1 Cost Minimization
In this handout, we will look at the problem of cost minimization and the
techniques to solve them. We will do this exercise using three equivalent
methods.
We have a production function ( CobbDouglas function) which uses two
inputs capital
K
and labor
L;
q
=
F
(
K;L
) =
K
a
L
b
where
a >
0
;b >
0
;a
+
b
6
1
(1)
and
r
( rental rate for capital) and
w
(wage rate for labor) are strictly positive.
output,
q
. The problem under consideration is:
min
(
K;L
)
wL
+
rK
(2)
subject to
q
=
K
a
L
b
:
(3)
1.1 Method 1: Graphical
In this method, we refer to the isoquant and isocost curves for two input
case. Let us keep labor
(
L
)
on the horizontal axis and capital
(
K
)
on the
vertical axis. Recall that the slope of the isocost curve is equal to
w
r
:
Also
the slope of the tangent at any point on the isoquant curve is equal to
MP
L
MP
K
where
MP
L
and
MP
K
are marginal product of labor and capital respectively.
To minimize cost, we need to equate these two ratios,
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 '06
 MASSON
 Economics, Microeconomics, #, 1 lb, a+b, 0 K

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