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1
Costs
1.
Cost Minimization (Ch 20)
2.
Cost Curves (Ch 21)
Shortrun total costs
±
The shortrun costminimization problem is
min
x
wx
1
0
11
22
≥
+
′
fx x
y
(, ) .
12
′
=
±
Note x2 is fixed at x2 = x2’
WEEK 8 Part II
ECON2101
S1 2010
2
Short run costs: an example
±
Consider the Cobb Douglas case again:
x
x
x
f(x
y
1/2
1/2
=
=
±
Let x2 be fixed at 4.
.
)
,
2
1
2
1
±
Substituting x2 = 4 above we get
1/2
1/2
1/2
2x
4
x
y
=
=
±
Rearranging this gives the short run
1
1
demand function for x1
y
x
2
1
=
WEEK 8 Part II
ECON2101
S1 2010
3
4
Short run costs: an example
±
The conditional demand function for x1 and
the short run cost function are given by (a)
d (b)
ti
l
and (b) respectively
(a)
y
2
S
2
4
y)
,
w
,
(w
x
2
1
1
=
(b)
2
1
2
1
4
)
4
(
)
,
,
(
w
y
w
y
w
w
c
s
+
=
WEEK 8 Part II
ECON2101
S1 2010
4
Computing different costs
±
Let w1 = 4 and w2 = 1/4. Then
1
2
+
=
=
y
c
y
w
w
s
±
Fixed costs: c(0) = 1
)
(
)
,
,
(
2
1
y
c
Fixed costs: c(0)
1
±
Average fixed costs:AFC(y) = c(0)/y = 1/y
±
Variable costs:
2
y
±
Average variable costs: AVC(y) =
Variable cost/y = y
±
Average costs: AC(y) = AVC + AFC =
y + (1/y)
WEEK 8 Part II
ECON2101
S1 2010
5
±
Marginal costs: MC(y) = dc(y)/dy = 2y
Diagram: AVC, AC, MC for the example
WEEK 8 Part II
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