Utility Problems
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Consider the following utility functions:
(please see the attached file)
a) Explain what the relationship between a utility function and preference is.
b) What types of preferences (please see the attached file), (please see the attached file), and represent, respectively?
c) For each of the utility functions,(please see the attached file), and, (please see the attached file) show whether it has the same preferences as.
d) Suppose and (please see the attached file) represent the preferences for consumer E and consumer F, respectively. Determine whether each commodity (please see the attached file) and (please see the attached file) is an economic good, an economic bad or an economic neutral for E and F.
e) Do and (please see the attached file) represent the same preference? Explain.
f) For each of and, check whether they represent monotonic preferences? Explain in detail by marginal utilities.
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Solution Summary
This solution provides an explanation for series of utility problems. The types of preferences are provided. The relationship between utility function and preferences respectively are given.
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a) So, utility functions represent a set of preferences. Better put, utility functions provide us with a straightforward way of ranking preferences with a single measure. The typical emphasis is that utility functions are ordinal, in that they merely provide ranking. Utility cannot be used as an absolute measure. A person who prefers ice cream to candy would be represented by a utility function that assigns a higher utility level (ranking) to a bundle that contains more ice cream than candy.
b) So, U1 describes a special case of Cobb-Douglas utility, and is strictly increasing in both goods. Notice that the consumer must consume a positive amount of each good in order to have any utility. Secondly, it appears that the consumer does not have a preference between the goods.
U2 is very similar to the case ...
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