Market Power
Without Strategic Behavior
(Monopoly or Monopolistic Competition)
Monopoly
• Firm with monopoly or market power has
the ability to set its price and produce at
any point on the market demand curve
• Whether the ONLY seller in the market
depends on the definition of the market
– Tylenol?
– Pace Salsa?
– Dallas Morning News?
– Raleigh/Durham Intl. Airport?
Barriers to Entry
• Barriers to entry are the source of all monopoly
power
– there are two general types of barriers to entry
• Exclusive ownership of resources through
– Legal barriers (e.g. patents and copyrights, gov. franchise)
– Unique supply (Brad Pitt Eiffel Tower)
– Sole ownership (DeBeers)
• Economies of scale (Natural Monopoly)
– Rent seeking behavior (lobbying lawmakers) can be
used to secure barriers (e.g. tariffs or import
restrictions)
Price Setters
• Single Price Monopolist
– Assume they cannot price discriminate, or behave
strategically.
– Monopoly or Monopolistic Competition
• Price Discrimination
– first, second and third degree
Revenue: Price Setter
• Price Setter, the higher q, the lower the P.
P
Market Demand = Firm’s Demand
P = P(Q)
Q
• Firm chooses the price along with quantity.
• R depends on P and Q, but P = P(Q)
• R = P(Q)·Q
Revenue: Price Setter
• TR and MR if demand is linear.
TR, MR
TR = P(Q)·Q
Slope = 0
MR = 0
Q
Revenue: Price Setter
• R = P(Q)·Q
MR 
dP(Q)  Q 
dQ
dP
MR 
 Q  P(Q)
dQ
dP
MR 
Q  P
dQ
P(Q)  Q
AR 
 P(Q)
Q
AR  P
P
Market Demand = Firm’s Demand
P = P(Q)
P = AR
MR
Q
Revenue: Price Setter
• MR, think of dq = 1.
P
dP
dQ
D: P = P(Q); P=AR
P
MR
Q
dQ
MR 
dP
Q  P
dQ
Q
Revenue: Price Setter
• MR, think of dQ = 1.
elastic
P
dP
dQ
inelastic
D: P = P(Q); P=AR
P
MR
Q
dQ
MR 
dP
Q  P
dQ
• MR clearly depends on e.
Q
Elasticity and MR
• Start with definitions of MR and e
MR 
dP
dQ P
 Q  P, e 

dQ
dP Q
Multiply in the equivalent of 1, MR 
dP Q P
  P
dQ 1 P
1 dP Q
From e, 

e dQ P
Substitute and simplify (pull the neg. sign out of the e),
1 P
MR    P
e 1
P
MR  P 
e

1
 1
Voila, MR  P  1   or MR  P  1  
e
 e

\
Elasticity and MR

1
MR  P  1  
e

•
•
•
•
if |e| = 1.0, MR = 0
if |e| < 1.0, MR < 0
if |e| > 1.0, MR > 0
if |e| > ∞, MR = P
Firm Supply Decision
•
•
•
•
•
Firm chooses the Q that will maximize profit.
They do not respond to a market price.
Produce a Qs where MR = MC
MR comes from demand function
Although shut down is still possible, 95% of
treatments of market power ignore the short
run and just look at the long run.
Profit Max
p
MC
SMC
AC
ATC
P*
PBE
D=AR
Q*
•
•
•
•
MR
Q
On the expansion path, SMC=MC and ATC=AC.
Use the SR curves to discuss the differential effects of changes in FC or VC in the short run.
But there is no LR entry or exit of firms (except the potential exit of the monopolist).
In the LR, the firm will choose a level of K to be on the expansion path, so long as P > AC.
Zoom In
D
SMC
ATC
MC
AC
PBE
• At Q* where MR=MC, SMC = MC
and ATC=AC.
dATC
dAC
=
dQ
dQ
dATC
≠0
dQ
• And while
• However,
MR
Q*
Price Setter in the Long Run
• Simple, just MR = MC
• Maximize profit w.r.t. Q
• Maximize profit w.r.t. K, L
Profit Maximizing Alternative 1
• Simple, set MC = MR, find q.
C*  C  v,w,Q  as from cost chapter  C*  w  L  v,w,Q   v  K  v,w,Q  
dC
 MC  v,w,Q 
dQ
Revenue: from demand, multiply inverse demand times q
P  P(Q), R  P(Q)  Q
dR
 MR  Q 
dQ
Set MR=MC and solve for Q *  Q  w,v 
Check to ensure that  > 0, if not, then exit
Profit Max , Choose q
• Assuming you know C*=C(v, w, Q)
max   P(Q)  Q  C  v,w,Q  , where C(v,w,Q) comes from cost minimization.
q
FOC
Q  MR(Q)  MC(Q)  0
Q  MR(Q)  MC(Q), choose q such that the MR = MC
Solve for Q to get the firm supply function, Q *  Q  v,w 
SOC, check that profit is decreasing where FOC are satisfied:
d2  d MR(Q)  d MC(Q) 
d(MR) d(MC)
QQ 



