Shomu Banerjee
ECON 201
COST MINIMIZATION #2 ANSWERS
Suppose a firm has a production function:
y
= 2
x
1
+
x
2
where
y
is the output and
x
1
and
x
2
are inputs.
(a) In the graph below, an isoquant for
y
= 8 is shown. The prices of the inputs
are
w
1
= $1 and
w
2
= $2. Draw the isocost line corresponding to an expenditure of
$16.
See the solid red line.
(b) What is the costminimizing expenditure for
y
= 8 when
w
1
= $1 and
w
2
= $2?
Note that the slope of the isocost is 1/2 while the slope of the isoquant is 2.
While it is possible to produce at point
A
using only
x
2
=8, this would cost $16. By
sliding the red isocost to the left until it just touches the isoquant at
B
shows that
the same output of 8 can be produced using only
x
1
=4, costing only $4. Therefore
the insight is that so long as the isocost is flatter
than the isoquant, using
x
1
=4
only at point
B
is cheaper.
(c) What is the costminimizing expenditure for
y
= 8 when
w
1
= $8 and
w
2
= $2?
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 Summer '07
 Dr.ShomuBanerjee
 Economics, Microeconomics, optimal input combination

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