Skelton
Eco 3301
Homework 5 Answers
1.
A)
Since capital is fixed at 10, then the shortrun production function would be Q = 40L.
This implies that for any level of output (Q), the number of labor teams hired will be L =
Q/40.
The total cost function is thus given by the sum of the costs of capital labor and
raw materials:
TC = rK + wL + 2,000Q
= 12,000*10 + 3,000*(Q/40) + 2,000Q
= 120,000 + 2,075Q
Therefore, the average cost function is then given by:
AC = TC/Q = 120,000/Q + 2,075
And, since the total cost function is linear and each unit has a marginal cost of $2,075,
then marginal cost is fixed at $2,075 (because each unit costs us an additional $2,075).
Lastly, in looking at the average cost function, we can see that average costs will decline
as output increases and that average costs will increase as output decreases.
B) To produce 80 units, labor must be 2 (because L = Q/40 from part A).
C) Now, we move into the longrun and capital will no longer be fixed at 10.
So, we need to
find the cost minimizing combination of K and L for any level of output Q.
Recall that
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 Spring '08
 Skelton
 Economics, dry erase markers

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