Second Midterm Exam
Econ 150b. Intermediate Microeconomics
April 9, 2009
Please write your
name and discussionsection time
on each blue book.
1. (50 points.) Consider an economy with two goods, labeled 1 and 2, two consumers,
labeled
A
and
B
, and one firm. Write
.!
A
1
; !
A
2
/
and
.!
B
1
; !
B
2
/
for the endowments of
consumers
A
and
B
, respectively. Let
A
2
.0; 1/
designate
A
’s share of the firm’s
profit, so that
B
0
s
share is
B
D
1
A
. Denote the consumers’ utility functions by
u
A
.x
A
1
; x
A
2
/
and
u
B
.x
B
1
; x
B
2
/
. Suppose that the firm produces good
2
as an output using
good 1 as input according to the production function
y
2
D
f .y
1
/
.
(a) (5 points.) Define
feasible allocation
.
(b) (10 points.) Define
Pareto efficient allocation
.
(c) (10 point.) What is the budget constraint of consumer
A
assuming he takes prices
.p
1
; p
2
/
and the firm’s profit
as given?
(d) (10 points.) What is a
competitive equilibrium
?
(e) (15 points.) Explain the logic behind the First Welfare Theorem: “The allocation
of every competitive equilibrium is Pareto efficient.” (That is, provide the intuition
for the proof. Be as precise as you can.)
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 Spring '09
 SAMUELSON
 Microeconomics, Supply And Demand, producer, Inverse demand function

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