Consider the utility-maximization of a consumer with preferences
U(Dc;Df) = (Dc)^a(Df)^1-a; with 1< a<0 and a budget constraint of the form
PcDc+PfDf <-(less than or equal to) I=Income.
1. Solve for the marginal utility of consuming clothing, that is @U(Dc;Df)=@Dc.
2. Solve for the marginal utility of consuming food, that is @U(Dc;Df)/(Df/Dc)a/(1-a). Show your work.
3. 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.