EconS 305 - Pricing and Advertising - Part 2 · 2017. 10. 18. · Introduction Today, we will...

EconS 305 - Pricing and Advertising - Part 2

Eric Dunaway

Washington State University

[email protected]

November 2, 2015

Eric Dunaway (WSU) EconS 305 - Lecture 27 November 2, 2015 1 / 47

Introduction

Today, we will nish up our unit on price discrimination andadvertising.

There is one more type of price discrimination to cover:second-degree price discrimination.


Second Degree Price Discrimination

Second-degree price discrimination is probably the most di¢ cult ofthe three to understand.

Rather than guring out how their consumers are di¤erent, insecond-degree price discrimination the monopolist creates a menu ofdi¤erent options designed for di¤erent types of people and then lets theconsumers self-select into their best bundle.Most of the math involved is too complicated for this course. We willbe focusing on intuition.

In essence, it can be broken down into four di¤erent types.

Quantity DiscountingBlock pricingTwo-part tari¤sBundling


Quantity Discounting

With quantity discounting, a monopolist gives a discount with everyadditional unit purchased.

We see this all the time at the grocery store. A two liter bottle ofsoda typically costs much less per ounce than a twenty ounce bottleof the same soda.



To implement this, the monopolist uses a pricing schedule.

The monopolist creates a menu of quantities and their respective prices.The consumers then can observe the menu of quantities and prices,then self-select into whichever bundle gives them the highest utility,subject to their own budget constraints.

The non-linear aspect of this type of price discrimination comes fromthe fact the expenditure function (the amount the consumer pays) isnow curved as we increase price, as opposed to straight (as it wasbefore).



pq

q

TotalExpenditure



Under quantity discounting, the consumer will eventually pay less at ahigher quantity than they will under traditional linear pricing.

At the same time, the monopolist can take advantage of theconsumer and raise prices for small quantities to encourage theircustomers to buy more of the good.

This type of pricing is very similar to our next type of second degreeprice discrimination: block pricing.


Block Pricing

With block pricing, a monopolist charges an initial price for the rstfew units of a good, then a lower price for the next few units, then aneven lower price for the next few and so on.

Avista uses this kind on pricing for electricity, and the US Income taxsystem works similarly (although it is not a form of pricediscrimination).

Basically, if we looked at the producer and consumer surpluses, themonopolist prices such that it takes blocks out of the consumersurplus.

This could actually be welfare improving.


Block Pricing

Heres an example.

Consider a monopolist facing a linear inverse demand curve of

p = 45� q

and constant marginal costs of MC = 5.

Our marginal revenue will be

MR = 45� 2q


Block Pricing

Setting up our optimal marginal revenue equals marginal costequation

MR = MC

45� 2q = 52q = 40

q� = 20

and from the inverse demand curve

p� = 45� 20 = 25

Putting it all together,

TR = p�q� = 20(25) = 500

TC = 5q� = 5(20) = 100

π = TR � TC = 400Eric Dunaway (WSU) EconS 305 - Lecture 27 November 2, 2015 11 / 47

Block Pricing

p

q

D

SMR

45

20

25

45


Block Pricing

p

q

D

SMR

45

20

25

45

CS

PSDWL


Block Pricing

Now, lets have the monopolist use block pricing. Arbitrarily pickingquantity breakpoints, the monopolist can charge the correspondinginverse demand curve price for all units under that breakpoint.

Sounds complicated. Basically, pick a breakpoint, plug it in to theinverse demand function, and charge that price up to the breakpoint.

Using breakpoints of 10 units

Breakpoint PriceFirst 10 units p1 = 45� 10 = 35Second 10 units p2 = 45� 2(10) = 25Third 10 units p3 = 45� 3(10) = 15


Block Pricing

In this case, our total revenue, total costs, and prots will be

TR = p1q1 + p2q2 + p3q3 = 35(10) + 25(10) + 15(10) = 750

TC = 5q1 + 5q2 + 5q3 = 5(10) + 5(10) + 5(10) = 150

π = TR � TC = 600

Clearly, prots rise signicantly under block pricing.

