Pricing – multimarket price discrimination
I Sometimes, di¤erent prices can be charged to di¤erent
customers
B Based on location – China and North America
B Based on observables – discounts for youth and elderly
I Actually keeping consumers in separate markets is often
di¢ cult – they can "arbitrage" by going to China for DVDs,
or the next state over for cigarettes
Pricing – multimarket price discrimination practice
FinalPracticeP38
A monopolist is selling a good in two markets and has
marginal cost MC = 2(Q1 + Q2 ). (Inverse) Demand in the
two markets is given by
P1 = 100
Q1
P2 = 190
3Q2
If there are di¤erent prices, it is not due to di¤ering costs!
I What prices should the monopolist charge in the two markets
to maximize pro…ts?
Hint: the optimal quantity is sold in each market
MC = MR1 and MC = MR2
Pricing – multimarket price discrimination practice
A monopolist selling a good in two markets has marginal cost
MC = Q1 + Q2 . (Inverse) Demand in the two markets is given by
PD1 = 70
Q1
PD2 = 50
Q2
M
I What quantities QM
1 and Q2 should the monopolist sell in the
two markets?
M
I What prices PM
1 and P2 should the monopolist set in the two
markets?
Pricing – multimarket price discrimination practice
A monopolist selling a good in two markets has marginal cost
MC = 3 (Q1 + Q2 ). (Inverse) Demand in the two markets is given
by
PD1 = 75
3Q1
PD2 = 65
Q2
M
I What quantities QM
1 and Q2 should the monopolist sell in the
two markets?
M
I What prices PM
1 and P2 should the monopolist set in the two
markets?
Pricing – some cases
I The monopolist cannot see which bundle is bought.
(For a single good, this means seeing how many units the
buyer chooses.)
B The monopoly case we studied earlier.
B Now: a monopolist serving two markets.
I The monopolist sees which bundle is bought, but cannot
make a full price menu.
B Two-part tarri¤s
B Block pricing
I The monopolist sees which bundle is bought, and can set
di¤erent prices for every bundle.
B "Direct price discrimination" – it charges PD (q) for each unit,
altogether collecting W
B A useful baseline case
Pricing – going upmarket or downmarket
I Another example
Type
A
B
C
#
10
10
20
WTP
15
7
5
B What is the optimal price?
B What would the optimal price be if there were no type C
consumers?
I We can think of the monopolist as making a plan for each
customer type
Pricing – two goods practice
Type
A
B
#
100
200
WTP for H
10
6
WTP for L
4
2
Which goods should the monopolist sell, and at what prices PL
and PH ?
I If selling H to A and L to B, we must make sure that A does
not want to switch
...Convince the rich folks not to buy the cheap seats...
I What are possible plans?
B drop low-value customers
B drop low-quality product
B sell di¤erent goods to each
Pricing – two goods practice
Type
A
B
#
100
200
WTP for H
10
4
I We need to consider three options
B drop low-value customers
B drop low-quality product
B sell di¤erent goods to each
WTP for L
4
3
Pricing – two goods practice
Type
A
B
#
100
600
WTP for H
10
4
WTP for L
4
3
I Which goods should the monopolist sell, and at what prices
PL and PH ?
Type
A
B
#
100
200
WTP for H
10
3
WTP for L
5
1
Firm behavior for a monopoly (practice later)
WB16#1 Setup for the full problem (…nal only)
p
p
p
B Tech F (L, K) = LK, MPL = 12 K/L, MPK = 12 L/K
B Input prices w = 9, r = 4
B Market (inverse) Demand PD = 66 3Q
I Find
B
B
B
B
B
The
The
The
The
The
monopolist’s
monopolist’s
monopolist’s
monopolist’s
monopolist’s
total cost function C (Q)
optimal quantity QM , given MC = 12
optimal input purchases LM and KM
optimal price PM
pro…t ΠM = QM PM QM MC