The productivity of a certain country with the utilization of x units of labor and y units of capital is given approximately by the function f(x,y)=100x0.65y0.35. (A) Find fx(x,y) and fy(x,y). (B) If the country is now using 300 units of labor and 200 units of capital, find the marginal productivity of labor and the marginal productivity of capital. (C) For the greatest increase in the country's productivity, should the government encourage increased use of labor or increased use of capital?
The productivity of a certain country with the utilization of x units of labor and y units of capital is given approximately by the function f(x,y)=100x0.65y0.35. (A) Find fx(x,y) and fy(x,y). (B) If the country is now using 300 units of labor and 200 units of capital, find the marginal productivity of labor and the marginal productivity of capital. (C) For the greatest increase in the country's productivity, should the government encourage increased use of labor or increased use of capital?
Chapter9: Production Functions
Section: Chapter Questions
Problem 9.1P
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Question
The productivity of a certain country with the utilization of x units of labor and y units of capital is given approximately by the function
f(x,y)=100x0.65y0.35.
(A)
|
Find
fx(x,y)
and
fy(x,y).
|
(B)
|
If the country is now using
300
units of labor and
200
units of capital, find the marginal productivity of labor and the marginal productivity of capital. |
(C)
|
For the greatest increase in the country's productivity, should the government encourage increased use of labor or increased use of capital?
|
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