UNIVERSITY OF LONDON
BSc EXAMINATION 2018
For Internal Students of
Royal Holloway
DO
NOT
TURN
OVER
UNTIL
TOLD
TO
BEGIN
EC1102: QUANTITATIVE METHODS IN ECONOMICS
Time Allowed:
TWO
hours
Answer
ALL
questions
EC Calculators are permitted
c Royal Holloway, University of London 2018
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EC1102
QUESTION 1
Answer YES or NO to the following questions:
(a) Suppose
(ln(
x
) + 1)
y
= 4
. Is
y
0
=

2
at
(
x, y
) = (1
,
4)
?
(4 Marks)
(b) Suppose
f
(
x
) = 4
x
2

12
x
+ 9
. Is
f
0
(2) = 4
?
(4 Marks)
(c) Suppose
g
0
(
x
*
) = 0
and
g
00
(
x
*
)
>
0
.
Is
x
*
a local minimum?
(4 Marks)
(d) Is
f
(
K, L
) = 14
K
3
10
L
2
10
homogenous of degree
1
/
2
?
(4 Marks)
(e) Does
lim
x
→
3
x
2

9
x

3
exist?
(4 Marks)
(f) Is the function
f
(
x, y
) =
xy
+ 4
homothetic?
(4 Marks)
(g) Is it true that
R
e
1
3
x
dx
= 3
?
(4 Marks)
(h) Suppose
f
(
x, y
) = 3
x
2
+ 4
xy

6
y
2
.
Is
∂
2
∂y∂x
f
(
x, y
) =

8
?
(4 Marks)
(i) Consider
f
(
x
) = 2 ln(
x
)
.
Is it true that
El
x
f
(2) =
1
2
?
(4 Marks)
(j) Let
f
(
x, y
) =
x
4

y
2
.
Is
(
x, y
) = (0
,
0)
a saddlepoint?
(4 Marks)
(k) The linear equation through
(1
,
1)
and
(3
,
4)
is
y
=
3
2
x

1
2
.
True or false?
(4 Marks)
(l) The inverse function of
y
=
e
x

2
is
y
= ln(
x
+ 2)
.
True or false?
(6 Marks)
(Total 50 marks)
QUESTION 2
Consider an individual who derives utility
U
(
x, y
) = 2 ln
x
+ ln
y
from consuming two
goods in quantities
x
and
y
. The individual has an income of
m
. The unit price of good
x
is
p
and the unit price of good
y
is
q
.
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