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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Marginal Utility The utility function U = f ( x , y ) is a measure of the utility (or satisfaction) derived by a person from the consumption of two products x and y. The utility function for two products is U   = 5 x 2 + x y 3 y 2 .

(a) Determine the marginal utility of product x.

(b) Determine the marginal utility of product y.

(c) When x = 2 and y = 3, should a person consume one more unit of product x or one more unit of product y? Explain your reasoning.

(d) Use a three-dimensional graphing utility to graph the function. Interpret the marginal utilities of products x and y graphically.

(a)

To determine

To calculate: The marginal utility of product x if the utility function U=f(x,y) is a measure of the ability (or satisfaction) derived by a person from the consumption of two products x and y. The utility function for two products is U=5x2+xy3y2.

Explanation

Given information:

The provided function is U=5x2+xy3y2.

Formula used:

If a function is z=f(x,y), then the partial derivative with respect to x is,

zx=fx(x,y)zx=x[f(x,y)]

If a function is z=f(x,y), then the partial derivative with respect to y is,

zy=fy(x,y)zy=y[f(

(b)

To determine

To calculate: The marginal utility of product y if the utility function U=f(x,y) is a measure of the ability (or satisfaction) derived by a person from the consumption of two products x and y. The utility function for two products is U=5x2+xy3y2.

(c)

To determine

Whether a person should consume one more unit of product of x or one unit of product of y if x=2, y=3, and explain the same.

(d)

To determine

To graph: The function U=5x2+xy3y2 and interpret the marginal utility of products x and y graphically.

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