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
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This note was uploaded on 09/18/2011 for the course ECON 331 taught by Professor Heaps during the Spring '06 term at Simon Fraser.
 Spring '06
 Heaps

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