Income and Substitution Effect

We all know that if you are not a morning person, waking up can be a challenge. Especially leaving bed for a cold winter morning seems to be a challenging task. If you feel like this, you probably already found out the importance of a cup of hot coffee. But what is better than a cup of coffee you bought from your favorite coffee place? Obviously, a discount at that coffee place! Discounts will create income and substitution effects in our daily consumption patterns. If you want to learn what the income and substitution effects are and how they affect our daily lives, make sure that you keep reading!

Income and Substitution Effect and Indifference Curves

Income and substitution effects can easily be explained with the help of indifference curves. Let’s assume that we have two goods \(x,y\). In addition to that, we have a budget line, \(B_1\). We can show all possible bundles of goods that we can buy as follows.

Fig. 1 - A Budget Line for the Bundle of Goods that Contains x and y

Now, let us denote our first indifference curve with \(IC_1\) in the second figure.

Fig. 2 - Indifference Curve and the Budget Line

We know that the consumer selects a bundle of \(x\) and \(y\) for consumption where indifference curve \(IC_1\) is tangent to the budget line \(B_1\). In this case, the bundle can be summed up as \(Q_1,Q_2\).

Now, let’s assume that the price of x, \(P_x\), decreased. Our new budget line will be aligned accordingly since we can consume more X with the same amount of money. Now our budget line, \(B_2\), will look as follows.

Fig. 3 - New Budget Line B2 and Old Budget Line B1

Since we can consume more, our indifference curve will be higher than the previous indifference curve. We can denote our new indifference curve as \(IC_2\) as follows.

Fig. 4 - The new indifference curve IC₂ and the old indifference curve IC₁

As you can notice, since we can consume more, our new indifference curve, \(IC_2\), is higher than our previous indifference curve, \(IC_1\). Due to lower price of \(x\), our consumption of \(x\) increased from \(Q_1\) to \(Q_3\).

This is the total effect of lower prices over the consumption of \(x\). We can show this as follows.

\(\Delta Q = Q_3 - Q_1 =\)

\(=\hbox{Total Effect of Decreasing Price Over Consumption}\)

The difference between the two consumption levels occurs due to two main reasons. One is more intuitive than the other one. Since we can buy more goods with the same amount of money as we could previously, our real income level has increased. The second reason is that now between these two goods, we can substitute more \(x\) with one unit of \(y\). The former is called the income effect, and the latter is called the substitution effect.

The total effect can be stated as the two different effects combined.

Therefore, we can denote it as follows.

\(\text{Total Effect} (\Delta Q) = \text{Substitution Effect} + \text{Income Effect} \)

Income and Substitution Effect Graph

Since we know that the total effect is just the sum of the income and substitution effects, how can we show them separately on a graph?

The substitution effect causes the slope of the budget line to change and the income effect causes an increased budget line. We can go over this step by step to clarify the changes in the graph. First, let us keep our budget line at the same level but let’s change its slope.

We can graph this new budget line with \(B_{DS}\). Did you notice the difference between \(Q_1\) and \(Q_s\)? This is the result of the substitution effect. It is important to notice that this is just an imaginary line and doesn’t exist in reality. On the other hand, it is important for us to understand the slope of the new budget line. Let us show the new budget line as follows.

Fig. 6 - Income and Substitution Effect Combined

It is important to notice that the final budget line,\(B_F\), has the same slope as the \(B_{DS}\). Our new consumption bundle is at the point where the second indifference curve,\(IC_2\), is tangent to the final budget line,\(B_F\). As we have mentioned before, the change between \(Q_1\) and \(Q_3\) is the total effect. The change due to the difference in the slope of the budget line is the substitution effect and it is the distance between \(Q_s\) and \(Q_1\). Finally, the difference between \(Q_s\) and \(Q_3\) is the income effect.

Income and Substitution Effect Examples

We can elaborate on our knowledge while giving examples of income and substitution effects in a more numerical way. Let us assume that you have to spend your savings between hamburgers and pizza, an unhealthy but delicious dilemma. You have $90 to spend and a pizza costs $10, while a hamburger costs $3. At most, you can get 9 pizzas or 30 hamburgers. Let’s denote our budget line and indifference curve as follows.

Fig. 7 -The Indifference Curve and The Budget Line for Pizza and Hamburger

Let us assume that a local pizza shop made a deal for loyal customers, and now the prices are halved.

The prices of hamburgers remained the same.

What do you think will happen?

First of all, we know that the rate of substitution will change between two commodities. Due to the discount, now a pizza costs $5. This means that, with a budget of $90, you can get 18 pizzas. So our maximum possible consumption level of pizza increased from 9 to 18. Therefore, the slope of our budget line will also change. Now since our relative income has increased, our budget line will be higher than our previous budget line. We can denote the changes as follows.

Fig. 8 - The Indifference Curve and The Budget Line for Pizza and Hamburger After the Discount

It is important to notice \(IC_{\text{Substitution}}\) curve. This curve represents the change due to the substitution effect of the decreased price. This increases the consumption of pizzas from 5 to 6, the consumption bundle at point A. After this, the income effect increases from 6 to 8, where the indifference curve is tangent to the new budget line, \(B_2\). In total, our total consumption of pizzas increased from 5 to 8. The change between 5 and 6 was the result of the substitution effect, and the change between 6 and 8 was the result of the income effect.

Income and Substitution Effect and the Law of Demand

It is obvious that the income and substitution effect is the driving force behind the law of demand. We know that decreased prices will affect us in two ways, and the total effect will cause us to increase our demand for the commodity. This is highly rational since the law of demand stresses the idea that lower prices will cause more demand. To grasp the idea fully, we can give an example.

Income and Substitution Effect Importance

The importance of the income and substitution effect is directly related to the firm’s decision-making process. For example, if we assume that a decrease in prices is a marketing strategy, we can analyze consumer behavior. Such as how consumers act when their real income is increased or how their patterns of consumption of other products change. Therefore, the income and substitution effect takes an important place in consumer choice theory and it may help us to explain the complex behavior of consumers in a more simple manner.

From another standpoint, the income and substitution effect is also important in creating a demand curve. Since they represent consumer behavior as a response to a discount, they can offer an answer to different questions. For example, if we ask what happens to a commodity’s demand after a discount, we can analyze the income and substitution effects.

Finally, income and substitution effects can help us to analyze the relationship between different goods. This can be important for marketing strategies. For example, if a discount on chips causes increased consumption of sodas, the two producers can promote a discount together to increase their sales.