0,
or

2
dQ
dQ
dQ
dQ
dQ
Finally, check to ensure that  > 0, if not, then exit
Profit Max 3, MRPK=v, MRPL=w
• Optimize by choosing K and L.
max   P  f K,L    f K,L   vK  wL
L ,K
FOC
f
 P f 
L  
f
K,L

P
f
K,L
w 0








f

L

L


  P 

L  fL    Q  P  f K,L     w  That is: MPL  MR  w
  f 

e.g., let
Demand: P  a  bQ
Production: Q  K  L


  a  b K  L  K  L  vK  wL
f
 P f 
K  
f
K,L

P
f
K,L
r  0
Maximizing π means hiring each input







K
 f K 
until MRP = its price.
  P 

K  fK    Q  P  f K,L     v  That is: MPK  MR  v
  f 

Solve for L* and K* to get the profit maximizing factor demand functions
L*  L  v,w  , K*  K  v,w 
Plug into Q  f K,L  to get profit maximizing supply function Q *  Q  v,w 
and check that   0, exit otherwise.
Profit Max, choose K and L
• SOC
The  function is strictly concave at L* , K*
H
LL
LK
KL
KK
 0, negative definite
H  LL  KK   LK   0
2
Negative definite if: LL  0, KK  0,
and LL  KK   LK  , which holds so long as LK2 is small.
2
Profit Max, choose K and L
• Profit function, maximal profits for a given w, v.
Plug K* =K(v,w) and L*  L(v,w) into
  P  f K,L    f K,L   vK  wL
to get the profit optimizing profit function:
  P  f K(v,w),L(v,w)    f K(v,w),L(v,w)   vK(v,w)  wL(v,w)
Note, there is no P in this equation as determining profit
maximizing K and L determines Q*, which sets P* according to demand.
Monopoly Result
• Compared to perfect competition, higher price, lower quantity,
economic profit, higher producer surplus, lower consumer
surplus. In the long run, producer surplus = profit.
P
MC
CS
P*
AC
DWL
π
D
Q
Q*
MR
Competitive Comparison
• In long run, no profit or producer surplus (constant cost case
anyway).
• Because of the deadweight loss from monopoly, it is considered a
market failure.
P
Competitive Market supply = Market MC
PM
CS
AC
PC
D
QC
QM
MR
Q
The Inverse Elasticity Rule

1
MRis defined as MR  P  1  
e

When maximizing profit, MC  MR, so the folowing must hold:

1
 1
MC  P  1   or MC =P  1  
e
e


Since monopolists only produce where e  -1
MC will always  the price.
For example
1
e = -2, MC = P
2
3
e = -4, MC = P
4
e = - , MC = P
The Inverse Elasticity Rule
 1
MC  P  1  
e

MC
1
Solve for P to get: P 

 MC
 1  1
1   1  
e 
e

And we get the price as a multiple of MC (again, with e  -1)
e  -1, P    MC, b / c MC  MR  0
e  -2, P  2  MC
e  -5, P  1.25  MC
e  - , P  MC
Markup Pricing
MC
P
 1
1  
e

 e 
Rearrange again to get P  MC 

 e 1 
P  e  1   MC  e P  MC
P  e  P  MC  e
P  e  MC  e  P
e P  MC   P
P
e
P  MC
1

p
e
P  MC 
 1
1  
e

The Inverse Elasticity Rule
• The gap between a firm’s price and its marginal cost is
inversely related to the price elasticity of demand
facing the firm
P
P  MC
1

