The Consumption Function - Online Tutor, Practice Problems & Exam Prep

The consumption function illustrates the relationship between disposable income and household spending. As disposable income increases, consumption typically rises, reflecting the marginal propensity to consume (MPC), which indicates how much consumption changes with a change in income. The equation for the consumption function can be expressed as $C=\mathrm{MPC}Y+C(0)$, where C(0) represents consumption when income is zero. Understanding these concepts is crucial for analyzing economic behavior and national income dynamics.

Consumption Function (Consumption Schedule)

So let's learn a little bit more about consumption by looking at it on the graph. We're going to check out the consumption function. Remember, consumption is the amount of household spending. When we think about consumption, it's money that households spend on consuming things, right? They're going to buy things and use them, so this is the consumption we're talking about. It's part of GDP, right? So when we think about consumption, we have to consider the level of disposable income. When we think about disposable income, it's the money that households have left after they pay for taxes. They're going to earn some income, pay for taxes, and then whatever's left over, they will have as disposable income. Sometimes, the consumption function is called the consumption schedule; it's just another name for it. We're just going to be looking at it on the graph, okay?

Like I just said, disposable income is the amount left after paying for taxes‚ What do you think we can do when we have some money left over? The disposable income can either be used for consumption or, if we don't consume it, we're going to save it. So, consumption or saving, okay? On a macro level, disposable income is all of the national income, all the income that gets earned in every shape or form minus the taxes that get paid. What's left over is going to be consumption or savings. Cool?

Now, let's think about consumption logically. You work in a candy factory that has been making tons of sweet, sweet profit. For all your hard work and dedication, you receive a bonus of $10,000 and an annual raise of 20% of your current salary. That sounds pretty nice. Due to this, what do you think is going to happen? You now have more money, an additional $10,000, and a salary increase. Your total consumption is likely to increase. You're not going to spend all that money, right? You're going to have more disposable income. That means you're going to consume more. You'll probably consume a portion of that extra money, go out, and buy yourself something nice, and you might save some of it too, right? Your savings will go up as well. So, the more disposable income you have, the more you're likely to consume, and that's what we're going to see here in the consumption function.

So let's bring it down to the graph and talk about some key features when we think about consumption. The first thing I want to show you is what we call the 45-degree line. Every dollar of disposable income is getting used for consumption. The 45-degree line is going to look something like this, and it's going to be a reference point when we look at the consumption function.

Now, let's draw a random consumption function; it might look like this. Even if you had no disposable income, you're still going to consume stuff, like food, shelter, and all sorts of things during the year. So, you're going to have some level of consumption regardless of having any disposable income. As you have more disposable income, your consumption is going to increase as well.

So let's look at a few features of this consumption function. At one point on the graph, where the 45-degree line touches the consumption function, all disposable income is being consumed. At other points, say, for example, at point B on the consumption function, where we have a high level of disposable income but less consumption, the difference represents savings. This green area is the amount of disposable income that was saved.

Down here at point C, where we have $1,000 of disposable income but we're consuming more than our disposable income, we have what's called dis-savings, where we're either dipping into our previous savings or taking on new debt to manage this level of consumption. So, these are the key things to know about the consumption function, including the dis-savings where we are consuming more than our disposable income.

Let's pause here, and then we'll talk about another key feature of the consumption function, the marginal propensity to consume, in the next segment.

Marginal Propensity to Consume and Save

Alright, so now that we're familiar with the consumption function, let's think about one more feature here and it's going to be called the marginal propensity to consume. Just like we saw, as we have more candy stored, right? What we saw is we got a big bonus at work, we got a lot of extra money and what were we expecting to do? We're expecting to consume more, maybe buy ourselves a gift, but we are not going to spend all of that bonus. We might save some of it as well. So, what's going to happen is that as we add disposable income, some of it's going to be consumed. Some of it's going to be saved and that's the idea of the marginal propensity to consume is actually how much we are going to consume and how much we are going to save. So, the marginal propensity to consume, remember when we talk about this word marginal, what's marginal meant all throughout this class? Class? Marginal. Adding one more, right? When we add one more. How do things change when we add one more? So in this case, we're going to see how much consumption changes when disposable income changes, right? How much is consumption going to change when disposable income changes?

