CALIFORNIA STATE UNIVERSITY, SACRAMENTO
Department of Economics
Economics 100A
Prof. Yang
Solutions to Homework Problems Chapter: 1 2 3 4 5 6 7 8 9 12
Chapter 12
Numerical
1. a) Endogenous: Y, C, I, X, R, E
Exogenous: G, M, P, Pw.
b) Y = C + I + G + X
= (220 + .63Y) + (400 -
2000R + .1Y) + G +
[600
- .1Y - 100(.75 + 5R)]
= 1145 + .63Y - 2500R +
G, or,
IS: R = .458 - .000148Y + .0004G.
Also, as before,
LM: R = .0001583Y - .001M/P.
Solving the IS and LM
equations for R and Y gives
AD: Y = 1495.2661 + 1.30591G + 3.26477M/P.
So, if G = 1200, M =
900, and P = 1, then
Y = 6000.65, C = 4000.41, R = .0499 =
4.99%, I = 900.25, X = -100.02, E = .9995.
c) Use the already derived AD equation above. When G = 1200 and M = 900, the AD equation becomes
Y = 3062.3581 + 2938.293/P.
d) If G decreased by $10 billion, according to the AD equation,
national income Y will decrease
by $13.059 billion. So the new level of nationa
income will be Y = $5987.59. Using the LM equation and
the new value of Y adn remembering that M/P =
900, the new value of R can be found. R = .0478 = 4.78%.
Using the new values of Y and R, the new values
of C, I, X, and E can be obtained. C = 3992.18, I = 903.09,
X = -97.59, and E = .9892. Notice that
the sum of C, I, G, and X is $5987.68, which is approximately equal
to Y = $5987.59.
If money supply M increase by $20, then Y would
increase by $65.30 billion; the new value of Y would
be $6065.95 billion. The value of the
remaining endogenous variables can also be calculated.
C = 4041.55, R = .0402 = 4.02%, I = 926.12, E =
.9512, and X = -101.71. Notice that
C + I + X + G = 6065.95, which is the same as
the value of new Y.
5. a) This economy is more open because net exports are more
sensitive to the terms of trade, and terms
of trade are more sensitive
to domestic interest rates, so adjustments heppen more quickly.
b) First derive the IS, LM and AD equations:
Y = C + I + G + X
=
(220 + .63Y) + (400 - 2000R + .1Y) + G +
=
[900 - .1Y - 400(.50 + 10R)]
=
1320 + .63Y - 6000R + G, or
IS: R = .22 -
.00006167Y + .000167G
Also,
as before,
LM: R = .0001583Y -
.001M/P
Solving
the IS and LM equations for R and Y gives
AD: Y = 1000.1515 +
.75769G + 4.54614M/P
Usng the new
equations of IS, LM, AD, and the Phillips curve gives the following result for the case
when
the money supply
increases by $10 billion to $910 billion:
Year 0 1 Long Run
M
900
910
910
G
1200
1200
1200
P
1.000
1.000
1.011
Y
6000.91
6046.37
6000.91
R(%)
4.99
4.71
4.99
C
4000.57
4029.21
4000.57
I
900.20
910.36
900.20
X
-100.03
-93.20
-100.03
E
.9994
.9714
.9884
And, when government spending increases by $10 billion to reach $1210 billion, the following will result:
Year 0 1 Long Run
M
900
900
900
G
1200
1210
1210
P
1.000
1.000
1.002
Y
6000.91
6008.49
6000.91
R(%)
4.99
5.11
5.16
C
4000.57
4005.35
4000.57
I
900.20
898.42
896.87
X
-100.03
-105.42
-106.53
E
.9994
1.0114
1.0142