Download Homework 3 – Due at the start of class on Wednesday, April 19th

Homework 3 – Due at the start of class on Wednesday, April 19th. NAME:_________________
Consider the following economy:
Consumption behavior is represented by the following function:
C = a + mpc (Y-T), where a = 10000 and mpc is 0.75
Investment is I = 20000
Government Spending: G = 0
NX = 5000
a)
What is the equilibrium level of Y?
140000
b)
What if the government selects to introduce both, the government spending and taxation in
the following form: G = T = 10000? What will the equilibrium level of Y be then?
150000
c)
What if the government were to set each, G and T to 15000? What will the level of Y be
now?
155000
d)
Now, assume that the government decides to replace the autonomous tax system with income
taxes so that the new T in the consumption function is T = tY where t is the income tax rate
and is set to 20%. Also assume that the G level is at 15000. What will the Y level be now?
125000
Note, in this problem the multiplier changes. The starting GDP identity equation is:
Y = a + mpc ( Y - t Y ) + I + G + NX
(1)
Which, when solved for Y becomes:
Y = {/(1-mpc(1-t))} [a + I + G + NX]
(2)
The new multiplier is 1/0.4 = 2.5.
e)
Now, assume that the income tax remains at 20%, the government spending is still at 15000
and the autonomous taxes are still at zero. Also assume that the investment level declines to
15000. What should the change in the government spending be to keep the level of Y
constant (i.e. return to the level when Investment was 20000)?
Since in the above equation (2) of the answer to part d the terms I and G are put together in the group of
autonomous expenditures, any change in I can be offset by an equal change in G. Thus, the government
spending has to increase by 5000.
f)
Using a clearly labeled Keynesian Cross diagram indicate the effect of an introduction of
income taxes (note, this does not need to relate to part d of this problem, simply assume that
an economy introduced income taxes while everything else is held constant).
This will simply rotate downward around the Expenditures axis intercept the planned
expenditures function. Note, the rotation takes place because the tax changes the multiplier, not
any of the autonomous expenditures (which would have shifted the curve).