1. 15. Firms, and monopoly
Varian, Chapters 23, 24, and 25

2. The firm The goal of a firm is to maximize profits Taking as given
Necessary inputs
Costs of inputs
Price they can charge for a given quantity
We will ignore inputs for this course (Econ 102, or I/O will cover this)

3. Standard theory Intuition Our approach today p(q)
Firm chooses a price, p, at which to sell, in order to maximize profits
Our approach today
The firm chooses a quantity, q, to sell
Inverse demand function is given
p(q)

4. Firm decision in the short run
Max p(q)q – c(q)
Differentiate wrt q and set equal to zero:
MR = MC
p(q) + qp’(q) = c’(q)
Revenue, R(q) = p(q)q
Cost
Marginal
cost
Revenue from
extra unit sold
Revenue lost on all
sales due to price fall

5. Perfect competition (many firms)
Max p(q)q – c(q)
Perfect competition: p(q) = p
p=MR = MC
p + 0 = c’(q)
Revenue, R(q) = p(q)q
Cost
Marginal
cost
Revenue from
extra unit sold
Firm is too small
to affect price

6. Pricing in the short run
Perfect competition:
p = 20
c(q) = q+0.1q2
Find the firm’s profit-maximizing q
Monopolist
p(q)= q
c(q) = q+0.1q2
Find the firm’s profit-maximizing q

7. Cost function definitions
c(q) = q+0.1q2
Fixed cost: the part of the cost function that does not depend on q
Variable cost: the part of the cost function that does depend on q
Total cost: FC+VC
Average total cost: (FC+VC)/q=c(q)/q

8. How many firms will there be?p
Perfect competition
In long run, competition forces profits to 0
P = ATC(q)
P = MC(q)
C’(q) = C(q)/q
Solve for q
ATC MC q

9. How many firms will there be?p
Perfect competition
Knowing q
P = MC(q)
Q=D(P)
#firms = Q/q
ATC MC
D(p) q

10. The long run outcome Perfect competition: D(P) = 600 - 20P
c(q) = q+0.1q2
Find the long run q
Find the long run price, and # of firms
Natural monopoly:
D(P) = P
c(q) = q+0.1q2
What is q when MC=ATC?
How many firms will there be?

11. Natural monopoly D(p)<q at p where MC=ATC
Happens when fixed cost high relative to
marginal cost
inverse demand
Fixed cost can only be covered by p>MC
ATC MC
D(p) q

12. Monopolist Natural monopolies
Electricity
Telephones
Software?
Monopoly can also be by government protection
Patented drugs
Imposed with violence
Snow-shovel contracts in Montreal

13. Monopolist No competition Monopolist free to choose price
MR(q) no longer constant p
Single price: set MR(q) = MC(q)
More elaborate pricing schemes to follow
Price discrimination

14. Monopoly pricing (no price discrimination)
Note:
When demand is linear, so is marginal revenue
P = A – Bq
MR = A – 2Bq pm
Profit MC
Demand MR qm
Optimal quantity set by monopolist

15. Inefficiency of monopoly
Dead weight loss pm
Mark-up over
Marginal cost MC
Demand MR qm q*

16. (Price) elasticity of demand
The elasticity of demand measures the percent change in demand per percent change in price:
e = -(dq/q) / (dp/p)
= -(p/q)*(dq/dp) < 0

17. Optimal mark-up formula
p(q) + qp’(q) = c’(q)
can be rearranged to make:
p = MC / (1 – 1/|e|)
This can be rearranged to yield:
(p – MC)/MC = 1 / (|e| - 1) > 0

18. Demand elasticity p p q q Elasticity > 1 Elasticity = 1
Constant elasticity
of demand
Elasticity < 1 q q
p = q -e
p = a - bq

19. Monopolist’s decision
Natural monopoly:
D(P) = P
c(q) = q+0.1q2
What q will monopolist choose?
What is their profit?
What is elasticity of demand at this price/quantity?

20. Monopoly in an Edgeworth box
Can we understand the inefficiency of monopoly in terms of our Edgeworth box analysis?
Recall: the market got the right prices…
…but monopolist doesn’t

21. “Market”-determined prices
Person B
wBx y
wBy
Contract curve
Endowment
wAy
Person A x
wAx

22. Suppose A could choose a price
Person B
wBx y
wBy
B’s price
offer curve
Endowment
wAy
Person A x
wAx

23. A chooses a point off the contract curve
Person B
wBx y
Competitive
equilibrium
wBy
A’s best
bundle
B’s price
offer curve
Endowment
wAy
Person A x
wAx

24. Price discrimination
Idea is to charge a different price for different units of the good sold
What does “different units” mean
Purchased by different people
E.g., children, students, pensioners, military
Different amounts purchased by a given person
E.g., quantity discounts, entrance fees, etc.

