• MonashU
• ECC5650MicroTheory
• ProblemSet02

Preference Relations

1. [JR Ex 1.2] Let

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   be a preference relation, prove the following:

   • NB: Sice

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     is a 'preference relation', it must satisfy the axioms of completeness and transitivity.

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2. [JR Ex 1.6] Cite a credible example where the preferences of an "ordinary consumer" would be unlikely to satisfy the axiom of convexity.

Utility Functions

1. [JR Ex 1.12] Suppose

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   and

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   are both utility functions.

   1. If both u and v are homogeneous of degree r. Prove that the function

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      is also homogeneous of degree r.

   2. If both u and v are quasiconcave, then

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      is also quasiconcave.
2. [JR Ex 1.17] Suppose that preferences are convex but not strictly so. Give a clear and convincing argument that a solution to the consumer's problem still exists, but that it need not be unique. Illustrate your argument with a two-good example.

Indirect Utility Functions Consider the Indirect Utility Function version of the Utility Maximization Problem:

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such that

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. Prove the following two propositions:

1. Prop I v(p,y) is homogeneous of degree 0 in (p,y).

2. Prop II v(p,y) is increasing in y. (Hint: use the Envelope Theorem)