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:
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.
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)
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.
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?
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.
- 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)
- 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 )
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.
- 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.
- 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.
(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∂Q1 - ∂TC∂Q1 = 0 i.e. MR1 – MC = 0
∂(Profit)∂Q2 = P2 + Q2∙∂P2∂Q2 - ∂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).
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- 5Q2 so 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) = 17.4
P2 = 40 -2.5 (3.27) = 23.65
Combined output (Q1+Q2)=7.31
- 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.)
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
h1 as the price elasticity of demand in market 1
h2 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/ h1 ) = P2 ( 1 + 1/ h2 )
P1 = ( 1 + 1/ h2 )
P2 ( 1 + 1/ h1 )
e.g. if h2 =-2 and h1 =-3 then
P1/P2 = .5 / .67 < 1 so P1 < P2
(makes intuitive sense: those who are most price sensitive pay less)
- 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 cases
may largely be price discrimination.
- Price of same pharmaceuticals in poor and rich countries.
(see also Harford chapter on the Assignment 2 for examples)
Second-Degree Price Discrimination:
- The monopolist charges a schedule of prices with the price on extra units
declining as the consumer buys more.