Chapter Twenty-Four 29/10/2014 1 Chapter Twenty-Five Monopoly Behavior How Should a Monopoly Price? So far a monopoly has been thought of as a firm which has to sell its product at the same price to...

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Chapter Twenty-Four
29/10/2014
1
Chapter Twenty-Five
Monopoly Behavior
How Should a Monopoly Price?
So far a monopoly has been thought
of as a firm which has to sell its
product at the same price to every
customer. This is uniform pricing.
Can price-discrimination earn a
monopoly higher profits?
Types of Price Discrimination
1st-degree: Each output unit is sold
at a different price. Prices may differ
across buyers.
2nd-degree: The price paid by a
buyer can vary with the quantity
demanded by the buyer. But all
customers face the same price
schedule. E.g. bulk-buying
discounts.
Types of Price Discrimination
3rd-degree: Price paid by buyers in a
given group is the same for all units
purchased. But price may differ
across buyer groups.
E.g., senior citizen and student
discounts vs. no discounts for
middle-aged persons.
First-degree Price Discrimination
Each output unit is sold at a different
price. Price may differ across buyers.
 It requires that the monopolist can
discover the buyer with the highest
valuation of its product, the buyer with
the next highest valuation, and so on.
First-degree Price Discrimination
p(y)
y
$/output unit
MC(y)
y
p y( )
Sell the th unit for $y p y( ).
29/10/2014
2
First-degree Price Discrimination
p(y)
y
$/output unit
MC(y)
y
p y( )
y
p y( )
Sell the th unit for $ XXXXXXXXXXLater on
sell the th unit for $
y p y( ).
y p y( ).
First-degree Price Discrimination
p(y)
y
$/output unit
MC(y)
y
p y( )
y y
p y( )
p y( )
Sell the th unit for $ XXXXXXXXXXLater on
sell the th unit for $ XXXXXXXXXXFinally
sell the th unit for marginal
cost, $
y p y( ).
y p y( ).
y
p y( ).
First-degree Price Discrimination
p(y)
y
$/output unit
MC(y)
y
p y( )
y y
p y( )
p y( )
The gains to the monopolist
on these trades are:
and zero.
p y MC y p y MC y( ) ( ), ( ) ( )     
The consumers’ gains are zero.
First-degree Price Discrimination
p(y)
y
$/output unit
MC(y)
y
So the sum of the gains to
the monopolist on all
trades is the maximum
possible total gains-to-trade.
PS
First-degree Price Discrimination
p(y)
y
$/output unit
MC(y)
y
The monopolist gets
the maximum possible
gains from trade.
PS
First-degree price discrimination
is Pareto-efficient.
First-degree Price Discrimination
First-degree price discrimination
gives a monopolist all of the possible
gains-to-trade, leaves the buyers
with zero surplus, and supplies the
efficient amount of output.
29/10/2014
3
Third-degree Price Discrimination
Price paid by buyers in a given group
is the same for all units purchased.
But price may differ across buyer
groups.
Third-degree Price Discrimination
A monopolist manipulates market
price by altering the quantity of
product supplied to that market.
So the question “What discriminatory
prices will the monopolist set, one for
each group?” is really the question
“How many units of product will the
monopolist supply to each group?”
Third-degree Price Discrimination
Two markets, 1 and 2.
y1 is the quantity supplied to market 1.
Market 1’s inverse demand function is
p1(y1).
y2 is the quantity supplied to market 2.
Market 2’s inverse demand function is
p2(y2).
Third-degree Price Discrimination
For given supply levels y1 and y2 the
firm’s profit is
What values of y1 and y2 maximize
profit?
( , XXXXXXXXXXy y p y y p y y c y y XXXXXXXXXX   
Third-degree Price Discrimination
( , XXXXXXXXXXy y p y y p y y c y y XXXXXXXXXX   
The profit-maximization conditions are
 









y y
p y y
c y y
y y
y y
y1 1
1 1 1
1 2
1 2
1 2
1
0
 





( )
( )
( )
( )
Third-degree Price Discrimination
( , XXXXXXXXXXy y p y y p y y c y y XXXXXXXXXX   
The profit-maximization conditions are
 









y y
p y y
c y y
y y
y y
y1 1
1 1 1
1 2
1 2
1 2
1
0
 





( )
( )
( )
( )
 









y y
p y y
c y y
y y
y y
y2 2
2 2 2
1 2
1 2
1 2
2
0
 





( )
( )
( )
( )
29/10/2014
4
Third-degree Price Discrimination


( )y y
y
1 2
1
1




( )y y
y
1 2
2
1

and so
the profit-maximization conditions are
 



y
p y y
c y y
y y1
1 1 1
1 2
1 2
( )
( )
( )



and  



y
p y y
c y y
y y2
2 2 2
1 2
1 2
( )
( )
( )
.


Third-degree Price Discrimination
   





y
p y y
y
p y y
c y y
y y1
1 1 1
2
2 2 2
1 2
1 2
( ) ( )
( )
( )
 


Third-degree Price Discrimination
   





y
p y y
y
p y y
c y y
y y1
1 1 1
2
2 2 2
1 2
1 2
( ) ( )
( )
( )
 


MR1(y1) = MR2(y2) says that the allocation
y1, y2 maximizes the revenue from selling
y1 + y2 output units.
E.g. if MR1(y1) > MR2(y2) then an output unit
should be moved from market 2 to market 1
to increase total revenue.

