Problem set 7.
Due at the beginning of your tutorial week 9.
Problem 1.
Production function
f
(
x
1
, x
2
) =
x
1
x
2
. The prices for the inputs are 2
and 8, respectively.
a.
If
x
2
is fixed at
x
2
=
10 derive the shortrun cost function of the firm as a function
of
Y
 output level, and the prices for inputs given above.
(Hint: with 1 input there
is no cost minimization.)
b.
Now suppose that
x
2
is also free to vary. Derive the demands for the inputs and
the longrun cost function of the firm.
c.
What value of
Y
makes the value of the shortrun (in a) and longrun (in b) cost
functions equal. Draw the two cost functions on the graph. Do they cross? Which
one lies higher?
Problem 2. Cost functions.
Consider a firm with average cost function
AC
(
y
) = 1+
y
+1/
y
.
a.
What is the firm’s total cost function?
b.
What is the firm’s variable cost function? What is the firm’s average variable cost
(
AVC
) function?
c.
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 Three '09
 NONE
 Economics, cost functions

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