If the monopolist could identify this, they could maximize their protsby charging that person exactly that price.

In this case, the rm captures all of the surplus that would be sharedbetween the producer and the consumer.



We can show graphically what would happen using a supply anddemand curve.

Recall that we can think of the demand curve as having many di¤erentconsumers distributed across the line, with those with a higherreservation price higher on the demand curve.In this case, the rm charges every person the price where they land onthe demand curve.

Lets look at it graphically.



Q

p

DS



Q

p

DS

ProducerSurplus



Its interesting to see that there is no dead weight loss under rstdegree price discrimination.

Every consumer who should enter the market enters the market.Everyone pays their maximum willingness to pay, meaning that there isno consumer surplus.

Is this e¢ cient?

Yes, becuase there is no dead weight loss.

Is this fair?

Thats an opinion.



Why dont we see more of rst degree price discrimination?

Its not feasible.First of all, rms dont know every consumers reservation price.Furthermore, it would be in the interest of consumers to hide their truereservation price in order to get a better deal.The costs involved to actually determine these values are huge, andwould eat up the majority of the monopolists prots.



A quick example.

Consider a banana market where a single rm acts as a monopolist.There are three consumers, Stuart, Kevin and Bob.

Stuart values a banana at 5, Kevin values a banana at 3, and Bobvalues a banana at 1.It costs 2 to make a banana.

If the banana monopolist knew all the reservation prices and couldprevent the consumers from reselling bananas, what price would itcharge to each of them?



The banana monopolist would charge Stuart 5, Kevin 3, and wouldntsell a banana to Bob.

Poor Bob.

The banana monopolist captures all of the surplus from Stuart andKevin, and lives happily ever after.

Lets look at another type of price discrimination.


Third Degree Price Discrimination

Lets talk about third degree price discrimination.

This is also known as group price discrimination.

In this case, the rm seperates the consumers into di¤erent groupswith di¤erent demand functions, then charges individual prices forthose groups.

Figuring out groups is much easier than guring out every singleindividual.



Lets go back to our example with movie theaters. Suppose thedemand for students (t) and the demand for seniors (e) were asdepicted on the next slide.

For simplicity, we will assume that the supply curve is at (This isactually very close to reality for a movie theater).



Q

p

Dt

S

De



As we can see, the demand for the elderly is atter than the demandfor the students.

They are more elastic, and more sensitive to the price of a movie ticket.

If the monopolist were only able to charge one price to the entiremarket, it would have to aggregate the demand curves and then solve.



Q

p

Dt

S

De



Q

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D

S



Q

p

D

S

MR



In this case, we see our standard kinked demand curve. This results ina jump (discontinuity) in the marginal revenue curve.

Otherwise everything else remains the same.

Like before in monopoly, we nd where marginal revenue equalsmarginal cost, then set the price based on the aggregate demandcurve.



Q*

p*

Q

p

D

S

MR



Now, lets consider a situation where the monopolist could pick adi¤erent price for both groups of consumers.

It could enforce this price by checking identication at the door.

In this case, the monopolist would set its price and quantity level foreach group seperately.



Q

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Dt

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Q

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Dt

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MRt



Q

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Dt

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MRt

Qt

pt



Q

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De



Q

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MRe



Q

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MRe

Qe

pe



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Qe

pe

Dt

Qt

pt

De



Q

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Qe

pe

Dt

Qt

pt

Q*

p*D

De



As we can see, the monopolist will charge a lower price to the elderly,but a higher price to the students.

Comparing this with the uniform price equilibrium, we would nd thatthe single price would be somewhere inbetween the two.

Intuitively, the monopolist gives up a small amount of quantity bycharging a higher price to students, but gains a large quantity bycharging a lower price to seniors.

In the end, the monopolists prots increase.



What about welfare?

This depends.We will still have dead weight loss.Welfare might go up or down from the monopoly level. It depends a loton the shape of the curves and how much the quantities vary.Its also nearly impossible to draw.



Example from Perlo¤ (12.3)

A monopoly book publisher is selling in two di¤erent countries thathave inverse demand curves of

p1 = 6�12q1

p2 = 9� q2

and marginal costs are constant at MC = 1.

First, lets look at the equilibrium if the monopolist cannot pricediscriminate.



First, we have to aggregate the demand curve. (Remember to turnthem back into demand curves before adding them together. Iskipped this.)

For prices above 6, only country 2 will be in the market. We end upwith the aggregate inverse demand curve of

p = 9� q if p > 6

p = 7� 13q if p � 6

These have corresponding marginal revenue curves of

MR = 9� 2q if p > 6

MR = 7� 23q if p � 6



Q

p

D

S

9

6

1

18



Q

p

D

S

9

6

1

18

MR



We can nd the equilibrium price by setting marginal revenue equal tomarginal cost.

From the gure, it appears that this will happen at p � 6, so I will usethat equation.

MR = MC

7� 23q = 1

23q = 6

q� = 9

Plugging this back in to the demand curve yields

p� = 7� 13q� = 4



Q

p

D

S

9

6

1

18

MR

4

9



What would happen if the rm could e¤ectively price discriminate bygroup?

Fortunately, this is much easier.

For each individual country, we optimize as if it were a monopoly.

For country 1, we have

MR = MC

9� 2q = 12q = 8

q1 = 4

and country 1 demands only 4 units. To get the price we plug it backinto its demand function

p1 = 9� q1 = 8



For country 2, we have

MR = MC

6� q = 1q2 = 5

and country 2 demands 5 units. Once again, to get the price, we plugit back into its demand function

p2 = 6�12q2 = 3.5

and as we can see, country 2 is charged a much lower price thancountry 1.



Lets look at prots.

For uniform pricing, the rm receives

TR = p�q� = 4(9) = 36

TC = q� = 9

π� = 36� 9 = 27

And for third degree price discrimination, the rm receives

TR = p1q1 + p2q2 = 8(4) + 3.5(5) = 49.5

TC = q1 + q2 = 9

π = 49.5� 9 = 40.5

and the monopolists prots from price discriminating are much higher!



Some intuition.

Country 1 had much more elastic demand than country 2. (Its demandcurve is atter.)Giving each country a di¤erent price allowed for a much larger quantityof country 1, and less of a reduction of quantity from country 2 due totheir higher price.This resulted in much higher prots for the monopolist.


Summary

Price discrimination increases prots for the monopolist.

Depending on how groups can be identied, the monopolist will try tocharge as many di¤erent prices as possible to di¤erent groups.


Preview for Monday

Second degree price discrimination.

What does Costco have in common with the local bar?

Advertising.


econs 305 - pricing and advertising - part 1 · 2017. 10. 18. · price discrimination is a method...

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