Third-degree Price Discrimination
   





y
p y y
y
p y y
c y y
y y1
1 1 1
2
2 2 2
1 2
1 2
( ) ( )
( )
( )
 



The marginal revenue common to both
markets equals the marginal production
cost if profit is to be maximized.
Third-degree Price Discrimination
MR1(y1) MR2(y2)
y1 y2y1* y2*
p1(y1*) p2(y2*)
MC MC
p1(y1)
p2(y2)
Market 1 Market 2
MR1(y1*) = MR2(y2*) = MC
Third-degree Price Discrimination
MR1(y1) MR2(y2)
y1 y2y1* y2*
p1(y1*) p2(y2*)
MC MC
p1(y1)
p2(y2)
Market 1 Market 2
MR1(y1*) = MR2(y2*) = MC and p1(y1*)  p2(y2*).
29/10/2014
5
Third-degree Price Discrimination
 In which market will the monopolist
set the higher price?
Third-degree Price Discrimination
 In which market will the monopolist
cause the higher price?
Recall that
MR y p y1 1 1 1
1
1
1
( ) ( ) 






MR y p y2 2 2 2
2
1
1
( ) ( ) . 






and
Third-degree Price Discrimination
 In which market will the monopolist
cause the higher price?
Recall that
But,
MR y p y1 1 1 1
1
1
1
( ) ( ) 






MR y p y2 2 2 2
2
1
1
( ) ( ) . 






and
MR y MR y MC y y XXXXXXXXXX( ) ( ) ( )
* * * *  
Third-degree Price Discrimination
p y p y1 1
1
2 2
2
1
1
1
1
( ) ( ) .
* *





  





 
So
Third-degree Price Discrimination
p y p y1 1
1
2 2
2
1
1
1
1
( ) ( ) .
* *





  





 
So
Therefore, XXXXXXXXXXonly ifp y p y1 1 2 2( ) ( )
* *
1
1
1
1
1 2
  
 
Third-degree Price Discrimination
p y p y1 1
1
2 2
2
1
1
1
1
( ) ( ) .
* *





  





 
So
Therefore, XXXXXXXXXXonly ifp y p y1 1 2 2( ) ( )
* *
1
1
1
1
1 2
1 2    
 
  .
29/10/2014
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Third-degree Price Discrimination
p y p y1 1
1
2 2
2
1
1
1
1
( ) ( ) .
* *





  





 
So
Therefore, XXXXXXXXXXonly ifp y p y1 1 2 2( ) ( )
* *
1
1
1
1
1 2
1 2    
 
  .
The monopolist sets the higher price in
the market where demand is least
own-price elastic.
Two-Part Tariffs
A two-part tariff is a lump-sum fee,
p1, plus a price p2 for each unit of
product purchased.
Thus the cost of buying x units of
product is
p1 + p2x.
Two-Part Tariffs
Should a monopolist prefer a two-
part tariff to uniform pricing, or to
any of the price-discrimination
schemes discussed so far?
 If so, how should the monopolist
design its two-part tariff?
Two-Part Tariffs
 p1 + p2x
Q: What is the largest that p1 can be?
Two-Part Tariffs
 p1 + p2x
Q: What is the largest that p1 can be?
A: p1 is the “entrance fee” so the
largest it can be is the surplus the
buyer gains from entering the
market.
Set p1 = CS and now ask what
should be p2?
Two-Part Tariffs
p(y)
y
$/output unit
MC(y)
y
)y(pp2 
Should the monopolist
set p2 above MC?
29/10/2014
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Two-Part Tariffs
p(y)
y
$/output unit
y
CS
Should the monopolist
set p2 above MC?
p1 = CS.
MC(y)
)y(pp2 
Two-Part Tariffs
p(y)
y
$/output unit
y
CS
Should the monopolist
set p2 above MC?
p1 = CS.
PS is profit from sales.
MC(y)
PS
)y(pp2 
Two-Part Tariffs
p(y)
y
$/output unit
y
CS
Should the monopolist
set p2 above MC?
p1 = CS.
PS is profit from sales.
MC(y)
PS
Total profit
)y(pp2 
Two-Part Tariffs
p(y)
y
$/output unit
y
)y(pp2 
Should the monopolist
set p2 = MC?
MC(y)
Two-Part Tariffs
p(y)
y
$/output unit Should the monopolist
set p2 = MC?
p1 = CS.
CS
y
MC(y)
)y(pp2 
Two-Part Tariffs
p(y)
y
$/output unit Should the monopolist
set p2 = MC?
p1 = CS.
PS is profit from sales.
y
MC(y)
CS
PS
)y(pp2 
29/10/2014
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Two-Part Tariffs
p(y)
y
$/output unit Should the monopolist
set p2 = MC?
p1 = CS.
PS is profit from sales.
y
MC(y)
CS
Total profitPS
)y(pp2 
Two-Part Tariffs
p(y)
y
$/output unit Should the monopolist
set p2 = MC?
p1 = CS.
PS is profit from sales.
y
MC(y)
CS
PS
)y(pp2 
Two-Part Tariffs
p(y)
y
$/output unit Should the monopolist
set p2 = MC?
p1 = CS.
PS is profit from sales.
y
MC(y)
CS
Additional profit from setting p2 = MC.
PS
)y(pp2 
Two-Part Tariffs
The monopolist maximizes its profit
when using a two-part tariff by
setting its per unit price p2 at
marginal cost and setting its lump-
sum fee p1 equal to Consumers’
Surplus.
Two-Part Tariffs
A profit-maximizing two-part tariff
gives an efficient market outcome in
which the monopolist obtains as
profit the total of all gains-to-trade.
Answered 2 days AfterMay 05, 2021

Solution

Himanshu Sangail answered on May 08 2021
18 Votes

Ans
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