More on the Multiplier

What the multiplier tells us is that a change in autonomous consumption results in a multiple change in equilibrium. Algebra apart, how can that happen? To better understand, let's look at one more example. Suppose that autonomous consumption increases by $100. Someone in society simply changes her plans and spends $100 more for consumption goods. The multiplier theory tells us that (with a marginal propensity to consume of 0.7) the increase in equilibrium income will be $333.33. How does this happen?

The additional $100 of autonomous consumption is spent on consumer goods of some kind -- let's say, for the example, a pair of shoes. This increases the shoemaker's income by $100. With a marginal propensity to save of 0.7, the shoemaker spends $70 of the $100 on additional consumption. This is not "autonomous" consumption -- rather it is "induced" consumption, "induced" by the shoemaker's $100 increase in income. The shoemaker will add the other $30 of the $100 to his saving.

Let's say the shoemaker spends this $70 dollars on a hat. That will increase the hatter's income by $70, and the hatter will spend 0.7*70 on additional consumption -- a $49 shirt, let's say. That increases the shirt-maker's income by $49, and the shirtmaker will in turn spend 0.7*49 = 34.30 on additional consumption, and so on.

At each step, somebody's income is increased, and that person increases her or his consumption spending by seven-tenths of the increase in income. Here is a table that shows the successive rounds of this getting and spending.

Table 2: The Multiplier Step By Step

Round	Increase in Spending	Running Total
1	100	100
2	70	170
3	49	219
4	34.30	253.30
5	24.01	277.31
6	16.81	294.12
7	11.76	305.88
8	8.24	314.12
9	5.76	319.88
10	4.04	323.92
11	2.82	326.74
12	1.98	328.72
13	1.38	330.10
14	0.97	331.07
15	0.68	331.75
16	0.47	332.23
17	0.33	332.56
18	0.23	332.79
19	0.16	332.95
20	0.11	333.07
ultimate total		333.33

We see that after 20 rounds, the increase in spending is already over $333. Because the marginal propensity to consume is less than one, at each step the increase is less than the previous one, so we know that the running total increase in consumption spending will never go beyond 333.333....

Perhaps this example helps to explain why we call it an "income-expenditure" theory. The fact that each person's spending is someone else's income is a key to the multiplier. In equilibrium, production will be a multiple of the "autonomous" income. But why does the economic system move toward equilibrium? That's a question we need to look at next.

Disequilibrium