The Multiplier
There is another way to get this same result -- with a little algebra. It's not really difficult, and it has some advantages -- so hold onto your seats!
In our example, we have
1. C = 500 + 0.7*Y
and
2. Y = C +1000
We now know that the equilibrium comes where the two lines intersect. In algebraic terms, it means that both equations are solved at the same time -- simultaneously. So, solving these simultaneously, we substitute 500 + 0.7*Y into Y = C + 1000 and get3. Y = 500 + 0.7*Y +1000
Subtracting 0.7*Y from both sides, the next step is
4. Y - 0.7*Y = 500 +1000
That is
5. Y*(1 - 0.7) = 1500
The next step is to divide both sides by (1 - 0.7):
6. Y = 1500/(1-0.7)
Now, (1 - 0.7) is 0.3, and so, dividing 1500 by 0.3, we get the equilibrium income -- 5000 billion dollars.
In ordinary language, here is what the algebra tells us to do: Add the autonomous expenditures, that is, autonomous consumption plus investment; subtract the marginal propensity to consume from one, and divide the sum of the autonomous expenditures by the difference of one minus the marginal propensity to consume.
Using algebra to get the market equilibrium may not come very naturally to many economics students, but it has one big advantage: it does come naturally to computers. The example we have looked at is much too simple to have practical use, but the principles it illustrates are used practically in just about every computer system used to understand and forecast the economic system. The "models" used in these computer programs are called "econometric models," and most of them have many more than two equations. They may often have hundreds of equations. Using advanced computer algebra, even these systems of hundreds of equations can be solved simultaneously in just the way we have done; and that's the way the computer systems work.
So let's look at the method in a still more general way.
The Multiplier
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