Question

a. Consider the following long-run model:

Real GDP (Y) = 2,000; Consumption (C) = 300 + 0.6 (Y-T);
Investment (I) = 500 -30r where r is the real interest rate; Taxes
(T) = 450;

Government spending (G) = 400.

i. Compute consumption, private savings, public savings, national
savings, investment

and the real interest rate.

ii. Using the same model, except now C= 200 + 0.6(Y-T). Compute
consumption,

private savings, public savings, national savings, investment and
the real interest

rate.

iii. What is the real interest rate in the loanable funds market in
(i) and (ii) ?

iv. Using the model in (a), compute the new equilibrium interest
rate when government

spending decreases by 100 (i.e. the new G = 300).

v. Using the model in (a), compute the new equilibrium interest
rate when taxes

decrease by 100 (i.e. the new T = 350).

b. During the Great Recession, U.S investors suffered a huge loss
in business confidence once the stock market crashed in 2008.
Consider the model below:

Y = 1650; C = 200 + 0.6(Y – T); G = 250; I = 400 – 2000r; T=
150

i. Find the equilibrium interest rate (r), investment (I), and
consumption (C), public

savings, private savings, and national savings.

ii. Suppose that taxes are cut by 10%, so that the new level of
taxes is T= 135. Find the

new equilibrium r, I, and C. How much investment is crowded out by
the tax cut?

iii. Compute the new public savings, private savings, and national
savings after the tax

cut.

iv. Illustrate the effects of the tax cut on a savings-investment
diagram

v. Suppose there is a decrease in business confidence. Find the new
equilibrium interest

rate (r), investment (I) and consumption (C) with the new
investment function: I =

350 – 2000r. What happens to private and public savings? Total
savings?

vi. Illustrate the effect of a decrease in business confidence on a
savings-investment

diagram.

Answer #1

Solution: a.

(i) Real GDP (Y) = 2,000; Consumption (C) = 300 + 0.6 (Y-T); Investment (I) = 500 -30r where r is the real interest rate; Taxes (T) = 450, Government spending (G) = 400.

Consumption (C) = 300+0.6(2000-450) = 300+930= 1230

Private saving = Y-T-C = 2000-450-1230 = 320

Public saving = T-G = 450 -400 = 50

National saving = Private saving + public saving = 320+50 = 370

At equilibrium, Y = 2000 = C+I+G = 1230 + 500-30r + 400

Thus rate of interest (r) = 130/30 = 4.33%

And investment = 500 - 30*4.33 = 370

(ii) When C = 200+0.6(Y-T)

Consumption (C) = 200+0.6(2000-450) = 200+930= 1130

Private saving = Y-T-C = 2000-450-1130 = 420

Public saving = T-G = 450 -400 = 50

National saving = Private saving + public saving = 420+50 = 470

At equilibrium, Y = 2000 = C+I+G = 1130 + 500-30r + 400

Thus rate of interest (r) = 30/30 = 1%

And investment = 500 - 30*1 = 470

(iii) Real interest rate = 4.33 and 1% in (i) an (ii)

(iv) When new G = 300

At equilibrium, Y = 2000 = C+I+G = 1230 + 500-30r + 300

r = 30/30 = 1%

(v)

When new T = 350

At equilibrium, Y = 2000 = C+I+G = 1260 + 500-30r + 400

r = 160/30 = 5.33%

A. Classical/General Equilibrium
Model: Assume that GDP (Y) is 8,500B. Consumption (C) is
given by the equation C = 210B + 0.9(Y – T). Investment (I) is
given by the equation I = 1,200B – 100B(r), where r is the real
rate of interest. Taxes (T) are 400B and government spending (G) is
500B. Show/type your work/calculations!
1. In this economy, compute private savings, public savings, and
national savings (9 points)
Private savings =
Public savings =
...

