Fundamental keynesian three-sector model

Question

Given the fundamental Keynesian three-sector model:

Y = C + I + G i = interest rates

where C = a + bY_dY = aggregate income and I = f ( i …) but I ≠ f (Y f = is a function of with G = G_o and T_x = T_xo

Question 1: Suppose: C = 20 + .75Y_d

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

Question 2: Suppose: S = -35 + .25Y_d

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

Question 3: Suppose: C = 42 + .8Y_d

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

Question 4: Suppose: C = 20 + .7 Y_d

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

Question 5: Suppose that the current level of income in the economy is $700 billion. It is determined that in order to decrease the unemployment rate to the desired level, it will be essential to raise the level of aggregate income to $760 billion. Suppose that S = -25 + .2Y_d. How much would government spending have to be increased in order to accomplish the desired outcome?

Question 6: Suppose that the current level of income in the economy is $700 billion. It is determined that in order to decrease the unemployment rate to the desired level, it will be essential to raise the level of aggregate income to $760 billion. Suppose that S = -25 + .2Y_d. How much would taxes have to be cut in order to accomplish the desired outcome?

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

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

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