• MonashU
• ECC5650MicroTheory
• ProblemSet05

A useful identity, Shephard's Lemma

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1. Provide a proof for the Slutsky Equation,

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   recalling that,

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   .

2. Graphically illustrate and explain the resulting change in

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   for a given change in

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   by appealing to the components of the Slutsky Equation.

3. Given that the following elasticity relations hold for the Marshallian Demand Functions,

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   show that:

   1. Engel aggregation is given by:

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   2. Cournot aggregation is given by:

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      (Hint: make use of Walras' Law,

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      .)