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The intuition comes from the fact that the marginal propensity to consume (MPC) is positive. MPC is the money people spend when they get an extra dollar of income. When MPC = 0.8, for example, when people gets an extra dollar of income, they spend 80 cents of it. So the Keynesian multiplier works as follow, assuming for simplicity, MPC = 0.8. Then when the government increases expenditure by 1 dollar on a good produced by agent A, this dollar becomes A's income. As MPC = 0.8, A will spend 80 cents of this extra income on something is wants to consume. Suppose A spends the 80 cents on a good produced by B, then B would have an extra income of 80 cents. B would then spend 0.8 of this 80 cents, ie, 64 cents, on something else. This 64 cents becomes someone else's income, and this someone will spend 0.8 of it. The process repeats itself. The GDP added to the economy is the sum of all the spending, 1 + 0.8 + 0.64 + 0.512 + ... which has a larger effect than the 1 dollar that the government originally spent. In other words, the government spending is "multiplied".
Mathematically, the sum 1 + 0.8 + 0.64 + ... is a geometric series. When you sum them up, it takes the form . The effect of the government spending is multiplied 5 times, and thus the multiplier is
The key to solving these question is to isolate GDP (Y) on one side. That gives us the multiplier. We will see an example below:
Q Consider the following multiplier model:
C = 100 + 0.8Yd; I = 200; T = 0; G = 0; NX = 0 (Yd is disposable income)
A The steps are:
In this case firms will increase their inventories by 100 and unplanned (inventory) investment is 100.
.
Thus the government multiplier is now 1/0.15 > 4. The multiplier is larger because as G increases we have all the previous effects plus now investment also increases, adding to the overall effect of increased government spending. Investment is not exogenous anymore.
Transfer/lump-sum tax T
When tax depends on income at a rate t
Note that in the case with both the lump-sum tax and the tax at rate t, the GDP becomes:
Balance budget condition: set G = T