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1. An individual’s utility function is given as, where x1 and x2 denote the number of units consumedof goods 1 and 2 respectively:U = x121 x132,(a) Express the marginal utilities of x1 and x2. (b) Show that the marginal utility of x1 is positive and interpret this result. (c) Find the value of the marginal utilities when x1=16 and x2=8. (d) Find the marginal rate of commodity substitution at this point. (e) Estimate the change in utility when x1 and x2 both increase by 1 unit.

1. An individual’s utility function is given as, where x1 and x2 denote the number of units consumedof goods 1 and 2 respectively:U = x121 x132,(a) Express the marginal utilities of x1 and x2. (b) Show that the marginal utility of x1 is positive and interpret this result. (c) Find the value of the marginal utilities when x1=16 and x2=8. (d) Find the marginal rate of commodity substitution at this point. (e) Estimate the change in utility when x1 and x2 both increase by 1 unit.

Economics (MindTap Course List)
Economics (MindTap Course List)
13th Edition
ISBN:9781337617383
Author:Roger A. Arnold
Publisher:Roger A. Arnold
Chapter20: Consumer Choice: Maximizing Utility And Behavioral Economics
Section: Chapter Questions
Problem 3WNG
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1. An individual’s utility function is given as, where x1 and x2 denote the number of units consumed
of goods 1 and 2 respectively:
U = x
1
2
1 x
1
3
2
,
(a) Express the marginal utilities of x1 and x2. 
(b) Show that the marginal utility of x1 is positive and interpret this result. 
(c) Find the value of the marginal utilities when x1=16 and x2=8. 
(d) Find the marginal rate of commodity substitution at this point. 
(e) Estimate the change in utility when x1 and x2 both increase by 1 unit. 

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