Lets see what happens to surplus.


Block Pricing

p

q

D

SMR

45

20

25

45

CS

PSDWL


Block Pricing

p

q

D

S

45

20

25

45

35

15

5

10 30

CS

PS

DWL


Block Pricing

As we can see, the producer surplus clearly goes up, while theconsumer surplus does go down a bit.

The most impressive part is that the dead weight loss has almostcompletely disappeared.

If the monopolist used more "blocks," it could reduce the dead weightloss even more, with an innite amount of blocks eliminating itcompletely.

That would actually just turn in to rst degree price discrimination,though.

Lets look at the expenditure function.


Block Pricing

pq

q

TotalExpenditure


Block Pricing

This expenditure function is similar to its quantity discriminationcounterpart. The only di¤erence is that this curve is not smooth, butrather a set of kinked lines.


Two-Part Tari¤

Our next type of second-degree price discrimination is a two-parttari¤.

Perlo¤ calls this two-part pricing.Finally, the Costco example!

In a two-part tari¤, the monopolist charges an access fee, then onlycharges the marginal cost per unit purchased.

Essentially, the monopolist makes the consumers pay for the right topurchase the good.


Two-Part Tari¤

Lets break that down a bit.

Having the price be equal to marginal cost actually gives themonopolist zero prots for each unit sold.They key is the access fee. The monopolist can charge an access feeequal to the entire consumer surplus and take it all for themself.

Lets see it graphically when the monopolist prices at marginal cost.


Two-Part Tari¤

p

q

D

S

45

20

25

45

5

CS


Two-Part Tari¤

In this situation, all of the welfare is in the form of consumer surplus.

To optimize with a two-part tari¤, the monopolist needs to gure outwhat the consumer surplus is, and charge that as a fee.

In our example,

CS =12(45� 5)40 = 800

and thus, the monopolists optimal two-part tari¤ would be to chargean access price of 800, and then a price of 5 per unit sold.The monopolists prots are equal to 800 in this case.


Two-Part Tari¤

p

q

D

S

45

20

25

45

5

PS


Two-Part Tari¤

Now, the entirety of welfare is in the form of producer surplus.

At the same time, there is no dead weight loss.

If designed well, and all consumers are identical, two-part tari¤s aree¢ cient.

If consumers are di¤erent, there are many di¤erent kinds of access feesthat are possible. All of them will yield dead weight loss.


Two-Part Tari¤

This is the pricing model used by both Costco and local bars.

At Costco, you pay a yearly membership fee. This is where all ofCostcos prots come from.

Costco only breaks even (covering all its operation costs), but doesntmake any prots from the sale of its goods.

At the local bar (typically on weekends), you pay a cover charge.

This results in the drinks being cheaper (in theory ). The bar alreadyextracted all of your estimated surplus for the night in the cover charge.

As a note, these two-part tari¤s are not perfect since all consumersare di¤erent.


Two-Part Tari¤

pq

q

TotalExpenditure


Two-Part Tari¤

In this case, the expenditure function jumps from zero to the higherpoint, and then grows very slowly. It is non-linear just because of thisdiscontinuity.


Bundling

The last case of second-degree price discrimination I wanted to coveris bundling.

This can be either mandatory bundling, or nonmandatory.

The monopolist groups multiple products together and sells them forless than the sum of their individual parts.


Bundling

Bundling happens all the time. They even call it by name.

Cable companies want to bundle cable, phone and internet.Printers come bundled with ink cartridges.

I nd it interesting that it is often cheaper to buy a new printer than itis to replace the ink.

Razors with replacement blades.Etc.


Bundling

Mathematically, the rm will have one product that depends onanother product for success.

For example, printers are useless without a compatible ink cartridge.By grouping them together, rms can get higher sales of both, anddont have to worry about their competitors selling knock o¤s.

They sacrice prots on the printer itself, making it up with a higherprice of ink.


Advertising

Advertising is a method for a monopolist to increase the demand ofits product.

