Consider utility-maximization of consumer with preferences

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Consider the utility-maximization of a consumer with preferences U(Dc;Df ) = (Dc)alpha (Df )1-alpha ; with 1 < alpha < 0. and a budget constraint of the form PcDc + PfDf <= I.

1. Solve for the marginal utility of consuming clothing, that is @U(Dc;Df )=@Dc. @= derivative

2. Solve for the marginal utility of consuming food, that is @U(Dc;Df )=@Df .

3. Check that the marginal rate of substitution is equal to -(Df/Dc)alpha/(1-alpha). Show your work.

4. Using the fact that MRS = -Pc/Pf and that PcDc+PfDf = I, solve for the demand for each good in terms of the prices and income.

Reference no: EM131242466

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