So, let's before we fill this in, let's look at our formula here. So the marginal propensity to consume, we call it MPC. It's the change in consumption. The little delta there meaning change. So how much more consumption when we change disposable income? So let's say we increase disposable income by 1. How much is consumption going to increase, right? So, we could expect maybe we have 1 more dollar of disposable income. We earn 1 more dollar. Maybe we'll spend $0.75 of that dollar and we'll save the rest of it, right? It could be any number. In this case, let's say it's $0.75, right? So we would have a marginal propensity to consume of 0.75, okay? So it's going to have to be something between 0 and 1, right? We're going to have $1 of income and we're either going to spend some proportion of it in between 0 and 1. So in this case, we're spending 75% of it and of course, the rest of it we would be saving. So that's what we have in the marginal propensity to save. That's the amount your savings change. How much savings change when disposable income changes. So you're going to get an extra dollar of disposable income and in this case, how much are you going to save, right? So for each dollar of disposable income, well, you're going to save some of it, right? So naturally, if you didn't consume it, you're going to save it. So in this case, we'll say you save 25% of that extra money that you get.

So let's go back up to the graph. What does that tell us about the graph? Think let's think about the marginal propensity to consume and the consumption function. What does it tell us? Remember, the marginal propensity to consume is the change in consumption over the change in disposable income. So for every extra dollar that we get in disposable income as we move right on this graph, how much are we going up? What does that sound like? What's one of those key words about a line? Notice the consumption functions a line here. What do you think the marginal propensity to consume is? It's the slope of the marginal propensity to consume is? It's the slope of the line, right? How much is it going to go up? How much is our consumption going to go up as we get extra disposable income, right? So that's what we see here for each dollar of extra disposable income. So as we move from this point out here let me do that a little better. I'll do it in black actually. New color. So as we move here and now we move out, how much are we moving up? Right? So that is our marginal propensity to consume and notice that it's constant along our consumption function because we have a line and lines have a constant slope. Okay? So that's what we're going to be dealing with here is that the slope is that marginal propensity to consume. Cool? Let's take a pause here and we're going to dive into these topics of marginal propensity to consume and save a little more on the next page.

1 = MPC + MPS

All right. So let's learn a detail here about the marginal propensity to consume and to save. So recall that when we talked about disposable income, we said that whenever we have disposable income, wherever we're either going to use it for consumption or saving, right? It's going to be one or the other here. So it follows that any increase in disposable income, if we have extra disposable income just like we saw, it's either going to be consumed or saved, right? Any extra money we have, it's either going to be consumed or saved and that's going to depend on that marginal propensity of whether how much of that disposable income you want to consume or save. So what follows here, what we see is that the disposable income equals the consumption or savings, right? Because any disposable income we're either going to consume it or save it so that means any change in disposable income and I'll do change in I'm going to say Y for disposable income because we've been using Y for income in other videos, so change in Y is going to equal the change in consumption plus the change in savings, right? If we have an extra dollar of disposable income, well it's either going to increase our consumption or increase our savings. So they're going to stay equal there.

So now what I want to do is I want to take this and I want to divide it by the change in Y. So notice, divide by the change in Y, if we do that to everything here which we can do thanks to the rules of algebra. You're just going to have to trust me if you don't remember that one. We can divide everything by the change in Y and what does that leave us with? Notice, change in Y divided by change in Y, what does that equal? Anything divided by itself, well that's going to equal 1, right? dY/dY=1 and what does change in consumption over change in disposable income? Look back on the previous page when we defined marginal propensity to consume right? The change in consumption divided by the change in income, disposable income, well, that's your marginal propensity to consume plus your marginal propensity to save. Okay? So that's what if the marginal propensity to consume plus the marginal propensity to save, they're always going to equal 1 and that's because this whole identity of whenever we have extra income, well it's going to either be consumed or saved, okay? So it's either going to go towards the marginal propensity to consume or the marginal propensity to save there. Okay? So sometimes they might give you, let's say in a problem, they might tell you oh the marginal propensity to consume is 0.6. Well, you can already infer that the marginal propensity to save is going to be the other 0.4, right? Because they have to equal out to 1.

All right, let's pause here and let's talk about the consumption function as the equation of a line, all right? Let's do that in the next video.

Equation of the Consumption Function

Alright. So, do you guys remember back to algebra when we learned the equation for a line? A lot of us might have learned it as y=mx+b, right? y=mx+b. Some of us learned it as y=ax+b either way, we're talking about the same thing here, and we're talking about a line. If you look back on the graph, remember when we talked about the consumption function, it was a line, right? And we knew what the slope was, and we know what the variable is that's going to change our consumption. Let's go ahead and define some of these things here.