25. Three degrees of discrimination
First degree PD
Each consumer can be charged a different price for each unit she buys
Second degree PD
Prices can change with quantity purchased, but all consumers face the same schedule
Third degree PD
Prices can’t vary with quantity, but can differ across consumers

26. If you buy x units, you pay a total of T + cx
First degree PD
Outcome is
Pareto efficient
Consumer earns
no consumer
surplus
Profit of fully
discriminating
monopolist
MC = c
Profit of non-
discriminating
monopolist
Demand xm x*
Alternative pricing mechanism:
If you buy x units, you pay a total of T + cx
Entry fee

27. Entry fees in the Edgeworth box
Person B
wBx y
A’s best bundle
with PD is on the
contract curve
Entry fee paid
by B to A
wBy
B’s price
offer curve
Endowment
A’s best
without PD
wAy
Person A x
wAx
Recall: The 2nd fundamental theorem

28. With more than one consumer...
….charge a different entry fee to each
….but the same marginal price
Profit from consumer A
Profit from consumer B
MC = c
MC = c
Demand
Demand
x*A
x*B
Consumer A
Consumer B

29. Entry fees as “two-part-tariffs”
Let A’s consumer surplus be TA and let B’s be TB .
Monopolist sets a pair of price schedules:
Consumer A
RA = TA + cx
Consumer B
RB = TB + cx
Entry fees
Price per unit = c

30. Second degree PD
Suppose again there are two types of people – A-types and B-types
Half is A-type, half B-type
…but now we cannot tell who is who
Can the monopolist still capture some of the consumer surplus? Yes - airlines
All of it? No

31. A problem of information….TA
Best pricing policy:
Offer two options:
Option A: x*A for $(U+V+W)+cx*A
Option B: x*B for $U+cx*B
But then A would choose option B
She gets surplus V from option B, and 0 from option A
Monopolist gets profit U
A’s demand
B’s
demand TB V W U MC
x*B
x*A x

32. R RA RB x x*B x*A Option A Option B is better than option A
for person A RA RB
Option B x
x*B
x*A

33. The monopolist can do a little better….
A’s demand
Option A’:
x*A for $(U+W)+cx*A
A will be happy to take this offer
She gets a surplus of V
Monopolist gets profit U+W
B’s
demand V W U MC
x*B
x*A x

34. …but it can do even better
Option A’’:
x*A for $(U+W+DW)+cx*A
Option B’’
x’’B for $(U-DU)+cx’’B
A still willing to take option A’’ over option B’’
Profit up by DW-DU
A’s demand DW
B’s
demand V W U MC DU
x*B
x*A
x’’B x

35. …and the best it can do is?
Gain from higher fees paid by
A-types from further decreasing x+B
A’s demand
B’s
demand
Loss from lost sales to B-types
from further decreasing x+B V
Stop when = W U MC
x*B
x*A x
x+B

36. Should the monopolist bother selling to low-demand consumers?
Going further, you lose more
on the B-types than you gain
on the A-types
Going all the way to zero, you
lose less on the B-types than
you gain on the A-types
YES: Sell to B-types
NO: Sell only to A-types MC MC A B A B
x+B
x*A x
x+B=0
x*A x

37. 2nd degree price discrimination
High type:
DH(P) = P
Low type:
DH(P) = 70 – P
MC=10
What bundles should the monopolist offer?
At what prices?

38. 2nd degree price discrimination
High type:
DH(P) = P
Low type:
DH(P) = X – P
MC=10
For what value of X will the monopolist not sell to low types?

39. Outcome
B-types
They buy less than the Pareto efficient quantity: x+B < x*B
They earn zero consumer surplus
A-types
They buy the Pareto optimal amount, x*A
They earn positive consumer surplusFN
this is always what they could earn if they pretended to be B-types
FN: Whenever x+B >0

40. Third degree price discrimination
Monopolist faces demand in two markets, A and B
Suppose marginal cost is constant, c
Then the monopolist just sets prices so that
pA = c / (1 – 1/|eA|)
pB = c / (1 – 1/|eB|)

41. Some problems Non-constant marginal cost?
Replace c above with c’(xA+xB)
What if demands are inter-dependent?
E.g., xA(pA,pB) and xB(pB,pA)
Applications
Peak-load pricing
A: Riding the metro in rush-hour
B: Riding off-peak
Children’s and adults’ ticket prices

42. Bundling Suppose a monopolist sells two (or more) goods
It might want to sell them together – that is, in a “bundle”
E.g.s
Software – Word, PowerPoint, Excel
Magazine subscriptions

43. Software example
Two types of consumer who have different valuations over two goods
Assume marginal cost of production is zero
Consumer type
Word processor
Spreadsheet
Type A
120
100
Type B

44. Selling strategies Sell separately
Highest price to sell 2 word processors is 100
Highest for spreadsheet is 100
Sell two of each, for profit of 400
Bundle
Can sell a bundle to each consumer for 220
Total profit is 440
Dispersion of prices falls with bundling