The productivity of an automobile manu- facturing company is given by the functi
ID: 2873762 • Letter: T
Question
The productivity of an automobile manu- facturing company is given by the function f(x,y) = 50 xy with the utilization of x units of labor and y units of capital.
i ) Find fx and fy.
(ii) If the company is now using 250 units of labor and 490 units of capital, find the marginal productivity of labor.
(iii) If the company is now using 250 units of labor and 490 units of capital, find the marginal productivity of capital.
(iv) To achieve the greatest increase in pro- ductivity when the company is using 250 units of labor and 490 units of capital, should the management encourage increased use of labor or increased use of capital, or neither?
Explanation / Answer
The productivity of an automobile manufacturing company is given by,
.
(a)
Find the partial derivatives.
(b)
Find the marginal productivity of labor at .
(c)
Find the marginal productivity of capital at .
(d)
Therefore, to achieve the greatest in productivity when the company using 250 units of labor and 490 units of capital, management need to encourage increased to use of labor.
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