Equilibrium Values and Saving
Assume that GDP (Y) is 5,000. Consumption (C) is given by the
equation C = 1,000 + 0.3(Y – T). Investment (I) is given by the
equation I = 1,500 – 50r, where r is the real interest rate in
percent. Taxes (T) are 1,000. Government spending (G) is 1,500.
What are the equilibrium values of C, I, and r?
What are the values of private saving, public saving, and
national saving?
Now assume there is...

Consider the following economy
Y = C + I + G
Y = 5,000
G = 1000
T = 1000
C= 250 + 0.75(Y-T)
I = 1000 – 50r
Compute private savings, public savings and national
savings.
Find the equilibrium interest rate.
Suppose G rises to 1,250. Compute private savings, public
savings, national savings and the interest rate. Explain
intuitively why these variables have changed

Consider an economy with the given equations.
Y = C + I + G + NX
Y=$5500
G=$1100
T=$1200
C=$200+0.60(Y−T)
I=1100−50r
NX=1270−1270?
r=r*=5
b. Suppose now that G rises to $1400. Solve for private saving,
public saving, national saving, investment, the trade balance, and
the equilibrium exchange rate.
Public savings = $_____
National savings = $____
Investment = $_____
Net exports (trade balance) = $____
Exchange rate _____
c. Suppose that the world interest rate rises
from 5 to 12...

MACROECONOMICS
given:
Crowding out with algebra. Consider an economy
described by the following model.
Y = K1/3L2/3
K = 1000; L = 1000
G = 100
T = 100
C = 250 + 0.5(Y-T)
I = 600 – 100r
i. Calculate the equilibrium real interest rate, national
saving, public saving, private saving, consumption, output, and
investment. List your numbers out like this:
Y = 1000
r = 4
S = 200
Spub = 0
Spriv = 200
C = 700...

Consider an economy described by the following
equations:
Y=C+I+G+NX,
Y=8,000
G=2,500
T=2,000
C=500 +
0.75(Y−T)
I=900−50r
NX=1,500−250ϵ
r=r∗=8.
a.
In this economy, solve for private saving, public saving, national
saving, investment, the trade balance, and the equilibrium exchange
rate.
b.
Suppose now that G is cut to 2,000. Solve for private saving,
public saving, national saving, investment, the trade balance, and
the equilibrium exchange rate. Explain what you find.
c.
Now suppose that the world interest rate falls from 8...

Economists in Fundlandia, a closed economy, have collected the
following information about GDP and public savings in their
country:
Y = 1000
G = 100
T = 100
They further estimate that national savings and investment are
governed by the following expressions:
S = 150 + 50*r
I = 600 - 100*r
Where r is the country's real interest rate in % terms (thus if you
find r = 5, then r is 5%).
Problem Set #2 - Part II...

Y = C + I + G + NX
Y = 18,500; G = 4,000; T = 2,000
C = 750 + 3/4 (Y - T)
I = 1,000 - 50r
CF = 750 - 25r
NX = 1,825 - 150ϵϵ
The world interest rate increases to r* = 10. Solve for
consumption, private and public saving, national saving,
investment, the trade balance, the net capital outflow (net foreign
investment), the domestic real interest rate, and the real exchange
rate....

3. The IS-LM Model
Consider an economy characterized by the following equations for
consumption (C), investment (I), government spending (G), taxes
(T), aggregate demand (Z), output (Y), and the interest rate
(i):
C = 54 + 0.3*(Y – T)
I = 16 + 0.1*Y – 300*i
G = 35
T = 30
Z = C + I + G
i = ?
Suppose the central bank has set the interest rate equal to 2%
(this is, ? = 0.02).
a)...

3. The IS-LM Model
Consider an economy characterized by the following equations for
consumption (C), investment (I), government spending (G), taxes
(T), aggregate demand (Z), output (Y), and the interest rate
(i):
C = 54 + 0.3*(Y – T)
I = 16 + 0.1*Y – 300*i
G = 35
T = 30
Z = C + I + G
i = ?
Suppose the central bank has set the interest rate equal to 2%
(this is, ? = 0.02).
a)...

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