MonashU/ECC5650MicroTheory/ProblemSet03 - WikiTeach

Unit	ECC2810
Topics	Indirect Utility Functions

Suppose a consumer faces the following utility maximization problem:
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Construct the consumer's indirect utility function v(p,y) and demand functions
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(i=1,2).
Prove that the solution to a consumer's constrained utility maximization problem in
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will occur when the slope of the indifference curve equals the slope of the budget line. That is, prove that:
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Consider the general indirect utility function,

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and a useful identity known as Roy's Identity, namely that

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. To show that in general,

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;

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;

And in particular, for the Cobb-Douglas Utility function,

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, that,

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(assuming that

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).

For the standard budget minimization problem, where the expenditure function,
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```
is given by:
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```
show that a good's price effect on the consumer's expenditure is given by the optimized demand for that good. That is,
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(Riley, Challenge) Suppose that a consumer has the utility function,
```
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```
and faces a budget constraint y and price vector p.
1. Show that the consumer's optimal consumption bundle can be represented by,
```
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```
  where a and b are constants.
2. (harder) Using the above result, show that the Marginal Rate of Substitution has the form,
```
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```
  where B and c are constants.

MonashU/ECC5650MicroTheory/ProblemSet03 (last edited 2009-03-02 06:25:54 by Supervisor2012)