1
Costs
1.
Cost Minimization (Ch 20)
2.
Cost Curves (Ch 21)
The Problem
±
Production function: y = f(x x )
Production function: y
f(x
1
,x
2
).
±
Take the output level y
≥
0 as given
Take the output level y
0 as given.
±
Given the input prices w
1
and w
2
, the
cost of an input bundle (x
1
,x
2
) is
w
1
x
1
+ w
2
x
2
.
WEEK 8 Part I
ECON2101
S1 2010
2
The Problem (contd.)
±
For given w
1
, w
2
and y, the firm’s
cost-minimization problem is:
min
,
xx
wx
12
0
11
22
≥
+
subject to
x
x
y
1
2
=
f x
(
,
)
.
WEEK 8 Part I
ECON2101
S1 2010
3
Solution
±
Variable: x1, x2
±
Parameters: w1, w2, y
±
x
1
*= x
1
*(w
1
,w
2
,y), x
2
* = x
2
*(w
1
,w
2
,y)
x
(w
x
(w
±
The (smallest possible) total cost for
producing y output units is therefore
cw w y
wx w w y
( , ,)
*
1
112
=
(,,
)
.
*
22 1 2
+
WEEK 8 Part I
ECON2101
S1 2010
4
Diagrammatically Speaking
±
ISOCOST LINE: A curve that contains
all of the input bundles that cost the
same amount is an iso-cost curve.
±
E.g., given w
1
and w
2
, the $100 iso-
cost line has the equation
100
+=
.
WEEK 8 Part I
ECON2101
S1 2010
5
Iso-cost Lines
±
Generally, given w
1
and w
2
, the
equation of the $c iso-cost line is
i.e.
c
1 1
2
2
+
=
x
w
x
c
2
1
1
= −
+
±
Slope is - w
1
/w
2
.
w
w
2
2
=
.
WEEK 8 Part I
ECON2101
S1 2010
6