# 1 The Multiplier. 2 Multiplier You may recall the RGDP by the expenditure approach is made up of the real levels of C, I, G and Xn in the following way:

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1 The Multiplier

2 Multiplier You may recall the RGDP by the expenditure approach is made up of the real levels of C, I, G and Xn in the following way: RDGP = C + I + G + Xn. We have talked about C and I more than about G and Xn, but that will change in a chapter or two. So, for now I still talk about C and I more but the same basic story holds for G and Xn. The multiplier is the general idea that as any of the spending components C, I, G, or Xn change RGDP changes. But RGDP ultimately changes by more than the initial change in one of the components.

3 The multiplier When investment increases we saw that the level of RGDP increases. In fact, we think RGDP increases initially by the change in investment. BUT, if RGDP increases we have a theory that consumption increases(BUT not the kind of change in C that shifts the curve). For every dollar change in RGDP consumption changes by the MPC. Now the increase in consumption leads to more RGDP being earned and thus even more consumption. Let’s move to a numerical example on the next screen to help us think about this idea.

4 multiplier example Say investment increases by 5 and the MPC =.75. The investment increase means RGDP increases initially by 5 because businesses increase spending by 5. But the 5 in spending will be earned by someone and thus consumption will increase by (.75)(5) = 3.75. The 3.75 in additional production will mean more income and thus more consumption for someone else in the amount (.75)(3.75) = 2.8125 or 2.81.

5 multiplier example The change in RGDP is thus the initial change in investment plus the consumption changes that occur because more income is earned. We have change in RGDP = 5 + 3.75 + 2.81 + more, but lower amounts. Now change in RGDP = 5 + 3.75 + 2.81 +... = 5(1 +.75 +.75 2 +... ) by distribution law = (1 +.75 +.75 2 +... )5 by association law = 1 5 1 -.75 = 20.

6 multiplier in general In general the change in RGDP = 1 1 - MPC initial change in spending. Note 1) the change in RGDP is more than the initial change in I because consumption occurs with the income increase, 2) the total change in RGDP is given by the above formula. 3) The same result would occur if a non-RGDP component of consumption changed or if G or Xn changed.

7 The multiplier The term 1/(1 - MPC) is called the multiplier because it is the amount by which the initial shift in the spending is multiplied by to get the final change in RGDP. If MPC =.75 the multiplier = 4. If MPC =.8 the multiplier = 5. If MPC =.9 the multiplier = 10. The MPC is out their in the world and we have to figure out the value of it. Some of you may want to take more economics and statistics to see how to find the value. In our class we just assume it takes on a value. Above we just made up some values and worked out the multiplier value.

8 The multiplier Another way to see this, maybe: RGDP = C + I + G + Xn. Round 1 of spending - If I goes up RGDP goes up. From our example before if I goes up by 5 RGDP goes up by 5. Round 2 of spending - But if RGDP goes up C goes up although C goes up by MPC times amount RGDP went up. This new C is part RGDP and thus RGDP goes up! So, when RGDP went up by 5 C goes up by.75(5) = 3.75 and thus RGDP goes up 3.75. Round 3 of spending – C goes up by.75(3.75) = 2.8125 and thus RGDP goes up by 2.8125.

9 The multiplier So the initial spending ignites more rounds of spending and all contribute to increased RGDP. The additional rounds of spending are at lower and lower amounts until there is no additional round to happen.

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