The production function in an economy is: Y=A(5N-0.0025N2) Where A is productivi
ID: 1123566 • Letter: T
Question
The production function in an economy is:
Y=A(5N-0.0025N2)
Where A is productivity. With this production function, the marginal product of labor is
MPN=5A-0.005AN.
Suppose A=2. The labor supply curve is
NS=55+10(1-t)w
Where NS is the amount of labor supplied. w is the real wage, and t is the tax rate on wage income, which is 0.5.
Desired consumption and investment are
Cd=300+0.8(Y-T)-200r;
Id=258.5-250r
Taxes and government purchases are:
T=20+0.5Y;
G=72.5.
Money demand is
Md/P=0.5Y-250i.
Where i is the nominal interest rate.
The expected inflation e is 0.02, and the money supply M is 9150.
The full employment level of output is:
1000
950
1050
900
QUESTION 17: At general equilibrium, the consumption level is
654
624
634
644
QUESTION 18: At general equilibrium, the investment level is
253.5
233.5
263.5
243.1
QUESTION 19:The price level that clears the asset market is
20.56
23.56
22.56
21.56
QUESTION 20:The real interest rate that clears the goods market is
0.1
0.15
0.00
0.05
Explanation / Answer
a)
Y=A (5N-0.0025N^2)
Suppose A=2
Y=2(5N-0.0025N^2)
Y=10N-0.005N^2
Now, MPN=Y/N
=10-0.01N
MRPN = MPN•P
= P (10-0.01N)
MRP = MFC
MRPN = MFC
MFC = W
P (10-0.01N) = W
10 - 0.01N = W/P
W/P is the real wage
Ld is the Labor demand
0.01N=10-W/P
N = 1000-100W/P
Ls is the Labor supply
N = 55+10 (1-t )W/P
t = 0.5
N = 55+5W/P
Ls = Lp
55+5W/P = 1000-100W/P
105W/P=945
W/P=9
N=55+5•9=100
N=1000-100•9=100 [Fixed employment]
Y = 10N - 0.005N²
= 10•100-0.005•100² = 950
The full employment level of output is: 950
b)
Y = C+I+G
C = 300+0.8(Y-T)-2000r
T=20+0.5Y
C = 300+0.8(Y-20-0.5Y)-2000r
= 284+0.4Y-2000r
I=285.5-250r
G=50
Y = 284+0.4Y-2000r +285.5-250r+50 = 619.5+0.4Y-2250r
0.6Y=619.5-2250r
Y=1032.5-3750r [IS~Y(r)]
3750r=1032.5-Y
r = 413/1500 - Y/3750 0.27533-0.0002667Y [IS~r(Y)]
Y=950
r = 413/1500 - 950/3750 = 11/500 = 0.022 = 2.2%
C = 284+0.4Y-2000r = 284+380-44 = 624
I = 285.5-250r = 285.5-5.5 = 280
The consumption is 624
c)
M/P=0.5Y-250(r+f)
f=0.02
M=9150
9150/P=0.5Y-5-250r
0.5Y=9150/P +5 +250r
Y=18300/P +10+500r [LM~Y(r;P)]
250r=0.5Y-5-9150/P
r=0.002Y-0.02-36.6/P [LM~r(Y;P)]
Aggregate demand:
IS=LM
[Y=1032.5-3750r] ~ [r=0.002Y-0.02-36.6/P]
Y=18300/P +10+500r
r=0.022
Real Interest Rate = 0.022 - expected inflation of 0.02
The real interest rate that clears the goods market is 0.002 =0.00
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.