Eco11, Fall 2008
Simon Board
Economics 11: Practice Problems 8 (Weeks 9–10)
December 3, 2008
1. First Welfare Theorem
There are two goods (
x
and
y
) and two agents (A and B). The agents’ utility functions are
u
A
=
v
A
(
x
) +
y
u
B
=
v
B
(
x
) +
y
where
v
A
= 2ln(
x
) and
v
B
(
x
) = 4
x
1
/
2
, The agents have incomes
m
A
= 10 and
m
B
= 10. The
price of good
y
is
p
y
= 1; the price of good
x
is to be determined.
A single ﬁrm produces good
x
. It has cost function
c
(
q
) =
q
2
/
2.
(a) Show that
p
= 2 is an equilibrium price. Find the equilibrium allocations (
x
A
,x
B
,q
).
(b) Suppose a social planner chooses (
x
A
,x
B
,q
) to maximise the total surplus,
v
A
(
x
A
) +
v
B
(
x
B
)

c
(
q
)
subject to
q
=
x
A
+
x
B
. Verify your allocations from part (a) satisfy the FOCs from this
optimisation problem.
2. Shifts in Supply Functions
Suppose the supply function is
q
=
p
, and the demand function is
q
= 10

p
.
(a) Find the equilibrium price and quantity.
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 Fall '08
 cunningham
 Supply And Demand, Utility, producer

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