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)=100x^{0.72}y^{0.28} ). find the marginal productivity of labor and capital ( f_x(x,y)=square )

Explanation:

Step1: Recall the formula for partial derivative

For a function \( z = f(x,y)=Ax^{a}y^{b}\), the partial derivative with respect to \(x\) (marginal productivity of labor) is given by \(f_{x}(x,y)=A\times a\times x^{a - 1}y^{b}\). Here \(A = 100\), \(a=0.72\), \(b = 0.28\).

Step2: Calculate \(f_{x}(x,y)\)

Using the power - rule for differentiation \((x^{n})^\prime=nx^{n - 1}\), we have:

$$
LATEXBLOCK0
$$

Answer:

\(\frac{72y^{0.28}}{x^{0.28}}\)