(i) Verify that the steady state (AY(t) = 0) equilibrium is given by abTxo +I+G + X - Mo 1-b(1-tx) + m (ii) (iii) Y* Let a = 110, b=0.75, Txo= -80, tx = 0.2, I = 300, G=200, X = 400, Mo = 10, m = 0.2, and λ=0.8. Verify Y* 1766.667 Verify the steady-state autonomous expenditure multiplier is 1.6667.
(i) Verify that the steady state (AY(t) = 0) equilibrium is given by abTxo +I+G + X - Mo 1-b(1-tx) + m (ii) (iii) Y* Let a = 110, b=0.75, Txo= -80, tx = 0.2, I = 300, G=200, X = 400, Mo = 10, m = 0.2, and λ=0.8. Verify Y* 1766.667 Verify the steady-state autonomous expenditure multiplier is 1.6667.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
just all three subparts please. i,ii and iii. spreadsheet attached too
![t
C(t) = a +byd (t)
Yd (t) = Y(t)-Tx(t)
Tx(t) = Txo+tx.Y(t)
|NX(t) = X + mY(t)
|E(t) = C(t)+I+G+ NX(t)
AY(t+1) = 2(E(t) - Y(t)) 2>0
0
1
2
Y(t)
2000
1888
Tx(t)
k(t)
Y(t+1)= a(a-bTx +I+G+X− M₁) +[1 − 2(1−b(1 – tx) + m)]Y(t)
NX(t) E(t)
E(t)-Y(t) k(t)
Yd(t) C(t)
1680
320
1370
410
-10
1860
-140 2.33333
297.6 1590.4 1302.8 387.6
12.4 1815.2 -72.8 1.21333
1829.76 285.952 1543.808 1267.856 375.952 24.048 1791.904 -37.856 0.63093
1799.475 279.895 1519.58 1249.685 369.895 30.10496 1779.79 -19.6851 0.328082
4 1783.727 276.7454 1506.982 1240.236 366.7454 33.25458 1773.491 -10.2363 0.170601
5 1775.538 275.1076 1500.43 1235.323 365.1076 34.89238 1770.215 -5.32286 0.088711
3
6 1771.28 274.256 1497.024 1232.768 364.256 35.74404 1768.512 -2.76789 0.046128
1769.066 273.8131 1495.252 1231.439 363.8131 36.1869 1767.626
7
-1.4393 0.023985
-0.74844 0.012471
8 1767.914 273.5828 1494.331 1230.748 363.5828 36.41719 1767.166
2.5
2
1.5
1
0.5
0
a =
b=
Tx0 =
tx=
m =
|=
G=
X =
MO=
lambda =
10
M(t)
t
Open economy dynamic multiplier
110
0.75
-80
9 1767.315 273.4631 1493.852 1230.389 363.4631 36.53694 1766.926 -0.38919 0.006483
10 1767.004 273.4008 1493.603 1230.202 363.4008 36.59921 1766.802 -0.20238 0.00337
11 1766.842 273.3684 1493.474 1230.105 363.3684 36.63159 1766.737 -0.10524 0.001751
12 1766.758 273.3516 1493.406 1230.055 363.3516 36.64843 1766.703 -0.05472 0.000909
13 1766.714 273.3428 1493.371 1230.028 363.3428 36.65718 1766.686 -0.02846 0.000471
14 1766.691 273.3383 1493.353 1230.015 363.3383 36.66173 1766.677 -0.0148 0.000243
15 1766.679 273.3359 1493.344 1230.008 363.3359 36.6641 1766.672 -0.00769 0.000125
16 1766.673 273.3347 1493.339 1230.004 363.3347 36.66533 1766.669 -0.004 6.34E-05
17 1766.67 273.334 1493.336 1230.002 363.334 36.66597 1766.668 -0.00208 3.13E-05
18 1766.668 273.3337 1493.335 1230.001 363.3337 36.66631 1766.667 -0.00108 1.47E-05
19 1766.668 273.3335 1493.334 1230.001 363.3335 36.66648 1766.667 -0.00056 6.04E-06
20 1766.667 273.3334 1493.334 1230 363.3334 36.66657 1766.667 -0.00029 1.54E-06
0.2
0.2
300
200
400
10
0.8
15
Y* = 1766.667
1.666667
k=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b2e65f2-c472-45bf-885c-00dffce84016%2F16f17cb8-b4b2-4a9e-95ec-64325077ce26%2F6e1go7_processed.png&w=3840&q=75)
Transcribed Image Text:t
C(t) = a +byd (t)
Yd (t) = Y(t)-Tx(t)
Tx(t) = Txo+tx.Y(t)
|NX(t) = X + mY(t)
|E(t) = C(t)+I+G+ NX(t)
AY(t+1) = 2(E(t) - Y(t)) 2>0
0
1
2
Y(t)
2000
1888
Tx(t)
k(t)
Y(t+1)= a(a-bTx +I+G+X− M₁) +[1 − 2(1−b(1 – tx) + m)]Y(t)
NX(t) E(t)
E(t)-Y(t) k(t)
Yd(t) C(t)
1680
320
1370
410
-10
1860
-140 2.33333
297.6 1590.4 1302.8 387.6
12.4 1815.2 -72.8 1.21333
1829.76 285.952 1543.808 1267.856 375.952 24.048 1791.904 -37.856 0.63093
1799.475 279.895 1519.58 1249.685 369.895 30.10496 1779.79 -19.6851 0.328082
4 1783.727 276.7454 1506.982 1240.236 366.7454 33.25458 1773.491 -10.2363 0.170601
5 1775.538 275.1076 1500.43 1235.323 365.1076 34.89238 1770.215 -5.32286 0.088711
3
6 1771.28 274.256 1497.024 1232.768 364.256 35.74404 1768.512 -2.76789 0.046128
