<p>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:</p>

<p>$\displaystyle\frac{\partial d_1}{\partial p_1}+\frac{\partial d_1}{\partial I}\frac{\partial I}{\partial p_1}$</p>

<p>The slutsky equation from class is probably of the form given in this answer : <a href="https://economics.stackexchange.com/questions/13242/applications-of-the-slutsky-equation/13247#13247">applications of the slutsky equation</a></p>

CC BY-SA 3.0
2016-09-01T21:47:27.097Z
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
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2016-09-01T22:18:30.123Z
You differentiate $d_1$ in 2 spots. First with respect to the first argument, then the third through I. chain rule
VCG
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2016-09-01T16:55:31.133Z
2016-09-01T16:55:31.133Z
2017-04-13T12:51:38.253Z
VCG
<p><a href="https://i.sstatic.net/vl2gs.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/vl2gs.jpg" alt="enter image description here"></a></p>

<p>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!</p>

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2016-09-01T07:06:28.407Z
You do not derive the demand function, it is given to you as $d_1()$.
Giskard
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2016-09-01T12:18:29.897Z
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
<microeconomics>
Advanced Microeconomics: Deriving Slutsky Equation
jlang
# Advanced Microeconomics: Deriving Slutsky Equation

(Asked by: username_0 on 2016-09-01)

[![enter image description here](https://i.sstatic.net/vl2gs.jpg)](https://i.sstatic.net/vl2gs.jpg)

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!

**Tags:** microeconomics
> **Comments:**
> **username_1**: You do not derive the demand function, it is given to you as $d_1()$.  
> **username_2**: 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.  

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## 1 answers

### Answer by username_3 on 2016-09-01. Score: 0

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:

$\displaystyle\frac{\partial d\_1}{\partial p\_1}+\frac{\partial d\_1}{\partial I}\frac{\partial I}{\partial p\_1}$

The slutsky equation from class is probably of the form given in this answer : [applications of the slutsky equation](https://economics.stackexchange.com/questions/13242/applications-of-the-slutsky-equation/13247#13247)

> **Comments:**
> **username_0**: How do you take the partial with respect to $p_1$ after substituting the present value of the initial endowment into the equation for $d_1$?  
> **username_3**: You differentiate $d_1$ in 2 spots. First with respect to the first argument, then the third through I. chain rule  

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