Given the fundamental Keynesian three-sector model:
Y = C + I + G i = interest rates
where C = a + bY_{d}Y = aggregate income and I = f ( i …) but I ≠ f (Y f = is a function of with G = G_{o} and T_{x} = T_{xo}
problem 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?
problem 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?
problem 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
problem 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)
problem 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?
problem 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?
problem 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?
problem 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!
problem 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.