1. The equations below represent the Open Economy Model of Mankiw’s Chapter 5, which determines the endogenous variables Y, C, I, NX, and in terms of the exogenous variables K , L , G , and T .

Suppose that the money demand function is [M/P]^d = 1000-100r where r is the interest rate in percent.?
The money supply M is 1000 and the price level P is 2.

What is the equilibrium interest rate?
Assume that the price level is fixed. What happens to the equilibrium interest rate if the supply of money israised from 1000 to 1200?
If the authority wished to raise the interest rate to 1 percent, what money supply should it set? a)
M/P=1000-100r
M=1000 & P=2
1000/2 = 1000-100r
500=1000-100r
100r=500 r=500/100=5 b)
M=1200 & P=2
1200/2 = 1000-100r
600=1000-100r
100r=400 r=400/100=4 Thus interest rate falls from r=5 to r=4
c)
r=1 & P=2
M/P=1000-100r
M/2=1000-100•1
M/2=900
M=1800
Fed should set M=1800

Suppose we have an economy described by the following functions:
C= 50+.8YD
I bar= 70
G bar= 200
TR bar= 100 t= .20

(a)(i) Calculate the equilibrium level of income and (ii)the multiplier in this model.
(b) Calculate the budget surplus, BS.
(c) Suppose that t increases to .25. (i)What is the new equilibrium income? (ii)And the new multiplier?
(d) (i)Calculate the change in budget surplus. (ii)Would you expect the changes in the surplus to be more or less if C= .9 rather than .8?
(e) Can you explain why the multiplier is 1 when t=1?

A. Y=C+I+G, government transfer payment is not included in GDP.
Y=50+.8(Y-T)+70+200.
Y=50+.8Y-.20Y+70+200
(1-.8+.20)Y=50+70+200
Y=320/.40=800.,multiplier=1/0.4=2.5
B. G-T=200-.2x800 budget deficit=200-160= 40.
C. multiplier= 1/(1-.8+.25)=2.22.The new level of income=320/.45=711.11
D. budget deficit=200-.25x711.11=22.22.If MPC=.9,The multiplier=1/(1-.9+.25)=1/.35=2.86
The new level of income=320x2.86=915.2. Budget surplus=200-.25x915.2=200-228.8=28.8.
E. if t=1, there will be no income left for consumption, or 0.8YD=0
In this case multiplier=1/1=1

c) We can calculate the effect of an equal increase in government expenditure and taxes by adding the two multiplier effects that we used in parts a and b:
DY = [(1/(1-MPC))* DG] – [(MPC/(1-MPC))*DT
Because government purchases and taxes increase by the same amount, we know that DG = DT.
Therefore we can rewrite the equation as:
DY = [(1/(1-MPC)) – (MPC/(1-MPC))*DG = DG
This expression tells us that an equal increase in government purchases and taxes increases Y by the amount that G increases. That is, the balanced-budget multiplier is exactly 1.

2. (a)Use the Keynesian cross to predict the impact of an increase in government purchases

a) The Keynesian cross graphs an economy’s planned expenditure function,
E = C + I + G + NX, and the equilibrium condition that actual expenditure equals planned expenditure. An increase in government purchases from G to G’ shifts the planned expenditure function upward. The new equilibrium is at point b. The change in Y equals the product of the government purchases multiplier and the change in government spending: DY = [1/(1 – MPC)]*DG. Because we know that the marginal propensity to consume MPC is less than one, this expression tells us that a one-dollar increase in G leads to an increase in Y that is greater than one dollar.

b) An increase in taxes of DT reduces disposable income Y – T by DT and, therefore, reduces consumption by MPC x DT. For any given level of income Y, planned expenditure falls. In the
Keynesian cross, the tax increase shifts the planned expenditure function down by MPC x DT. The amount by which Y falls is given by the product of the tax multiplier and the increase in taxes: DY = [-MPC/(1-MPC)]DT.