P
e
MC
For -1 < e < 0,
the markup
exceeds the
price. Huh?
p-MC
P
D, P = P(Q)
MR
Q
The Inverse Elasticity Rule
P  MC
1

P
e
• If e = -1, P-MC = P, the markup is p (since MC must = 0)
• If e = -1.25, the markup is 80% of price
• If e = -2, the markup with be 50% of price
• If e = -5, the markup will be 20% of price
• If e = -20, the markup will be 5% of price
Change in Price for a Change in MC
MC
 1
1  
e

P
1

, when e  -1
MC  1 
1  
e

For example
P
P
MC
 1
1  
e

P
 2, so price rises by twice the change in MC.
MC
P
e=-5,
 1.25, so price rises by 1.25 x the change in MC.
MC
P
e  10,
 1.11, so price rises by 1.11 x the change in MC.
MC
e=-2,
Natural Monopoly
• In a competitive market, so many firms can
produce at the Minimum Efficient Scale (MES) –
low point of AC curve – that no firm can change
the market price by altering its behavior.
• But if the MES is large enough that it only takes a
few firms to supply the market, they will start to
have market power.
• If MES is so large that one firm can produce at a
lower average cost than two firms can splitting the
market in half, then we get a natural monopoly.
Large MES
• Two firms each producing Q = X and charging P = AC. If one firm
gets a little larger, it can gain market share and profit.
• Long run equilibrium must be one firm.
P
MC
AC
D
x
2x
MR
Q
Large MES
• One firm, maximized profit like other monopolies.
• Barrier to entry is economies of scale
P
MC
P*
AC
DWL
π
D
Q*
Q
MR
Regulating This Monopoly
• Considered regular monopoly.
• Regulate price where MC = demand
• Profit > 0.
P
MC
AC
PR
π
D
QR
MR
Q
Natural Monopoly: Technically
• Definition is a firm for which AC is declining where AC = demand
• Still can earn economic profit in the long run.
• But why AC declining?
P
MC
P*
AC
DWL
π
D
Q*
Q
MR
Natural Monopoly: Technically
• If AC declining at intersection with demand, it requires MC < AC
where MC=MB.
• Sadly, regulation cannot require MC=MB without firm exit.
P
MC
AC
PR
Loss
D
QR
MR
Q
Natural Monopoly: Subsidized
• Could subsidize the firm (equal to loss).
• Not very popular. But it is one way to think about the economics
of mass transit, which is heavily subsidized.
P
MC
AC
PR
Subsidy
D
QR
MR
Q
Natural Monopoly
Average Cost Pricing
• Average cost pricing regulation ensures continued production.
• DWL results, but it is the more usual strategy.
P
MC
AC
DWL
PR,ACP
D
QR,ACP
MR
Q
Multi-plant Profit Max
Choose q1 and q2
• Assuming you know C1*=C(v, w, Q1), C2*=C(v, w, Q2)
max   p  q1  q2    q1  q2   C1  v,w,q1   C2  v,w,q2 
q1 ,q2
max   R  q1  q2   C1  q1   C2  q2 
q1 ,q2
FOC
q1  MR(q1  q2 )  MC(q1 )  0
q2  MR(q1  q2 )  MC(q2 )  0
MR the same in each FOC as
the market does not care
which plant each unit was
produced.
Choose q1 and q2 such that:
MR(q1  q2 )  MC(q1 )  MC(q2 )
The MC in each plant much equal MR of output as a whole.
Multi-plant Profit Max, SOC
SOC, profit decreasing (MR falling faster than MC -- easy if MR falling and MC rising)
 2R
 2R
 2R
slope of total MR curve =


,
q1q1 q1q1 q1q2
 2 C1
 2 C1
slope of each plant's MC curves: plant 1:
, plant 2:
q1q1
q1q1
 2 C1
 2R

