ECON 211, Fall 2009
Problem Set 9 (100 points)
Due on Friday, Nov. 13
Part I. Graded Questions
Problem 1: (40 points)
A multimarket (thirddegree) price discriminating monopolist offers tickets for children and
adults. The demand for adult tickets is given by p
a
=10  q
a
and the demand for children tickets is
given by p
c
= 5  (1/2)q
c
. Marginal cost equals to 2.
a. (5 points) What price does it charge for adult tickets?
p
a
=10q
a
=> MR=102q
a
Setting MR=MC gives 102q
a
=2 => q
a
=4 => p
a
=6
b. (5 points) What price does it charge for child tickets?
p
c
=5(1/2)q
c
=> MR=5q
c
Setting MR=MC gives 5q
c
=2 => q
c
=3 => p
c
=3.5
c. (5 points) How many tickets does it sell of each type?
From A and B we know that q
a
=4 and q
c
=3.
d. (5 points) What is the profit of the monopolist?
Profit = q
a
*(p
a
2) + q
c
*(p
c
2) = 4*(62)+3*(3.52) = 20.5
Suppose the monopolist is not allowed to discriminate between children and adults, so it has to
charge a single price to everybody.
e. (10 points) Calculate the demand function of the combined demand for tickets. Hint: Calculate
one equation for prices between 0 and 5 and another for prices between 5 and 10.
p
a
=10q
a
=>
q
a
=10p
a
p
c
=5(1/2)q
c
=>
q
c
= 10 – 2 p
c
If p<5 then both Children and Adults buy tickets:
q
a+c
= q
a
+ q
c
= 10p
a
+ 10 – 2 p
c
p
a
= p
c
= p => q
a+c
= 20  3p => p = 20/3 – q
a+c
/3 for p < 5
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If 5<p<10 then only Adults buy tickets:
q
a+c
= q
a
= 10p
a
p
a
= p
c
= p => p=10q
a+c
for 5<p<10
f. (5 points) Compute the equilibrium price and quantity without discrimination. Hint: Check
both of the two equations of the demand curve.
If we assume p<5
p = 20/3 – q
a+c
/3 => MR = 20/3 – 2*q
a+c
/3
Setting MR = MC => 2 = 20/3 – 2*q
a+c
/3 => q
a+c
= 7 => p = 4.333…
The demand function we used assumed p<5. So we must check our final answer for
p<5. 4.33… < 5 so the answer does not violate our assumptions
Profit = 7* (4.333… – 2) = 16.333…
If we assume 5<p<10
p=10q
a+c
=> MR = 10 q
a+c
Setting MR=MC gives 102q
a+C
=2 => q
a+c
=4 => p=6
The demand function we used assumed 5<p<10. So we must check our final answer
for 5<p<10. 5<6<10 so the answer does not violate our assumptions
Profit = 4*(62)=16
Profit is larger selling to both than just adults, so that price and quantity will be
chosen: q
a+c
= 7 , p = 4.333…
g. (5 points) Compute the profit without discrimination and compare it to the profit with
discrimination.
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