# Science:Math Exam Resources/Courses/MATH105/April 2011/Question 08 (a)

MATH105 April 2011
Other MATH105 Exams

### Question 08 (a)

The productivity (measured in the dollar value of goods produced) of a certain country is given by the function

$\displaystyle f(x,y)=160x^{3/4}y^{1/4},$ where $x$ denotes the amount (in dollars) invested in labor, and $y$ is the amount invested in capital. Recall that the marginal productivity of labor (respectively capital) is the rate of change of $f$ with respect to $x$ (respectively $y$ ), holding $y$ (respectively $x$ ) fixed.

Suppose that the country is currently utilizing 81 units of labor and 16 units of capital. Find the current marginal productivity of labor and also the current marginal productivity of capital.

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