What is the Slutsky substitution effect

Income and substitution effect

The Overall effect one price change is made with the help of the Slutsky decomposition in the Income effect and Substitution effect divided up. Income and substitution effect describe the cause of the Change in demand.The overall effect represents how a change in price will affect the budget.

For a change, do you want an explanation in which you can visualize the whole thing? Then watch our video now: Income effect Substitution effect to do this!

  • Substitution effect definition
    in the text
  • Income Effect Definition
    in the text
  • Calculate income effect
    in the text
  • Calculate the substitution effect
    in the text

Substitution effect definition

The Substitution effect give the relative change in demand after a good as a result of a price change of the second good. At a Price increase is the Substitution effectnegative, in the event of a decrease positive. For example, if the price of good 1 increases relatively compared to good 2, sinks the Purchasing power of Household for good 1. Hence the Substitution effect of the good 1 negative. From a good 2 he buys household on the other hand more than before, because good 2 is relatively cheaper than good 1. For this reason, this effect of good 2 is positive. So good 1 becomes good 2 substituted - therefore the name Substitution effect.

Income Effect Definition

The Income effect describes the Change in demand of a good following a Change in income. This is from Substitution effect and is delimited with the help of the Slutsky decomposition divided up. The Income effect can positive or negative be. Here the focus is on the aspect that the purchasing power of the Household at constant income decreases when the price of a good increases. The new Budget straight is then below the old one.

Slutsky decomposition: substitution effect income effect

The goal of the Slutsky decomposition is that Overall effect in the Income and substitution effect to split up. Let's look at how the change in demand in the event of a price increase can now be broken down into these effects. Basically the so-called Slutsky equation:

Formulated it looks Slutsky equation like this:

Overall effectt = Income effect + Substitution effect.

The Overall effect is obtained very simply by using the Substitution effect and the Income effect added.

Calculate income effect

Now let's look at the SlutskyDisassembly an example step by step. Let us assume the following information. We have a Utility function, a income in the amount of 100 and the prices of goods are two for good 1 and six for good 2. Then the price rises from good 1 to four. As a first step we now calculate that optimum before the Price increase. We call this bundle of goods A.

Then we still need that optimum after Price increase. We call this bundle of goods B. The Income effect shows that the household through the Price increase can buy less goods. Since goods bundle A contains more goods than goods bundle B.

Calculate the substitution effect

Now we want that Substitution effect to calculate. For this it is necessary that we Adjust income effect. Since this effect is based on the Purchasing power the budget has decreased, we are now fictitiously increasing that income of Householdso that he can still buy bundle A.

For this we need the following formula:

If we insert the values ​​in our example, the result is a value of 140. In the fourth step to calculate we now that optimum after Price increase and the notional income, that we calculated in the third step. We then call the result A ‘.


The Substitution effect of good 1 is thedifference of A. to A ‘. Therefore the following equation applies:

The Overall effect is the difference from A. to B.. So the result here is a value of -10. And since we know that the sum of that Substitution and income effects the Overall effect we also know that the Income effect then is -4.

Try it out with good 2. Here are the memory aids that we have learned from the calculation of good 1:

  • Substitution effect:
  • Overall effect:
  • Income effect:

The results are then for the Substitution effect of good 2 +4, den Overall effect 0 and the Income effect -4.

Income effect and substitution effect for superior and inferior goods

Income effect and Substitution effect contribute superior and inferior goods different than usual: Bei superior goods applies: and . Because at superior goods if the price increases, the consumption one Household of both goods is sinking. The Income effect can only be positive if both goods inferior are. The peculiarity here is that the household will buy more of such goods, the less income he has. An example of this would be bread. The less income the household the more bread he buys because he doesn't want to starve and can't afford anything else. Named after its discoverer Robert Giffen Giffen-Gut however, represents a special case of one inferior good In principle, one would assume that the demand for a good decreases when its price increases. This is at Giffen-Gut but exactly the other way around: S.if, for example, the price of bread rises, paradoxically, it also rises demand after this good. The reason for this is as follows: Before that, besides bread, people also have other things Types of goods Bought. As a result of the rise in prices, they now have relatively less money for other goods. you substitute therefore with additional units of bread


Here you can see all the steps again how to proceed with such a task:

  • Calculate optimum before price change (point A)
  • Calculate optimum after price change (point B)
  • Calculate the fictitious change in income
  • Calculate the optimum after price and income changes (point A ‘)
  • Calculate the substitution effect
  • Calculate the overall effect for the goods
  • Calculate income effect

We know, of course, that the subject is not that simple. So here are a few useful tips that you can use to check whether you have calculated correctly! For the good that expensive has become, must apply: The Substitution effect is always negative. The Income effect is negative at superior goods, but positive at inferior goods. The following applies to the other good: the Substitution effect is always positive and the Income effect is negative at superior Goods and positive at inferior Goods. Since we have superior goods twice in our example, the income effect is negative in both cases. In our example we have considered a price change in which the price of a good has risen. Proceed in the same way when considering a price reduction!

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