It can be murky though, as advertising is useless under perfectcompetition.

A dead giveaway that a market isnt perfectly competitive is if therms in it advertise.

Furthermore, advertising amongst competitors is only e¢ cient if itspurpose is to increase knowledge of the product.

Advertising to compare your product to another with the intent ofpoaching sales causes dead weight loss.We are not going to cover this type of advertising.


Advertising

As said before, the goal of advertising is to increase the demand forthe product.

This would shift the demand curve to the right.

When this happens, both the equilibrium price and quantity sold forthe monopolist will increase, causing a gain in prots.


Advertising

p

q

D

SMR

45

20

25

45

35

3515

20

Profit


Advertising

Like in almost everything else we do, the decision of whether toadvertise or not will come down to the margin.

We would want to be able to determine the marginal benet ofadvertising (how much extra revenue we get from an additional unitof advertising) as well as the marginal cost of advertising (how muchone more unit of advertising costs).

The rm will advertise at the level where marginal benet equalsmarginal cost of advertising.

Lets look at an example. Dont worry about the math.


Example

Lets return to our earlier example where our monopolist faced alinear inverse demand curve of

p = 45� q

and constant marginal costs of MCq = 5. Recall that our equilibriumunder the standard monopoly model is

q� = 20 p� = 25 π� = 400

Now, lets add advertising to the model. Our inverse demand functionbecomes

p = 45� q + A0.5

where A represents one unit of advertising (an online ad, facebookposts, etc.). The cost of each unit of advertising is constant atMCA = 2.


Example

Our new total revenue function is

TR = pq = (45� q + A0.5)q = 45q � q2 + qA0.5

and since the monopolist needs to choose both its quantity and itsadvertising level, we have to get marginal revenues for both q and A

MRq = 45� 2q + A0.5

MRA = 0.5qA�0.5

Next, we set the marginal revenues equal to their respective marginalcosts

MRq = MCq45� 2q + A0.5 = 5

MRA = MCA0.5qA�0.5 = 2


Example

45� 2q + A0.5 = 50.5qA�0.5 = 2

This is just a system of two equations and two unknowns, which wecan solve!

A bit tougher than what we usually see, though.

Rearranging the second equation, we get

A0.5 = 0.25q

which we can substitute into the rst equation to get

45� 2q + 0.25q = 51.75q = 40

q� = 22.86


Example

Plugging this back into our second equation,

A0.5 = 0.25q� = 0.25(22.86) = 5.71

A = 5.712 = 32.65

and we can nd our price from the inverse demand curve

p� = 45� q� + (A�)0.5 = 45� 22.86+ 5.71 = 27.85

Lastly, for our prots,

TR = p�q� = 27.85(22.86) = 636.65

TC = 5q� + 2A� = 5(22.86) + 2(32.65) = 179.6

π� = TR � TC = 636.65� 179.6 = 457.05


Example

As we can see, the quantity, price, and prots all increased due to theadvertising.

This is because the advertising increased the demand for the product,and was a¤ordable.

Dont expect to see an advertising problem on the exam, the math isrough.

Be sure to know the e¤ects of advertising, though.


Summary

Price discrimination helps the monopolist capture surplus away fromthe consumer.

It also brings more consumers into the market.

There are many ways to price discriminate, and perform di¤erentlydepending on the situation.

Advertising is a method to increase the demand for a product.


Preview for the Next Week

Review Session on Wednesday.

Quick exam overview from me, then we move into an AMA session.I wont be preparing questions.

Exam 2 on Friday.

On Monday we start Game Theory!

We are going to look at how people and rms behave strategically.Yay! I love game theory.


Assignment 5-1, 5-2, and 5-3 (1 of 1)

This is an open ended question designed to make you think. A singleparagraph answer should be su¢ cient.

Note: For those not from the US, Black Friday occurs on the fourthFriday of November and is the largest shopping day of the year. Google"Black Friday Sales" for more information.

1. Economically, why do Black Friday sales exist?


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