Aggregate Expenditures Model Components of Aggregate Expenditure Average and Marginal Propensities to Consume and Save Page 1 of 3

We’re building Keynes’s model of the macroeconomy. It’s a model that’s driven by demand. If people won’t buy stuff, then it accumulates on store shelves; and when factories cut back their production, people are laid off work. The economy keeps adjusting until we find an equilibrium. In this equilibrium, the spending plans of consumers, businesses, the government, and foreigners add up to create an income on which those spending plans are based. That is, we get a stable circular flow between what people are planning to spend, and the goods and services that are actually produced by factories to meet the demand. That’s macroeconomic equilibrium.

To understand macroeconomic equilibrium, we have to look at the plans that consumers, businesses, the government, and foreigners make. Those plans are based on, for example, consumer income, interest rates, and other environmental factors in the economy. We’ve been thinking about the consumption function, and now we’re going to discuss another way of describing consumer behavior, because it turns out that you can just as easily describe consumer behavior in terms of savings as you can describe it in terms of spending. That’s because consumer income can be used in one of three ways. When you get a paycheck, there are only three things you can do with it. You can either spend it, in which case we call it consumption; you can put it in a mutual fund, or in the bank, in which case we call it savings; or the government can take it, in which case we call it taxes. These three components add up to consumer income; consumers spend, they save, and they pay taxes.

Now for the time being we’re going to assume that consumers are not paying taxes; that is, taxes are equal to zero. And, in that case, consumer spending and consumer saving add up to the total of consumer income. Well, once you’ve seen this relationship, a kind of complementarity becomes obvious. That is, consumer savings is just as accurate a description of consumer behavior, and just as complete, as is consumer spending.

Let’s go back to the numbers that we considered in the consumption schedule in a previous exercise. Here we have income equal to 40, and consumer spending equal to 42. That means that the consumer’s spending $2.00 more than his income in this period, which means that he’s drawing down his savings by $2.00 – that is, dis-savings is enabling the consumer to spend more than his income. If income is 50 and consumer spending is 50, then savings is equal to zero – a kind of break-even point. And if consumer income is equal to 80 and consumer spending is equal to 74, then that means the savings is equal to 6 – the consumer is putting some money into the bank. Here you see this complementary relation between consumption and savings.

Now, before, we described consumer spending in a function, an algebraic equation that we called the consumption function. Now what we’re going to do is look at a relationship between the consumption function and the savings function. That is, once you know how the consumer behaves, you can describe also the savings function. Let’s look now at this relationship. Output, which is consumer income, is equal to consumption plus savings. We also know that consumption is equal to A, autonomous consumption – plus B, which is the marginal propensity to consume – multiplied by Y, which is income.

Well, both of these things are true; therefore, if we plug this description of consumption into the previous equation, we can get this: Y is equal to A plus B times Y plus S. And if we solve this equation for S, let’s see what we get: -A – I get that by moving A to the other side of the equation; I move BY to the other side of the equation, and I get 1 minus B times Y is equal to S. If I move everything over to the left-hand side except for savings, this is the equation that I get: Savings is equal to -A plus 1 minus B times Y.

Let’s take a moment and see if there isn’t some intuition in all of these symbols. Well, think about it. Anything that the consumers are going to be spending at zero income – that is, the autonomous component of consumption is going to be equal to dis-savings. That is, if income is equal to zero, and the consumers have to have food, clothing, and other necessary expenditures equal to A, the only way they can get that is to draw down their savings. So autonomous consumption is going to be equal to autonomous dis-savings. This is what you have to take out of your savings account when income is zero to meet your basic needs.

The next to think about is this slope. Up here, B represents the fraction of each additional dollar that you spend on

Aggregate Expenditures Model Components of Aggregate Expenditure Average and Marginal Propensities to Consume and Save Page 2 of 3 consumption goods and services. That means that what you’re doing with the rest must be savings. So if B is the fraction that you are consuming, then 1 minus B is the fraction of an additional dollar that you are saving. So you see here that B – the marginal propensity to consume – plus 1 minus B – the marginal propensity to save – is equal to 1. Every additional dollar that you get is broken into its two possible uses; one fraction of it you’re going to consume, and one fraction of it you’re going to save.

In the example we looked at previously, the fraction that was consumed of each additional dollar was $.80, so a .8. That means that the marginal propensity to save in this case is .2. For every additional dollar you receive, you’re going to save $.20. The marginal propensity to consume is 1 minus the marginal propensity to save. The marginal propensity to save is 1 minus the marginal propensity to consume. Every dollar is divided into the part that’s spent and the part that’s saved, and the two propensities – the two fractions – add up to 1.

