This preview shows page 1. Sign up to view the full content.
ECON 331
Written Assignment 9
due in class Nov. 25
1. Let
y
f
K
,
L
be a production function and suppose that the factors of
production are paid according to their marginal value products. That is if
p
is the price
of the output
y
,
r
is the price of capital
K
and
w
is the price of labour
L
then
pf
K
rp
f
L
w
Suppose also that the firm’s employment of capital and labour are both growing at
a continuous rate of
a
%
per year. That is
K
t
K
0
e
at
L
t
L
0
e
at
Then letting
y
t
f
K
t
,
L
t
show that
dy
/
dt
is also a constant times
e
at
.
2. Given the function
f
x
,
y
x
3
xy
2
x
4
find an expression for the slope of the tangent line to a level curve of
f
. Then find
the slope of the tangent line to the level curve which passes through the point
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '06
 Heaps

Click to edit the document details