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%