 0, MC in plant 1 must be rising relative to MR
q1q1 q1q1
 2C2
 2R

 0, MC in plant 2 must be rising relative to MR
q2 q2 q2 q2
Now the Hessian:
 2 C1
 2R

q1q1 q1q1
 2R
q1q2
 2R
q2 q1
 2C2
 2R

q2 q2 q2 q2
2
2
2
2
2


  2R





 C1
 C2
R
R




  
 0

q

q

q

q

q

q

q

q

q

q
 1 2  
 1 1
1
1  
2
2
2
2 
Let's break this down on the next slide...
Multi-plant Profit Max, SOC
2
2
2
2
2

  2R





 C1
 C2
R
R 




  
 0
 qq q1q1   qq q2q2   qq  
2
2
  2R 
 2C1  2C2   2R 
 2R  2C2
 2R  2C1




 
 0

q

q

q

q

q

q

q

q

q

q

q

q

q

q

q

q


 1 1
2
2
1
1
1
1
2
2
But the first and last terms cancel out, leaving us with:
 2 C1  2 C 2
 2R  2C2
 2R  2C1



0
qq q2q2 qq q1q1 q1q1 q2q2
If MR is negative (necessary for price setters) and MC is > 0, this must hold.
Even if MC at both plants = 0, this will hold.
Even if MC is < 0 at each plant, this MIGHT still hold.
Of course, we still need MC rising relative to MR in each plant.
Graphically
p
$
MC1
MC2
MCT
MCT
D
MR
q1
q2
Q
q1+q2=Q
Q
Example
Solution based on FOC
Demand: P  200  .05Q, Q=q1  q2
C1  .05q12 C2  .025q22
  200  q1  q2   .05q12  .025q22

 200  .1 q1  q2   .1q1  0
q1

 200  .1 q1  q2   .05q2  0
q2
Solve each for q1 and set equal:
1000-.5q2  2,000  1.5q2
q2  1,000
Into either of the FOC to get: q1 =500
Check that MR = MC1  MC2  50
Q  1,500, P  125
SOC
MC1
MC2
MR
 .1,
 .05,
 .1
q1q1
q2q2
QQ
MR MC1

 0;  .1  .1  .2
QQ q1q1
MR MC2

 0;  .1  .05  .15
QQ q2q2
2C1 2C2
2R 2C1
2R 2C2



0
qq q1q1 qq q2q2 q1q1 q2q2
  .1.1   .1 .05   .05  .1   0
.01  .005  .005  0
.02  0
Monopoly and Quality
• Firms purposely make goods less durable than
they could so that we have to buy
replacements more often!
Monopoly and Quality
• Demand
P  P(Q,X), Q is quantity and X is quality
P
 0,
Q
P
0
X
• Profit
MR
  P(Q,X)  Q  C(Q,X)
MC
FOC

P
C
P
C
 P(Q,X) 
Q 
0
Q P 
Q
Q
Q
Q
Q
 P
C
P
C
 Q 
 0  Q 
X X
X
X
X
MRx
MCx
So long as Q* such
that MR = MC, also
set the MR from an
increase in X = the
MC of that extra X.
Graphically
More quality means more demand and more profit
P
P
Low X
MC
Medium X
MC
AC
AC
D(X)
D(X)
MR
Q
Q*
MR
Q*
Q
Graphically
But only to a point
P
Medium X
MC
P
MC
High X
AC
AC
D(X)
D(X)
MR
MR
Q*
Q
Q*
Q
Monopoly and Tax Policy
•
•
•
•
•
Flat Tax (tax = t)
Unit Tax (tax = tQ)
Revenue Tax (tax = t·R(Q))
Profit (Earnings) Tax (tax = t·π)
For each, start with revenue function and total
cost function (C*).
• R=R(Q) =P(Q)*Q
• C*=C(Q)
No Tax
P
MC
  R(Q)  C(Q)
FOC
 R C
:

0
Q Q Q
R C

Q Q
P*
AC

D: P=P(Q)
Q
Q*
MR
Flat Tax
( t > 1)
P
MC
  R(Q)  C(Q)  t
FOC
 R C
:

