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UCLA
Economics 11 – Fall 2006
Professor Mazzocco
Problem Set 6 Answer Key
1)
Suppose the production function for widgets is given by:
Q=KL  0.8K
2
– 0.2L
2
a)
Suppose K=10, graph the total and average productivity of labor curves.
b)
At what level of labor input does the average productivity reach a maximum? How
many widgets are produced at this point?
c)
Again, assuming K=10, graph the MPL curve. At what level of labor input does
MPL=0?
d)
Does this production function exhibit constant, increasing or decreasing returns to
scale?
Answer:
a)
total productivity: Q=10L800.2L
2
average productivity: APL = 10 – 80/L 0.2L
b)
Max APL
L=20, q=25
c)
MPL=10 – 0.4L
MPL=0 when L=25
d)
Increasing returns to scale
2)
Suppose that a production function is given by q=L+K
0.5
, where v is the price of
K and w is the price of L.
a)
Find the marginal productivity of labor and capital.
b)
Find the most efficient combination of inputs for producing 347 units of output
when w=4 and v=1.
c)
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 Spring '08
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 Economics

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