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A. Algebra and mathematical analysis
Problem 1.
Let the national income model be :
0
0
G
I
C
Y
+
+
=
;
)
(
.
T
Y
C

+
=
8
0
20
;
Y
T
2
0
5
.
+
=
.
Find the equilibrium levels
Y
,
C
and
T
in terms of
0
I
and G
0
.
Problem 2
.
The demand and supply functions of a single market are as followed
2
2
6
0
3
2
4
0
2
48
P
P
Q
P
P
Q
s
d
.
;
.
+
+

=


=
a)
Express
the market equilibrium condition of this market in the form of a
quadratic equation of variable P
.
b) Find
the equilibrium price and
the equilibrium quantity
P
,
Q
.
Problem 3
.
Given the input – coefficient matrix and the finaldemand vector:
=
.
.
.
.
.
.
.
.
.
.
2
0
4
0
4
0
3
0
1
0
1
0
2
0
2
0
1
0
A
and
=
60
40
100
d
.
a)
Find the technology matrix T
and it’s determinant .
.
b)
Write down the specific inputoutput matrix equation
for this model and find
the “correct” output levels for the three industries.
Problem 4.
Given
an average cost
function AC=
Q
Q
+
+
20
400
a)
Find the total cost function and the fixed cost.
b) Find
the
minimum average cost output level.
Problem 5.
Given
a consumption function in term of the income Y :
Y
C
6
0
200
.
.
+
=
a)
Find the marginal propensity to consume and explain it’s economic meaning.
b) Find the elasticity
of
consume with respect to the income
level
when
Y=$1,000 and
explain the economic meaning of the obtained value .
Problem 6
.A single product monopolistic firm
supplies it’s products to two
separate markets .The
demand functions
in the first and second market are
respectively :
1
1
620
P
Q
d

=
;
2
2
700
P
Q
d

=
and the total cost function :
2
60
50
Q
Q
C
+
+
=
.
Find the output level and the quantities supplied to each market in order to
maximize it’s profit.
Problem 7
.
a)A single product firm faces
the marginal revenue function
and marginal cost
function
as following:
Q
MR
2
340

=
;
MC = 100+ Q
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View Full DocumentIt is known that
the fixed cost of the firm is 500.
a) Find the total revenue
and total cost function.
b) Find the profit function and maximum profit output level.
Problem 8
.
a) Find the present value of the perpetual cash flow A= $2,000
if
the discount
rate r = 0.08.
b) Evaluate the following improper integral :
I=
∫
∞
+
1
2
dx
x
x
ln
B. Probability
Problem 9
.
A person
intends to invest in
a stock market . There are two choices: stock
A or stock B .In the case
he invests in stock A ,
he obtains a return of 25
percent
if the economy is strong and
( 10 ) percent
if the economy is
weak. In
the case of stock B ,
he obtains the return of
15 percent
if economy is strong
and 10 percent
if the economy is weak. He believes
that the
that the economy
is strong with
the probability
0.60 and
weak with the probability 0.40.
He wants to invest in the stock which has higher expected return. Which stock
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 Summer '11
 HuyDuong

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