Chapter 14.3, Problem 19E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

For Problems 17-19, suppose that the number of crates of an agricultural product is given by

where *x* is the number of hours of labor and *y* is the number of acres of the crop.

Find and interpret the marginal productivity of the number of hours of labor (*x*) when *x* = 300 and *y* = 500.

To determine

**To calculate:** The marginal productivity of the number of hours of labor (*x*) when *x* is the number of hours of labor and *y* is the number of acres of the crop. Also, interpret the answer.

Explanation

**Given Information:**

The number of crates of an agricultural product is given by *x* is the number of hours of labor and *y* is the number of acres of the crop. Also,

**Formula used:**

For a production function, of the form *x* is given by *y* is given by

For a function *f* with respect to *y* is calculated by taking the derivative of *y* and keeping the other variable *x* constant. The partial derivative of *f* with respect to *y* is denoted by

Power of

Quotient rule for function

Constant function rule for a constant

The coefficient rule for a constant

**Calculation:**

Consider the problem,

The number of crates of an agricultural product is given by *x* is the number of hours of labor and *y* is the number of acres of the crop.

For a production function of the form *x* is given by

Recall that, for a function *f* with respect to *x* is calculated by taking the derivative of *x* and keeping the other variable *y* constant.

Use the power of *x* rule for derivatives, the quotient rule, the constant function rule, and the coefficient rule,

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