So, we can talk about the consumption function as a line, as an equation, just the same. So in this case, M is what's being moved; it is the rate that we're changing here. M is the slope of the line, which is just classic algebra there, right? y=mx+b. M is the slope of the line, and in this case, the slope, just like we saw in the graph, is the marginal propensity to consume, right? For every extra dollar of income, how much of it are we going to consume? That's going to be the increase in the line there. So, what's going to be the X here? What is driving the consumption? The disposable income, right? As we have more disposable income, we're consuming more. So, X is disposable income. Right, the disposable income. What we use sometimes for a symbol for this is we've been using Y for income, and sometimes we just call it Y_d. Sometimes with a little subscript d like that, sometimes you see a whole full lowercase letter d like we have in our equation below. And then, what's going to be b? What's b? Remember, b is the y-intercept, right? The y-intercept, and this is the amount of consumption that we have when disposable income equals 0, right? When we have no disposable income, well, we're still going to have to consume something, right? We're still going to have food to eat. We're still going to need shelter. We're still going to need some expenses when we have no disposable income. Okay?

So, you can be given an equation of the consumption function line. They can tell you an equation like C=0.75x+50, right? Something like that, and you can solve for consumption at any level of disposable income. If you had a disposable income of 10, well, you would put in 10 into this equation, and you would solve for disposable income. Or excuse me, solve for consumption there, right? Cool. So that's about it here. Let's get some practice using all of these equations in the next video.

Calculate the Marginal Propensity to Consume and the Marginal Propensity to Save using the following table: 

All right. So let's get some practice here. Let's see how you did. So what we have here, calculate the marginal propensity to consume and the marginal propensity to save using the following table. So what are we given here? We're given levels of disposable income and levels of consumption. It asks us to solve for savings, MPC, and MPS. Well, it's easy to solve for savings if you know disposable income and consumption, right? The savings is the difference between the two because disposable income is either used for consumption or for savings. So when we think about disposable income, we'll say YD, it's either going to be used for consumption or savings, right? So naturally, if we subtract C from both sides, well then YD minus C equals savings, right? So we just have to subtract the consumption from the disposable income and we will get the level of savings. So 18000 minus 16000, well, we consumed 16000 but we saved 2000 of it there. Right? Now what about let's just do all the savings since that's just easy subtraction here. So when we have a disposable income of 20000, well, we're consuming 17200, 2800 being saved. So that's the difference between the two. And what about the next one? 22000 minus 18400. That tells us we're saving 3600. And the next one, 24000 minus 19600, is 4400 and finally, at a level of 26000 in disposable income, we're consuming 20800 leaving us with 5200 in savings. So notice as our disposable income goes up, our consumption goes up and our savings go up and this has to do with the marginal propensity to consume as we have more income, how much more are we going to consume and the marginal propensity to save as we have more income, how much are we likely to save. So remember, when we're dealing with marginal, we have to think about the change in income and the change in consumption and savings. So when we calculate the marginal propensity to consume, we have to think about how much has it changed. So in this first case, we're not going to do anything because there's no change but let's think about when we change from 18000 to 20000. So remember, marginal propensity to consume, that was the change in consumption divided by the change in disposable income, right? So, in this case, what was our change in consumption? Well, we were at 16000 and we went up to 17200. So our consumption went up by 1200, right? 17200 minus 16000. Our consumption went up by 1200. And what about our disposable income? We were at 18000 and now we're at 20000. Our disposable income went up by 2000, right? 12002000. Well, that comes out to 0.6, right? So what does that tell us? In this case, that as we get an extra dollar of disposable income, we're going to consume 60 cents more, right? Do you know what the marginal propensity to save is going to be? Remember that the marginal propensity to consume plus the marginal propensity to save is equal to 1, right? Because we're either going to consume or save. So naturally, I would expect it to equal 0.4. But let's go ahead and calculate it just in case. So our savings here, remember, marginal propensity to save is change in savingschange in disposable income. How much are we going to save when we have some extra disposable income? So in this case, our savings went up from 2000 to 2800. We have an extra 800 of savings and the same thing on the bottom, right? We're still dealing with an extra 2000 of disposable income. So 8002000, well, guess what? It equals 0.4. So it follows 0.6 plus 0.4, it equals 1. Right? That's all of our change in disposable income either went to consumption or savings. So as we go down, we should expect since we're dealing with consumption functions that are linear at least in this class, we deal with them that are linear. We should expect it to stay constant here. So let's see what happens. Again, we see that our disposable income in each of these cases is going up by 2000, right? 20000 to 22000, 24000. It's always going up by 2000. So in the next one, we're going to have 2000 in the denominator and what about our consumption? It went up by 1200 again. Right? So 12002000, again we get 0.6. And what about savings? Again, it went up by 800, right? So our change in savings was 800 and our disposable income changed by 2000. valueType="d"> It holds constant here. This means that we're probably dealing with a line, a consumption function that's a line. We've got a constant marginal propensity to consume and as we go down, we're going to see the same thing, right? It changed by 1200 again our consumption from 19600 from 18400 to 19600 that was an extra 1200 disposable income went up by 2000, 0.6 again. And the same thing here, 800 divided by 2000 we're going to get 0.4. And finally in the last one, same thing again, consumption went up by 1200, 0.6. And finally, 800 more in savings from 4400 to 52002000 we get 0.4. Cool. So what did we see here? We've got a constant marginal propensity to consume of 0.6. Every dollar of extra disposable income, we spend 60 cents on consumption and we save the rest 40 cents. Cool? Alright. Let's go ahead and move on to the next video.

