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 Income and Substitution Effect

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Table of contents

    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.

     Income and Substitution Effect A Budget Line for the Bundle of Goods that Contains x and y StudySmarterFig. 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.

     Income and Substitution Effect Indifference Curve and the Budget Line StudySmarterFig. 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 \(Q_1,Q_2\).

    If you think that you are missing some points in understanding this part, don’t forget to check our detailed explanations of:- Indifference Curve;

    - Budget Constraint;

    - Budget Constraint Graph.

    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.

     Income and Substitution Effect New Budget Line B2 and Old Budget Line B1 StudySmarterFig. 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.

     Income and Substitution Effect The New Indifference Curve IC2 and the Old Indifference Curve IC1 StudySmarterFig. 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 income effect is the change in consumption of goods due to increased real income. The income effect causes indifference curves to move up or down. If the price of the good decreases, our real income increases, and the indifference curve will move upwards and vice versa.

    The substitution effect occurs due to a decrease in the price of one good while the other good’s price remains the same. This changes the marginal rate of substitution and the slope of the budget line.

    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.

     Income and Substitution Effect The New Budget Line and The Substitution Effect StudySmarterFig. 5 - The New Budget Line and The Substitution Effect

    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.

     Income and Substitution Effect Income and Substitution Effect Combined StudySmarterFig. 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.

     Income and Substitution Effect The Indifference Curve and The Budget Line for Pizza and Hamburger  StudySmarterFig. 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.

     Income and Substitution Effect The Indifference Curve and The Budget Line for Pizza and Hamburger After the Discount StudySmarterFig. 8 - The Indifference Curve and The Budget Line for Pizza and Hamburger After the Discount

    Did you notice how your utility increased after the discount? Your new utility curve, \(IC_2\), is higher than your previous utility curve, \(IC_1\).

    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.

    Let’s assume that we are analyzing any market. The price of the good in this market decreased. As the prices decrease, consumers may prefer to consume that good instead of buying other things. For example, you may say that instead of buying coffee, you may rather have tea since your utility from tea at a discounted price may be higher.

    As we mentioned before, this is what the substitution effect is. Lower prices will increase the demand since consumers would prefer that good over other goods. The other reason for increased demand is the income effect. If you can buy more tea with the money you have, you can indeed consume more tea. This will give you more utility.

    Therefore, it is rational to consume more tea. In total, decreased prices will increase demand. And this is why the substitution and income effect is related to the law of demand.

    If your knowledge of the demand curve is a little dusty, don’t hesitate to check our explanations on:- Supply and Demand.

    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.

    Eager to learn more?

    We’ve got you covered!

    Check out:

    - Consumer Choice;

    - Revealed Preference;

    - Trade Offs in Economics;

    - Utility Functions.

    Income and Substitution Effect - Key takeaways

    • The income effect is the change in consumption of goods due to increased relative income. The income effect causes indifference curves to move up or down. If the price of the good decreases, our relative income increases, and the indifference curve will move upwards and vice versa.
    • The substitution effect occurs due to a decrease in the price of one good while the other good’s price remains the same. This changes the marginal rate of substitution and the slope of the budget line.
    • Combined together, income and substitution effects will change the demand for a good in a market. They are the fundamental driving forces behind the negative slope of the demand curve.
    Income and Substitution Effect Income and Substitution Effect
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    Frequently Asked Questions about Income and Substitution Effect

    How do you find the substitution and income effect from a graph?

    We can find the income and substitution effects from a graph with the help of the total effect. The difference between the tangent point where the new indifference curve meets the new budget line and the tangent point where the old indifference curve meets the old budget line is the sum of the income and substitution effect. If we draw a linear line tangent to the old indifference curve with the slope of the new budget line, the difference between this point and the new tangent point where the new indifference curve meets the new budget line is the income effect. If we substitute this distance from the total effect, we can find the substitution effect.

    Do income and substitution effects work together?

    They are separate effects. Nonetheless, combined together, they compose the total effect of decreased prices over consumption.

    What is the substitution effect in economics?

    The substitution effect occurs due to a decrease in the price of one good while the other good’s price remains the same. This changes the marginal rate of substitution and the slope of the budget line. The exact difference between new tangent point where new budget line meets the indifference curve and the old tangent point where old budget line meets the indifference curve is the substitution effect.

    Why is the income and substitution effect important?

    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.

    What are examples of the substitution effect and or real income effect?

    Let us assume that you are consuming two goods, x and y. After a decrease in the price of x, people will consume more x due to the fact that their relative income has increased. People also consume more y since the marginal rate of substitution between y and x has changed. The former is called the income effect, and the latter is called the substitution effect.

    Test your knowledge with multiple choice flashcards

    We are defining the effect of decreasing or increasing prices over consumption amount as the total effect of income and substitution.

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

    Let’s assume that due to decreased prices of one good, you wanted to consume that good instead of the other good. This can be called substitution effect.

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