1769.066 273.8131 1495.252 1231.439 363.8131 36.1869 1767.626
7
-1.4393 0.023985
-0.74844 0.012471
8 1767.914 273.5828 1494.331 1230.748 363.5828 36.41719 1767.166
2.5
2
1.5
1
0.5
0
a =
b=
Tx0 =
tx=
m =
|=
G=
X =
MO=
lambda =
10
M(t)
t
Open economy dynamic multiplier
110
0.75
-80
9 1767.315 273.4631 1493.852 1230.389 363.4631 36.53694 1766.926 -0.38919 0.006483
10 1767.004 273.4008 1493.603 1230.202 363.4008 36.59921 1766.802 -0.20238 0.00337
11 1766.842 273.3684 1493.474 1230.105 363.3684 36.63159 1766.737 -0.10524 0.001751
12 1766.758 273.3516 1493.406 1230.055 363.3516 36.64843 1766.703 -0.05472 0.000909
13 1766.714 273.3428 1493.371 1230.028 363.3428 36.65718 1766.686 -0.02846 0.000471
14 1766.691 273.3383 1493.353 1230.015 363.3383 36.66173 1766.677 -0.0148 0.000243
15 1766.679 273.3359 1493.344 1230.008 363.3359 36.6641 1766.672 -0.00769 0.000125
16 1766.673 273.3347 1493.339 1230.004 363.3347 36.66533 1766.669 -0.004 6.34E-05
17 1766.67 273.334 1493.336 1230.002 363.334 36.66597 1766.668 -0.00208 3.13E-05
18 1766.668 273.3337 1493.335 1230.001 363.3337 36.66631 1766.667 -0.00108 1.47E-05
19 1766.668 273.3335 1493.334 1230.001 363.3335 36.66648 1766.667 -0.00056 6.04E-06
20 1766.667 273.3334 1493.334 1230 363.3334 36.66657 1766.667 -0.00029 1.54E-06
0.2
0.2
300
200
400
10
0.8
15
Y* = 1766.667
1.666667
k=
![Consider the following economy:
C(t) = a + bYa(t)
Ya(t)= Y(t) - Tx(t)
Tx(t)= Txotx. Y(t)
M(t) = Mo + mY (t)
NX (t) = XM(t)
E (t) = C(t) +I+G+ NX(t)
AY(t + 1) = A[E(t) - Y(t)]
The first equation is a consumption function, the second equation computes disposable
income, the third is the tax function, the fourth is the import function, the fifth equation
computes net exports, and the sixth is the national accounting identity showing the
components of aggregate demand. The final equation describes the adjustment to output if
there is excess demand. The speed of this adjustment is governed by the parameter 2
(lambda).
(i)
(iii)
(iv)
Verify that the steady state (AY(t) = 0) equilibrium is given by
abTxo +I+G+X - Mo
1-b(1-tx) + m
Y" =
Let a = 110, b=0.75, Txo= -80, tx = 0.2, I = 300, G=200, X = 400, Mo = 10, m = 0.2, and
λ=0.8.
Verify Y* 1766.667
Verify the steady-state autonomous expenditure multiplier is 1.6667.
Use the model set up in the spreadsheet
and set Y(0)= 1766.667, the
equilibrium value. Let investment rise by 100. Derive and plot the open economy
dynamic multiplier.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b2e65f2-c472-45bf-885c-00dffce84016%2F16f17cb8-b4b2-4a9e-95ec-64325077ce26%2Fxt12lug_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following economy:
C(t) = a + bYa(t)
Ya(t)= Y(t) - Tx(t)
Tx(t)= Txotx. Y(t)
M(t) = Mo + mY (t)
NX (t) = XM(t)
E (t) = C(t) +I+G+ NX(t)
AY(t + 1) = A[E(t) - Y(t)]
The first equation is a consumption function, the second equation computes disposable
income, the third is the tax function, the fourth is the import function, the fifth equation
computes net exports, and the sixth is the national accounting identity showing the
components of aggregate demand. The final equation describes the adjustment to output if
there is excess demand. The speed of this adjustment is governed by the parameter 2
(lambda).
(i)
(iii)
(iv)
Verify that the steady state (AY(t) = 0) equilibrium is given by
abTxo +I+G+X - Mo
1-b(1-tx) + m
Y" =
Let a = 110, b=0.75, Txo= -80, tx = 0.2, I = 300, G=200, X = 400, Mo = 10, m = 0.2, and
λ=0.8.
Verify Y* 1766.667
Verify the steady-state autonomous expenditure multiplier is 1.6667.
Use the model set up in the spreadsheet
and set Y(0)= 1766.667, the
equilibrium value. Let investment rise by 100. Derive and plot the open economy
dynamic multiplier.
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