non-trivial pricing strategies for firms with market power so far, we’ve been discussing cases...

Non-trivial pricing strategiesfor firms with market power

So far, we’ve been discussing cases when every unit of firm’s output was priced the same.

Now, it’s time to look at more interesting cases.

CS = MV – P

(marginal value)

Welfare measures Every consumer has some subjective valuation for each unit of the good, called marginal value, or marginal “utility”. Think of it as the highest price she would pay, or what the good is “worth” to her. Consumer surplus (CS) – equals the value (“utility”) a consumer gets from a good but doesn’t have to pay for. CS from an individual purchase: (price)

(price actually paid)

P

Q

Demand, derived from a schedule of

marginal valuesMarket priceCS

Total market CS is represented by the area under the demand curve and above the price.

By analogy, producer surplus (PS) is the difference between the actual price and the minimum price at which the producer would agree to sell the good (the latter usually equals the marginal cost, MC).

PS = P – MC

Note the concept of PS is somewhat similar to but not the same as profit!

P

Q

Total producer surplus in the market is represented by the area below the market price level and above the supply curve.

Supply, derived from a marginal

cost scheduleMarket pricePS

In a free market…

$

S

D

Q

… the sum of consumer and producer surpluses is maximized

CS

PS

Every opportunity to make someone better off through exchange of goods is taken advantage of.

P

Q

For a monopoly…

D

MC

MR10 20

60

35

10

Profit

CS

DWL

All pricing strategies to be discussed below are designed to increase the chunk of the market surplus that goes to the producer, thus further increasing its profit.

1. Price discrimination (3rd degree)

Price discrimination is a general name for the practice of charging different consumers or groups of consumers different prices for the same product.

Consider a town with 2000 college students and 1000 retirees.

Students want to see a movie as long as the price doesn’t exceed $8. Elderly people are interested only if the price is $5 or below.

If you set the ticket price at $8, the revenue is

TR = P * Q = 8 * 2000 = $16,000

If you lower the price to $5, the revenue is

TR = P * Q = 5 * (2000 +1000 ) = $15,000

If you frame it as a discount for seniors, your revenue is

TR = 8 * 2000 + 5 * 1000 = $21,000

An important condition is that students are ineligible for the discount.

Such practice of splitting the market into two or more groups and charging each a separate price – is called third-degree price discrimination.Conditions necessary for its success:

• Presence of at least two groups with known demand differences;

• The ability of the firm to distinguish among groups;The size of a group does not matter! All that matters is elasticity of demand by each group.The group with the more elastic demand gets charged a lower price, and vice versa

•Certain degree of market power to the firm;

•The possibility of product resale has to be eliminated.

Other examples of 3rd degree price discrimination:

• Bus fare

• Museum admissions

• Airfare contingent on Saturday night stay

• Store coupons

2. Perfect (first-degree) price discrimination

The hypothetical case when each consumer is charged the maximum price she is willing to pay (her subjective value, that is).

It is rarely observed in real-world situations due to the difficulty of determining each consumer’s Marginal Value.

Still, we can think of examples when a seller tries to achieve this.

The chances for success of such practice are higher when the seller has only a few customers. Also, consider person-to-person sales.

$

MC

QP

First-degree price discrimination

- For every customer, (individual) price gets pushed all the way up to his/her MU;

Individual prices

$

MC

QP

First-degree price discrimination

- For every customer, (individual) price gets pushed all the way up to his/her MU;- Producer gets the ENTIRE market welfare

3. Volume discounts (a.k.a. 2nd degree PD)

Also a form of price discrimination, since the buyers self-select themselves into high-volume and low-volume buyers, and each group pays a different per-unit price.

Suppose you are a seller who has certain stock of shirts you need to sell. For simplicity, let’s say your goal is to maximize revenue.

Every day, a hundred customers visit your store.

Let’s start with the unrealistic case when• All customers are identical;• You know everyone’s valuation for successive shirts:

Shirt # MarginalValue, $

1 152 103 64 2

You need to decide what price tag to put on the shirt rack.