0
Q Q Q
R C

Q Q
Same result as no tax.
P*t
ACt

t
AC
D: P=P(Q)
Q
Q*t
MR
Unit Tax
( t > 0)
  R(Q)   C(Q)  tQ 
FOC
 R C
:

t0
Q Q Q
R C

t
Q Q
Different output from no tax.
R C
Q where

Q Q
*
t
MCt=MC+t
P
MC
P*t
ACt=AC+t

t
AC
D: P=P(Q)
Q
Q*t
MR
Revenue Tax
(0 < t < 1)
  R(Q) 1  t   C(Q)
FOC
 R
C
:
1  t    0
Q Q
Q
R
C
1  t  
Q
Q
Different result from no tax.
R C
Q where

Q Q
*
t
P
MC
P*t
t

AC
D
Q
Q*t
P(1-t)
MR
MRt=MR(1-t)
Profit Tax
(0 < t < 1)
  R(Q)  C(Q) 1  t 
P
FOC
  R C 
:

 1  t   0
Q  Q Q 
R
C
1  t   1  t 
Q
Q
R C

Q Q
Same result as no tax.
MC
t  (1  t)
P*
t
t
D: P=P(Q)
Q
Q*
MR
Monopolistic Competition in
Long Run
• In the short run if π > 0, then there is no
difference between a monopoly and a
monopolistically competitive firm.
• But despite the fact that firms have market
power, there are firms providing close enough
substitutes that demand for all firms falls to a
level where π = 0.
Profit Max , Choose Q
• Assuming you know C*=C(v, w, q)
max   P(Q)  Q  C  v,w,Q 
q
FOC
q  MR(Q)  MC(Q)  0
q  MR(Q)  MC(Q), choose Q such that the MR = MC
R C
At the same time, if =0, then R=C and = , so AR = AC
Q Q
Monopolistic Competition in the
Long Run
• MR=MC, AR=AC
P
MC
AC
P*
D: P=P(Q)
MR
Q*
Q
Price Discrimination
• 1st degree
• 2nd degree
• 3rd degree
• Note, “1”, “2”, “3” mean nothing.
First Degree, Perfect Price
Discrimination
• All buyers are charged a price equal to their
willingness to pay. TC in green, TR =
blue+green.
P
MC
• No DWL
• No CS either
– Car dealerships
– Colleges
– Reverse Auction
AC
D: P=P(Q)
P=MR
• Priceline
q*
q
Third Degree Price Discrimination
• Firm can separate demanders with different
demand elasticities and charge different prices
to each group.
• A single price must be charged to all
consumers in each demand group.
• Arbitrage must be prevented.
Third Degree Price Discrimination
• It is easy, right… just set MR=MC
P
P
P
MC
D1
D2
Q
• But what is MR?
MR1
Q1
MR2
Q2
3rd Degree Price Discrimination
• If we set MR1 = MC for the first market, then
P
P
MC
MC’
D1
MC=MR2
D2
MC=MR1
MR1
Q1
MR2
Q2
• MC for the second market has to start where MC left off.
Now MR and MC are not the same in both markets. Oops!
3rd Degree Price Discrimination
• We need to know MR for each unit sold, whichever
market it is sold in. We need MR1=MR2=MC.
P
P
P
MC
D1
D2
MR1
Q1
MR2
MRT
Q2
• A horizontal sum of MR gets us the total MR curve.
• Set MC = MRT to get the P that allows MR1=MR2=MC
Q
3rd Degree Price Discrimination
• Set that MC =MR1=MR2 to get the q in each market.
P
P
P
MC
D1
D2
MR1
Q1
MR2
MRT
Q2
• At those q, use demand to get the P in each market to
maximize profit. MR1=MR2, but P1≠P2
Q
The Math
• Max π = P1(Q1)•Q1+P2(Q2)•Q2-C(Q1+Q2)
• FOC
Q1  RQ1 (Q1 )  CQ1 (Q 1  Q 2 )  0
Q2  RQ2 (Q 2 )  CQ2 (Q 1  Q 2 )  0
• Solve for Q1 and Q2, then use demand curves to
get P1 and P2
MR and Elasticity
• Remember that with price setters:
 1
MR  P  1  
e