Now since that’s the case, we’re able to do some calculations based on the numbers that we used in our previous example. So if it’s true that consumption is equal to 10 plus .8 times Y, then savings is going to be equal to -10 plus .2 times Y. You can see where I got this; if you take this amount of consumption and you subtract this formula from Y – S equals Y minus C equals Y minus this formula for consumption – and if you go ahead and do the algebra here, you get Y – take the minus sign into the parenthesis – Y minus. 8(Y) is .2(Y), and there’s no constant outside, so your constant is going to be left at -10; savings is -10 plus .2 times Y – there’s the savings formula.

Now let’s take this algebra and carry it back over to the graphs that we’ve seen earlier, because we’re going to see now a graphical complementarity between savings and consumption. Previously, we wrote consumption on the vertical axis as a function of income on the horizontal axis, and we drew it out, graphing it as this linear function. Here’s my intercept of 10 – my autonomous consumption, what you spend even at zero income – and the slope of my consumption curve is going to be rise over the run. The rise here is the change in consumption, the run is the change in income, and the change in consumption that results from the change in income is equal to the marginal propensity to consume, which we’ve labeled with the letter B – the slope in our consumption diagram.

Now the savings curve is going to look like the complement of that picture. Down here we have the intercept, which is -10, because if income is zero and you’re spending 10, that means when income is zero, you must be saving -10. So if we represent savings as a vertical coordinate, as a function of income, the horizontal coordinate – when income is zero, savings is -10.

Let’s find another point on the savings curve. Well, look at this point right here. When consumption is equal to income – that is, when the red line crosses the black dotted line – savings is equal to zero. The black dotted line indicates all of those points here where consumption is equal to income; those are all the points that are on that line. So if consumption – the planned consumer spending – is equal to the income that consumers receive, planned savings will be equal to zero. Therefore, since this curve is linear and has a slope of 1 minus C, we can go ahead and draw the savings function. Here’s savings as a function of income – just like up here, we have consumption as a function of income – we now have a slope of the change in savings that results from a change in income. The slope of this curve is equal to the marginal propensity to save. The change in savings that results from the change in income is the marginal propensity to save. And in this case the marginal propensity to save is going to be 1 minus B.

Look, there’s a nice, complementary relationship between these two curves. For any given income level – now let’s pick an income level, say Y0 – if we go up the diagram, the amount by which consumption – the red curve – exceeds income – the black curve – is going to be equal to the amount of dis-savings. This gap upstairs is equal to this same vertical gap downstairs. For any given income level, the difference between consumption – the red curve – and income – the black dotted curve – is going to be the amount of savings, which is seen in the downstairs diagram. Where consumption crosses income in the upstairs diagram, savings is equal to zero.

Over on this side of the break-even point, in this region up here, savings is going to be less than zero. That is, consumers are dis-saving in order to finance the excess of consumption over income. And if we’re on this side of the dotted line, savings is going to be positive. That is, since consumers are spending less than their total income, there’s

Aggregate Expenditures Model Components of Aggregate Expenditure Average and Marginal Propensities to Consume and Save Page 3 of 3 actually money, as we can see down here, being put into the bank. So it’s pretty easy to see here the complementary relationship between consumption and savings.

There’s one more term that I want to define, and that is “average propensity to consume.” Average propensity to consume is your total consumption divided by your total income. The average propensity to consume is the fraction of the their total income that consumers are spending. Remember marginal propensity to consume is how much you spend out of each additional dollar. But the average propensity to consume is your total overall spending as a fraction of your total overall income.

We can say the same thing about savings – S over Y is the average propensity to save – the fraction of your income that you’re saving; whereas the change in saving that results from a change in income is called the marginal propensity to save. Just as the marginal propensity to consume and the marginal propensity to save add up to 1, the average propensity to consume and the average propensity to save also add up to 1. Out of every dollar you get, part of it is going to be spent, part of it is going to be saved. Whether you’re talking about your total income, or whether you’re talking about a marginal dollar that you get, you make a decision about what fraction to spend and what fraction to save. In the United States right now, our average propensity to consume is about 0.98; that is, on average, we’re saving only about $0.02 out of every dollar. The complementary relationship between consumption and savings helps us then, to begin to build a model of how macroeconomic forces interact.