If charging a flat rate for each shirt:

P = $15, TR = 15*100 = $1,500P = $10, TR = 10*200 = $2,000P = $6, TR = 6*300 = $1,800P = $2, TR = 2*400 = $800

A better idea:

Recognize the fact that each successive shirt is valued less than the previous one and price them accordingly. For example:

P = $15, buy one, get second for 40% off

TR = (15 + 9)*100 = $2,400 – better than any of the above cases

Of course• People have different tastes, therefore different utility schedules. • You never know what those schedules are.

But stores do know that the willingness to pay falls with every successive shirt.

Therefore, the above example explains how some stores in some cases may benefit from running sales of the “Buy one, get second at X% off” type.

Other examples of volume discounts:

• declining rates in parking garages,

• pricing by (some) electric companies,

• frequent flyer programs.

4. Bundling, or tie-in sales

The table below shows how Bill and Linda value two rides at an amusement park.

RidePerson

Mamba Timberwolf

Bill $5 $1Linda $3 $2

Suppose you, the manager of the amusement park, first decide to charge a separate price for each ride.What is the best price to charge?

For Mamba:P = $5, TR = 5*1 = $5P = $3, TR = 3*2 = $6

For Timberwolf: P = $2, TR = 2*1 = $2P = $1, TR = 1*2 = $2

Total revenue from Linda and Bill = 6 + 2 = $8

A better idea: sell the two rides together, as a “bundle”.

Best price for the bundle:P = $5, TR = 5 * 2 = $10 - better than under “regular” pricing

This strategy works best when the valuations of different consumers for different goods or services are negatively correlated.

Other examples – Newspapers, Cable TV.

RidePerson

Mamba Timberwolf M + T

Bill $5 $1Linda $3 $2

$6$5

P

Q

5. Block pricing

D

MC

MR 6

1.5

2

1

0.5

If selling individually:The best price is $1.25

1.25

Demand of an individual consumer

63

5. Block pricing

If selling individually:Profit =


QD

MC

MR 6

1.5

2

1

0.5

1.25

63

5. Block pricing

If selling individually:Profit = (1.25 – 0.50)*3 = $2.25


QD

MC

MR 6

1.5

2

1

0.5

1.25

63

5. Block pricing

Each consumer values units up to #6 above MC


QD

MC

MR 6

1.5

2

1

0.5

1.25

63

5. Block pricing

What if we sell this product ONLY as a six-pack?


QD

MC

MR 6

1.5

2

1

0.5

1.25

63

Pricing the 6-pack:

A customer would pay:

Up to $1.75 for the first unit;Up to $1.50 for the second;Up to $1.25 for the third;Up to $1.00 for the fourth;Up to $0.75 for the fifth;Up to $0.50 for the sixth.(units after #6 are not worth producing)

Total value consumer places on a six-pack is $6.75. That is the price we should charge.

5. Block pricing

Profit under block pricing

QD

MC

MR 6

1.5

2

1

0.5

1.25

63

and under regular pricing

P

Q

6. Two-part pricing

D

MC

MR10 20

60

35

10


The profit-maximizing point is P = $35, Q = 10, Π = $250Same price + one-time fee equal to consumer’s CS from purchase

P

Q

6. Two-part pricing

D

MC

MR10 20

60

35

10


Same price + one-time fee equal to consumer’s CS from purchase

An even better idea: lower the per-unit price and keep charging the fee (which will now be larger)

P

Q

6. Two-part pricing

D

MC

MR10 20

60

35

10


An even better idea: lower the per-unit price (P=MC=$10) and keep charging the fee (which will now be larger)

P

Q

6. Two-part pricing

D

MC

MR10 20

60

35

10


The i-Phone case

Prices are falling over time – WHY?

Possible explanations:

- Obsolescence – Better products developed – demand drops

- More firms enter – stronger competition – profit margin drops- More efficient production technologies developed – production costs drop – price drops- “Intertemporal price discrimination”, or separating customers across time, based on their patience factor

$

MC

Demand from all the consumers who will ever want your product

Q

You could satisfy them all at once…

$

MC


Q

$

MC


Q

… or, you could serve them one group at a time,starting with those who value the good the most

April

May

June

July

$

MC


Q

non-trivial pricing strategies for firms with market power so far, we’ve been discussing cases...

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