Chapter 7.1, Problem 12E

Refer to Example 3. If labor costs $100 per unit and capital costs $200 per unit, express as a function of two variables, $C\left(x,y\right),$ the cost of utilizing $x$ units of labor and $y$ units of capital.

Example 3

Production in a firm

Suppose that, during a certain time period, the number of units of goods produced when $x$ units of labor and $y$ units of capital are used is $f(x,y)=60x^{3/4}{y}^{1/4}$.

How many units of goods will be produced by $81$ units of labor and $16$ units of capital?

Show that, whenever the amounts of labor and capital being used are doubled, so is the production. (Economists say that the production function has “constant returns to scale”)