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%

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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!
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Private savings =
Public savings =
...

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Y = 5,000
G = 1000
T = 1000
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I = 1000 – 50r
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T=2,000
C=500 +
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NX=1,500−250ϵ
r=r∗=8.
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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
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S = 200
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G = 100
T = 100
They further estimate that national savings and investment are
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S = 150 + 50*r
I = 600 - 100*r
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G=150, taxes are
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I = 16 + 0.1*Y – 300*i
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I = 16 + 0.1*Y – 300*i
G = 35
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Z = C + I + G
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