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6. Euler’s theorem (one of many): A function ?(?1,?2,…,??) is said to be homogeneous of degree...

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Economics

6. Euler’s theorem (one of many): A function ?(?1,?2,…,??) issaid to be homogeneous of degree k, if for any ? > 0,?(??1,??2,…,???) ≡ ?^? ?(?1,?2,…,??)

a. Explain why a demand function ?(??,??,?) is homogeneous ofdegree 0.

b. Using part a), prove the sum of the income elasticity and thecross-price elasticity equals the price elasticity of demand. Hint:differentiate the demand function identity in part a) with respectto λ.

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