# Advanced Microeconomics: Deriving Slutsky Equation

I am not sure how to derive the demand for consumption of today's bread; the first thing the problem asks for. I think it might be a piecewise function based on the interest rate that gets you from the price of today's to the price of tomorrow's, where depending on how high the interest rate is you either want strictly bread today or bread tomorrow. But like I'm said I'm not sure. So I would appreciate any help with this problem. Thanks!

• You do not derive the demand function, it is given to you as $d_1()$. – Giskard Sep 1 '16 at 7:06
• Typing up the questions makes them searchable by others and therefore the answers more of a resource to the community. This increases the likelihood that you will get a helpful answer. Also, if you wanted a precise answer instead of a helpful hint, you'll need to also supply the utility function. – BKay Sep 1 '16 at 12:18

We are given the demand function $d_1(p_1,p_2,I)$, the problem wants you to give the expressions without explicit functional forms. So do the substitution and take the derivative:
$\displaystyle\frac{\partial d_1}{\partial p_1}+\frac{\partial d_1}{\partial I}\frac{\partial I}{\partial p_1}$
• How do you take the partial with respect to $p_1$ after substituting the present value of the initial endowment into the equation for $d_1$? – jlang Sep 1 '16 at 21:47
• You differentiate $d_1$ in 2 spots. First with respect to the first argument, then the third through I. chain rule – VCG Sep 1 '16 at 22:18