Given the basic Keynesian three-sector model

Y = C + I + G i = interest rates

where C = a + bYd Y = aggregate income

and I = f( i …) but I ? f( Y f= is a function of

with G = Go

and Tx = Txo

 

 

1. Assume: C = 20 + .75Yd

Now assume that government spending is increased by $12 billion. That would (increase/decrease) the level of income by how much?

 

2. Assume: S = -35 + .25Yd

Now assume that taxes are cut by $15 billion. That would (increase/decrease) the level of income by how much?

3. Assume: C = 42 + .8Yd

Now increase taxes and government spending (simultaneously) by $33 billion. That would lead to a (decrease/increase) of __________ billion in the level of income

4. Assume: C = 20 + .7 Yd

Now cut taxes by $20 billion. This would have the effect of shifting the consumption function (upward/downward) by _________ billion. (Think Keynesian cross model)

 

5. Assume that the current level of income in the economy is $700 billion. It is determined that in order to reduce the unemployment rate to the desired level, it will be necessary to increase the level of aggregate income to $760 billion. Assume that S = -25 + .2Yd. How much would government spending have to be increased in order to accomplish the desired outcome?

6. Assume that the current level of income in the economy is $700 billion. It is determined that in order to reduce the unemployment rate to the desired level, it will be necessary to increase the level of aggregate income to $760 billion. Assume that S = -25 + .2Yd. How much would taxes have to be cut in order to accomplish the desired outcome?

7. Given a saving function of S = -25 + .2Yd, a $10 billion increase in government spending will bring about how many dollars of change in consumption?

8. Now, let’s modify our model a bit. Let’s add a fourth sector of spending so that Y = C + I + G + Xn with X = Xo and M = M = f (Y). Will this change, by itself, increase, decrease or not affect the magnitude of the government spending multiplier? Explain!

9. Thinking about modifications in the model again: Go back to the original model again, but add a marginal propensity to invest, this is, assume that I = f ( i and Y). The MPI is defined as ?I/?Y and has a positive value. Will this increase, decrease or not affect the value of the government expenditures multiplier? Explain!

10. Now if we assume (more realistically) that tax collections are related to the level of income, that is, rather than assuming Tx = Txo, we assume that Tx = To + tY where t is the tax rate, what will that change do to the magnitude of the investment multiplier? Explain!

11. In plain English, how is it (according to Keynesian theory) that a $1 increase in government spending can increase the level of national income by more than $1? (Assume that the MPC is 0.8)

12. Rather than the initial (top of first page) model, now assume a three sector economy with a tax rate (assume it is both average and marginal rate) of t and a marginal propensity to invest of f. Will this new model yield larger multipliers (say, government expenditures multiplier), smaller, or the same size as the initial model? Explain!