Download Macroeconomic Theory

Macroeconomic Theory
M. Finkler
Suggested Answers to Spring 2006 Midterm Examination #2
1a. Use the behavioral statements below along with the other needed identities and
equilibrium statements from the IS-LM model to answer all parts of this question.
Endogenous Exogenous
Consumption:
C = 200 + .8*Yd
Variables
Variables
Taxes
T = To + .25*Y
C, Yd, T, Y M, G, P, To
Investment
I = 200 – 20*R
AD, I, R, NX
Net Exports
NX = 100 - .2*Y – 5*R
Md
Money Demand Md = (.5Y – 50*R)*P
Assume Y<Yp
To complete the model, five equations need to be added.
Disposable Income
Yd = Y – T
Aggregate Demand
AD = C + I + G + NX
Goods Market Equilibrium Y = AD
Money Market Equilibrium M = Md
b. To find the IS Curve, we need to plug all components into the AD equation and then
solve for Y in terms of R.
Yd = Y – To - .25*Y = .75*Y – To
C = 200 + .8*(.75*Y – To) = 200 + .6*Y - .8*To
Y =AD = 200 + .6*Y - .8*To + 200-20*R + G + 100 - .2*Y – 5*R
Move all Y terms to the left hand side to yield
Y - .6*Y + .2*Y = .6*Y = 500 + G - .8*To – 25* R
Y = 500 + G - .8*To – 25* R with slope R/Y = -.6/25
.6
c.
The LM comes from plugging the money demand curve into the money market
equilibrium equation to yield
So the IS Curve becomes
M = (.5Y – 50*R)*P which can be solved for R to yield
R = .5Y – M/P
50
which has slope R/Y = .5/50
d. The reduced form statement for Y comes from plugging the LM curve into the IS
curve to yield
.6*Y = 500 + G - .8*To – 25*(.5Y – M/P) = 500 + G - .8*To - .25Y + .5*(M/P)
50
which can be solved for Y to yield Y = 500 + G - .8*To + .5(M/P)
.85
e.
The balanced budget multiplier = Y/G + Y/To = (1 - .8)/.85 = .235 which can
be interpreted as for every one dollar increase in expenditures matched by a dollar
increase in non-income tax revenues, GDP will increase by 23.5 cents.
2a.
b.
Divide both sides of the production function by L to yield
Y/L = Tech*K.5 L-.5 which can be rewritten as y = Tech*k.5
This becomes the long run supply with y, Tech, and k a function of time
Write down the long run demand curve from Model 1G as
y = (n+)*k
s
Solve the two equations together to yield y = Tech2*(s/(n +))
Thus, the equilibrium path for y depends upon the level of technology in period .
c.
Long run growth for y can be determined from either the production function or
the equilibrium statement. Since the growth of k = 0 or since n, , and s are
constants, the growth of y must equal the growth of Tech (i.e., g.)
d.
To determine the optimal level of population growth, the following equation must
be maximized with respect to n.
c = (1-s)*y = (1-s)* Tech2*(s/(n +))
c/n = -s*(1-s)* Tech2*( s/(n +))2 = 0 which can not be solved for any value
of n. In short, as n rises, c falls continuously; thus, the highest value of c would
occur where n is a large negative fraction with the largest feasible value near -1.
3a.
An increase in the stock of money shifts the AD (and LM) curve away from the
origin. As a result both Y and P rise; since P rises, W/P falls so labor demand
and, thus, L rises.
AS
P
AD
W/P
Y
L
3b. A decrease in the stock of capital shifts both the labor demand curve and the
production inwards. As a result, initial L falls and Y falls with P rising. The rise in P
reduces the real wage which leads to a partial recovery in L and Y. End result: P
increases; Y, W/P, and L decrease.
AS
P
AD
Y
W/P
L
4.
False. The statement should be modified to read “balance the cyclically adjusted
federal budget.” When the economy is booming (Y > Yp) , policy makers should aim for
a governmental budget surplus. When the economy is in a recession (Y < Yp), policy
makers should aim for a governmental budget deficit. Stated differently, the structural
(as opposed to cyclical portion of the budget deficit) portion of the budget should be in
balance.
5.
For fiscal policy to be potent, the LM must be relatively flat; thus, h – the
sensitivity of money holding to interest rates - should be high. Stated more
comprehensively, the fiscal policy multiplier Y/G should be greater than the monetary
policy multiplier Y/M. From the results of model 3 this means that
Y/G = 1/ (1-b*(1-t1) + m + (d+n))*(k/h) >
Y/M= [(d+n)/h ]*(1/P) / (1-b*(1-t1) + m + (d+n))*(k/h)
6a.
Uncertain. Examine the multiplier of M on Y. If import consumption rises, then
m becomes larger. Since m is in the denominator, the multiplier becomes smaller.
Monetary policy is less potent. Interest sensitivity also matters; so one needs to consider
n which enters both the numerator and the denominator.
Y/M= [(d+n)/h ]*(1/P) / (1-b*(1-t1) + m + (d+n))*(k/h)
b.
False. Examine the multiplier of G on Y. If import consumption rises, then m
becomes larger. Since m is in the denominator, the multiplier becomes smaller. Fiscal
policy is less potent. Interest sensitivity also matters; as n rises, the denominator
becomes larger, so again, fiscal policy becomes less effective.
Y/G = 1/ (1-b*(1-t1) + m + (d+n))*(k/h)