<p>Intuitively, if the price of a particular good in a basket rises, then the individual can no longer afford to buy the same overall basket of goods</p>

<p>If there were no substitution effect, then this would be likely to result in amounts of each of the goods being bought being reduced, even those whose price had not changed, since the overall effect would be similar to a real reduction in income. Since the impact is negative, the equation needs a negative sign for this income effect   </p>

<p>In general there will be a negative income effect on all goods and a positive substitution effect on all goods apart from the one whose price has increased.  Which is dominant for a particular good may depend on the particular situation </p>

CC BY-SA 3.0
2017-11-16T03:55:33.113Z
If we consider only the good whose price has changed then the substitution effect will always be negative. What about income effect?
Shoaib Ashraf
CC BY-SA 3.0
2017-11-16T04:02:40.080Z
In order to analyse substitution effect we change the income so the initial bundle is just affordable at New prices. That change in income is given by ∆m= x1*∆p. Am I right?
Shoaib Ashraf
CC BY-SA 3.0
2017-11-14T08:32:12.447Z
2017-11-14T08:32:12.447Z
Henry
<p>Slutsky identity is given by: ∆x/∆p = (∆x/∆p)|substitution effect + (∆x/∆p)|income effect
Now we know ∆m= x*∆p => ∆p=∆m/x
Therefore, ∆x/∆p = (∆x/∆p)|substitution effect + (x*(∆x/∆m))|income effect
But in HAL Varian's book there's minus sign in front of income effect. I am not being able to figure out how the minus sign came there.
I think of income effect as total effect minus substitution effect.</p>

CC BY-SA 3.0
2017-11-14T08:28:55.970Z
Perhaps your definition of income effect is wrong. Could you please include the definition in your question?
Giskard
CC BY-SA 3.0
2017-11-16T04:32:13.800Z
Have you looked at the [Wikipedia entry for Slutsky equation](https://en.wikipedia.org/wiki/Slutsky_equation)? By the way, please use [Mathjax](https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference) to format your equations. Currently they are very hard to decipher.
Herr K.
<microeconomics><supply-and-demand><price>
Why is there negative sign for income effect in slutsky equation?
Shoaib Ashraf
# Why is there negative sign for income effect in slutsky equation?

(Asked by: username_0 on 2017-11-14)

Slutsky identity is given by: ∆x/∆p = (∆x/∆p)|substitution effect + (∆x/∆p)|income effect
Now we know ∆m= x\*∆p => ∆p=∆m/x
Therefore, ∆x/∆p = (∆x/∆p)|substitution effect + (x\*(∆x/∆m))|income effect
But in HAL Varian's book there's minus sign in front of income effect. I am not being able to figure out how the minus sign came there.
I think of income effect as total effect minus substitution effect.

**Tags:** microeconomics, supply-and-demand, price
> **Comments:**
> **username_1**: Perhaps your definition of income effect is wrong. Could you please include the definition in your question?  
> **username_2**: Have you looked at the [Wikipedia entry for Slutsky equation](https://en.wikipedia.org/wiki/Slutsky_equation)? By the way, please use [Mathjax](https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference) to format your equations. Currently they are very hard to decipher.  

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## 1 answers

### Answer by username_3 on 2017-11-14. Score: 1

Intuitively, if the price of a particular good in a basket rises, then the individual can no longer afford to buy the same overall basket of goods

If there were no substitution effect, then this would be likely to result in amounts of each of the goods being bought being reduced, even those whose price had not changed, since the overall effect would be similar to a real reduction in income. Since the impact is negative, the equation needs a negative sign for this income effect

In general there will be a negative income effect on all goods and a positive substitution effect on all goods apart from the one whose price has increased. Which is dominant for a particular good may depend on the particular situation

> **Comments:**
> **username_0**: If we consider only the good whose price has changed then the substitution effect will always be negative. What about income effect?  
> **username_0**: In order to analyse substitution effect we change the income so the initial bundle is just affordable at New prices. That change in income is given by ∆m= x1*∆p. Am I right?  

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