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Homework 5
(Total 20 points)
Due on March 30, Tue.
We go over partial equilibrium analysis with a linear inverse demand. The
inverse
demand function is given by
p
D
(
q
) = 120

2
q
and the cost function
of the representative ﬁrm is given by
C
(
q
) =
q
2
.
Q1
: Assume that the market is competitive, i.e, the representative ﬁrm
behaves as a pricetaker.
(i) What is the
inverse
supply function
p
S
(
q
)? (2pt.)
(ii) What are the competitive equilibrium price
p
CE
and equilibrium quantity
q
CE
? (2pt.)
(iii) How much is the total surplus at the competitive equilibrium? (2pt.)
(iv) Suppose the government taxes on this good 10 dollars per unit.
(a) What is the quantity traded under taxation? (2pt.)
(b) How much is deadweight loss due to the taxation? (2pt.)
Answer
: (i) By the
p
=
MC
condition, it is
p
S
(
q
) = 2
q
.
(ii) From
p
D
(
q
) =
p
S
(
q
), we have 120

2
q
= 2
q
, hence
q
CE
= 30 and the
price is 60.
(iii) (a) Consumer’s inverse demand measured by ‘beforetax’ price shifts
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 Spring '10
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