• Since MR is the same for both markets
• And…


1
1
MR  P1  1    P2  1  
e1 
e2 



1
1  
e2 
P1 

P2 
1
 1   … so all you need is e1 and e2
e1 

Example
Demand 1: P1  80  5Q 1 ; R1  80Q 1  5Q 12
Demand 2: P2  180  20Q 2 ; R2  180Q 2  20Q 22
Cost: C  50  20  Q 1  Q 2 
Max   80Q 1 – 5Q 12  180Q 2  20Q 22 –  50  20  Q 1  Q 2  
FOC
Q1  80 – 10Q 1 – 20
Q2  180 – 40Q 2 – 20
Solve to get

1
Q 1  6; P1  50; e1  1.67;  1    .4
 e1 

1
Q 2  4; P2  100; e2  1.25;  1    .2
 e2 
1 

P1 1
 and ; 
P2 2
1 



e2  1

1  2
e1 
1
3rd Degree Price Discrimination
• Set that MC =MR1=MR2 to get the q in each market.
P
P
P
MC
100
50
D1
D2
6
MR1
Q
MR2
20
Q
MRT
6
4
• At those q, use demand to get the P in each market to
maximize profit. MR1=MR2, but P1≠P2
Q
Constant MC
If MC is constant, you can simply set MR = MC in each
market separately. Meh.
Price
P1
P2
MC
MC
D
Q1
MR
MR
Q1 *
0
Q2 *
D
Q2
Second Degree
• There are different definitions.
1. Sellers cannot differentiate buyers, so must set
pricing to let the buyer self-sort themselves.
2. Generally achieved through non-linear pricing (price
varies by quantity or quality).
• Includes
– Volume discount (as you buy more, the price falls)
– Two-Part Tariff (tariff meaning price)
– Bundling
Volume Discount, Electricity
• Graph is consumer specific
• Consumer surplus now A + B + C
• No so much a volume discount as a first use surcharge!
P
P1
A
B
P2
P3
PS
C
MC=AC
Q3
Q
Volume Discount: Shoes
• Buy one for full price, get a second pair for ½
price!
• Consumer surplus now A + B
P
A
P1
P2
PS
B
MC=AC
Q2
Q
Two-Part Tariff
• Tariff means “price”
• First part is an “entry fee” and the second is
the per unit fee.
• Even with volume discounts, we can think of
part of the initial higher price as an entry fee.
• Some times the analysis is for the market and
sometimes consumer specific.
Two-Part Tariff
(Demand is Market Demand with N consumers)
• Could max profit the usual way by PM, QM (PS = C+D+F+G+J+K)
• But if you can charge a fee to be able to buy, fee =
(A+B+C+D+E)/N, then charge PC for the good.
• PS = A+B+C+D+E+
F+G+H+J+K+L
• If demanders potential
consumer surplus varies
a lot from
(A+B+C+D+E)/N then
that cannot be the entry
fee.
P
MC
PM
PC
B
A
C
D
G
F
AC
E
H
I
K L
D: P=P(Q)
J
MR
QM
QC
Q
Laser Printers
• HP charges a low price for printers (the access fee)
• However, if 10 buyers each have consumer surplus of $892 (from printer plus
ink) and the other 90 have CS = $12 each, entry fee is problematic.
• When consumer demand varies a lot, low entry fee and higher unit price. For
printers, high demanders buy more as they use them up faster.
P
MC
PM
PC
B
A
C
D
G
F
AC
E
H
I
K L
D: P=P(Q)
J
MR
QM
QC
Q
Two-Part Tariff
• High demanders and Low demanders
• In this case, the entry fee must work for the low demanders,
and the price for use (ink cartridges), must be where the profit
comes from.
P
Representative High Demander
P
Representative Low Demander
Printer Price
PINK
MC=AC
D
MR
MR
Q
D
Q
Two-Part Tariff
• If mostly high demanders, then sacrifice the low.
• Profit off the cartridges =$0.
P
Representative High Demander
P
Representative Low Demander
Printer Price
PINK
MC=AC
D
MR
MR
Q
0
D
Q
Two-Part Tariff
• If mostly low demanders, get little from the high demanders.
• Profit off the cartridges =$0.
P
Representative High Demander
P
Representative Low Demander
Printer Price
PINK
MC=AC
D
MR
MR
Q
D
Q
Individual Analysis
• Sometimes you see this as an individual level analysis.
• Problem here is each consumer must be charged the same “A.”
• In this case, assumption is MC=AC as a horizontal line.