If the Keynesian consumption function is C = 10 + 0.8 Yd then, if disposable income is $1000, what is amount of total consumption?

• A. $0.80
• B. $800
• C. $810
• D. $0.81
• E. Cannot be determined

If the Keynesian consumption function is C = 10 + 0.8 Yd then, when disposable income is $1000, what is the marginal propensity to consume?

• A. 0.8
• B. 800
• C. 810
• D. 0.81
• E. Cannot be determined

An increase in the marginal propensity to consume will:

• A. Lead to the consumption function becoming steeper
• B. Shift the consumption function upwards
• C. Shift the consumption function downwards
• D. Not affect the consumption function

Here’s what students ask on this topic:

What is the consumption function in macroeconomics?

The consumption function in macroeconomics illustrates the relationship between disposable income and household spending. It shows how much households plan to consume at different levels of disposable income. The function is typically represented as C = MPC × Y + C₀, where C is consumption, MPC is the marginal propensity to consume, Y is disposable income, and C₀ is the autonomous consumption (consumption when income is zero). This function helps economists understand consumer behavior and predict changes in aggregate demand based on changes in income.

How does the marginal propensity to consume (MPC) affect the consumption function?

The marginal propensity to consume (MPC) is a key component of the consumption function. It measures the change in consumption resulting from a change in disposable income. Mathematically, MPC is defined as the change in consumption (ΔC) divided by the change in disposable income (ΔY). In the consumption function C = MPC × Y + C₀, MPC determines the slope of the function. A higher MPC means that households are likely to spend a larger portion of any additional income, leading to a steeper consumption function. Conversely, a lower MPC indicates that households will save more of their additional income, resulting in a flatter consumption function.

What is the significance of the 45-degree line in the consumption function graph?

The 45-degree line in the consumption function graph is a reference line where every dollar of disposable income is spent on consumption. It represents a situation where consumption equals disposable income (C = Y). This line helps to visualize the relationship between income and consumption. Points above the 45-degree line indicate that households are consuming more than their disposable income, leading to dissaving or borrowing. Points below the line indicate that households are saving part of their disposable income. The actual consumption function typically lies below the 45-degree line, reflecting that not all disposable income is consumed.

What is the difference between autonomous consumption and induced consumption?

Autonomous consumption (C₀) is the level of consumption that occurs even when disposable income is zero. It represents the basic consumption necessary for survival, such as food and shelter. Induced consumption, on the other hand, is the portion of consumption that changes with changes in disposable income. It is represented by the term MPC × Y in the consumption function C = MPC × Y + C₀. While autonomous consumption is constant, induced consumption varies directly with income, reflecting the marginal propensity to consume (MPC).

How do you calculate the marginal propensity to save (MPS)?

The marginal propensity to save (MPS) is calculated as the change in savings (ΔS) divided by the change in disposable income (ΔY). It represents the portion of additional income that households save rather than spend. Mathematically, MPS can be expressed as MPS = 1 - MPC, where MPC is the marginal propensity to consume. Since any additional income is either consumed or saved, the sum of MPC and MPS always equals 1. For example, if MPC is 0.75, then MPS would be 0.25, indicating that 25% of additional income is saved.