Chapter 14, Problem 9T

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

Find *x* and *y* that maximize the utility function

To determine

**To calculate:** The values of *x* and *y* which maximizes the utility function

Explanation

**Given Information:**

The provided utility function is

**Formula used:**

According to the Lagrange multipliers method to obtain maxima or minima for a function

(1) Find the critical values of

(2) The critical points of

(3) The critical points of

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

Constant function rule for a constant

Coefficient rule for a constant

**Calculation:**

Consider the function,

The provided constraint is

According to the Lagrange multipliers method,

The objective function is

Thus,

Substitute

Since, the critical points of

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

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

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