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.
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