P
A
PC
MC=AC
B
QC
Q
Consumer Analysis: Golf Club
• Demand for a round of golf: “A” is the cost of joining the club,
Pg is the price of a round.
• “B” is revenue from each round.
P
A
Pg
MC=AC
B
Qg
Q
Two-Part Tariff with Entry Fee Only
• Here we assume there are two types of
consumers. High demanders and Low
demanders
• Two different quantity or quality packages can
be offered.
• Two-part tariff, but while the entry fee > 0, the
unit fee is zero.
• Demanders self select whether they are
willing to pay more or less.
Phone Plans
• Assume MC = 0
• Plan L: Charge a price = size of area A for Q1
• Plan H: Charge a price = size of A+B+C for Q2
P
DH
B
DL
A
C
Q1
Q2
Q
Phone Plans
• But the high demanders would choose Plan L, get Q1 minutes
and gain CS = B.
• So it would seem that max charge for Play H is A + C.
• High demanders pay A + C, and get CS = B.
P
DH
B
DL
A
C
Q1
Q2
Q
Phone Plans
•
•
•
•
Even better, don’t offer Q1 as an option.
Plan L: Q’1 minutes for a price of A.
Plan H: Q2 minutes for a price of A + A’ + C + C’.
High demanders still choose Plan H, get CS = B (which is now
smaller) P
• Profit gains C’ and
loses A’
DH
B
DL
C’
A
C
A’
Q’1
Q1
Q2
Q
Phone Plans
•
•
•
•
Profit Max: Q*1 stops moving leftward when ΔA’ = ΔC’
Plan L: Q*1 minutes for a price of A.
Plan H: Q2 minutes for a price of A + A’ + C + C’.
Low demanders get no surplus, high demanders get CS = B
P
• Low demanders pay A and get A (no consumer surplus)
• High demanders pay A+A’+C+C’ and get A+A’+B+C+C’
• Consumer surplus = B
DH
B
Q*1 such that:
PH (Q’1) = 2 PL (Q’1)
ΔC’
DL
C’
A
ΔA’
C
A’
Q*1
Q1
Q2
Q
Quantity and Quality
• Phone carriers offer plans with more or fewer
numbers of unlimited minutes.
• But firms can vary quality instead of quantity.
– Airlines offer business and coach class.
• Don’t alter quantity, but quality
• Lower the coach quality to encourage high demanding
business travelers to pony up for business class.
Bundling
• There are several items that different consumers
are willing to pay different amounts for, but we
don’t know which items each consumers values
most.
• This is a version of buy one pair, get a second for
½ price, but you cannot buy one pair.
Bundling
• Econ students are willing to pay $80 for Excel and $40 for Word.
• History students are willing to pay $40 for Excel and $80 for word.
P
• Selling them for $80 each means selling
one of each so revenue is $160.
• Selling them for $40 each means selling
four, for a total revenue of $160.
• Microsoft only sells a package of both for
$120, so revenue is $240
A
80
B
40
MC=AC
Q=2
Q
Microsoft doesn’t need to know which program any buyer is willing to pay more for.
Monopoly and Patents
• New ideas (inventions, creative works, etc.) are costly to
produce.
• Once created, intellectual property has a low cost of
distribution.
• Perfect competition in production is assured.
• No incentive to do the hard work of creation.
• Writers of the US Constitution saw this
– Framers specified patent and copyright protection
• Yet guaranteed monopoly rights creates DWL.
– Framers saw this too and also specified limits.
Are the limits correct?
• 17 years for a patent
• How does the PDV of DWL compare to the
PDV of all future consumer surplus?
• Studies suggest the 17 year patent provides
about 90% of the CS that would be possible if
the 17 years were adjusted either direction
depending on the case.
Copyright Duration
Assumes the author lives for 35 years beyond the creation of the work.
So the current 105 year copyright is the 35 years while alive + 70.