Before developing the Keynesian Aggregate Expenditures model, we must understand the basic macroeconomic relationships that are the components of that model. The components of aggregate expenditures in a closed economy are Consumption, Investment, and Government Spending. Because government spending is determined by a political process and is not dependent on fundamental economic variables, we will focus in this lesson on an explanation of the determinants of consumption and investment.

To convert from nominal interest rates to real interest rates, we use the following formula: real interest rate ≈ nominal interest rate − inflation rate. To find the real interest rate, we take the nominal interest rate and subtract the inflation rate. For example, if a loan has a 12 percent interest rate and the inflation rate is 8 percent, then the real return on that loan is 4 percent. In calculating the real interest rate, we used the. Real Interest Rate = -1.50%. Hence, the real rate of interest is -1.50%, which clearly indicates XYZ will lose money in real terms since inflation is greater than the rate of.

Section 01: Consumption and Savings

In the simplest model we can consider, we will assume that people do one of two things with their income: they either consume it or they save it.

Income = Consumption + Savings

In this simple model, it is easy to see the relationship between income, consumption, and savings. If income goes up then consumption will go up and savings will go up. Consider the graph below, which shows Consumption as a positive function of Income:

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Notice the use of the 45˚ degree line to illustrate the point at which income is equal to consumption. At that point, labeled E in our graph, savings is equal to zero. At income levels to the right of point E (like Io), savings is positive because consumption is below income, and at income levels to the left of point E (like I'), savings is negative because consumption is above income. How can savings be negative? If you thought of borrowing, you are right. In economics we call this “dissavings.” Point E is called the breakeven point because it is the point where there are no savings but there are also no dissavings. The graph below demonstrates the relationship between consumption and savings:

The Consumption Function

The Consumption Function shows the relationship between consumption and disposable income. Disposable income is that portion of your income that you have control over after you have paid your taxes. To simplify our discussion, we will assume that Consumption is a linear function of Disposable Income, just as it was graphically shown above.

C = a + b Yd

In the above equation, “a” is the intercept of the line and b is the slope. Let’s explore their meanings in economics. The intercept is the value of C when Yd is equal to zero. In other words, what would your consumption be if your disposable income were zero? Can there be consumption without income? People do this all the time. In fact, some of you students may have no income, and yet you are still consuming because of borrowing or transfers of wealth from your parents or others to you. In any case, “a” is the amount of consumption when disposable income is zero and it is called “autonomous consumption,” or consumption that is independent of disposable income.

In the consumption function, b is called the slope. It represents the expected increase in Consumption that results from a one unit increase in Disposable Income. If Income is measured in dollars, you might ask the question, “How much would your Consumption increase if your Income were increased by one dollar?” The slope, b, would provide the answer to that question. It is the change in consumption resulting from a change in income. (Remember the idea of a slope being the rise over the run? Go back to the graph of the consumption function and satisfy yourself that the rise is the change in Consumption and the run is the change in Income, and you will see that this definition of b is consistent with the definition of a slope.) In economics, “b” is a particularly important variable because it illustrates the concept of the Marginal Propensity to Consume (MPC), which will be discussed below.

The Savings Function shows the relationship between savings and disposable income. As with consumption, we will assume that this relationship is linear:

S = e + f Yd

In this equation the intercept is e, the autonomous level of Savings. With savings, it is quite likely that “e” will be negative, which indicates that when Disposable Income is zero, Savings on average are negative. The slope of the savings function is “f,” and it represents the Marginal Propensity to Save—the increase in Savings that would be expected from any increase in Disposable Income.

Marginal Propensities to Consume and Save

The Marginal Propensity to Consume is the extra amount that people consume when they receive an extra dollar of income. If in one year your income goes up by $1,000, your consumption goes up by $900, and you savings go up by $100, then your MPC = .9 and your MPS = .1. In general it can be said:

MPC = Change in Consumption/Change in Disposable Income = ∆C/∆Yd

MPS = Change in Savings/Change in Disposable Income = ∆S/∆Yd

It is also important to notice that: MPC + MPS = 1

Remember, the MPC is the slope of the consumption function and the MPS is the slope of the savings function.

Example

Let’s do an example using data for a hypothetical economy. The data is presented in the table below. From this data I will graph both the Consumption Function and the Savings Function and calculate the MPC and the MPS. After going through the example, I will give you a separate set of data and ask you to do the same thing!

Disposable Income	Consumption	MPC	Savings	MPS
$15,000	$15,250	0.75	-$250	0.25
$16,000	$16,000	0.75	$0	0.25
$17,000	$16,750	0.75	$250	0.25
$18,000	$17,500	0.75	$500	0.25
$19,000	$18,250	0.75	$750	0.25
$20,000	$19,000	0.75	$1,000	0.25

Notice that as you move from an income of 15,000 to an income of 16,000, consumption goes from 15,250 to 16,000 and savings goes from -250 to 0. The MPC and MPS are therefore:

MPC = ∆C/∆Yd = 750/1000 = 0.75

MPS = ∆S/∆Yd = 250/1000 = 0.25

Since the Consumption Function and the Savings Function are both straight lines in this example, and since the slope of a straight line is constant between any two points on the line, it will be easy for you to verify that the MPC and the MPS are the same between any two points on the line. You can also see that that MPC + MPS =1 as was stated earlier.

Think About It: Calculating MPC and MPS

Graph the Consumption Function and the Savings Function for the data provided in the table below. Also calculate the MPC and the MPS in this example.

Disposable Income	Consumption	Savings
$4,575	$4,647	-$72
$4,755	$4,791	-$36
$4,935	$4,935	$0
$5,115	$5,079	$36
$5,295	$5,223	$72
$5,475	$5,367	$108
$5,655	$5,511	$144
$5,835	$5,655	$180
$6,015	$5,799	$216
$6,195	$5,943	$252

Some of the Non-Income Determinants of Consumption and Savings

Notice that when we graph the Consumption Function, Consumption is measured on the vertical axis and disposable income is measured on the horizontal axis. As disposable income goes up, consumption goes up and this is shown by movement along a single consumption function. But there are other things that influence consumption besides disposable income. What if one of these non-income dete

Equation For Real Interest Rate From Money Multiplier