Question

6. Consider an economy described by the following equations:
Y = C + I + G
Y = 5,000 G = 1,000 T = 1,000
C = 250 + 0.75(Y − T) I = 1,000 − 50 r.
a. In this economy, compute private saving, public saving, and national saving.
b. Find the equilibrium interest rate.
c. Now suppose that G rises to 1,250. Compute private saving, public saving, and national saving.
d. Find the new equilibrium interest rate.

Answer 1

Solution:

a.). In this economy, compute private savings, public savings, and national savings. 

$National\; savings=Y-C-G$

$=5000-(250+0.75(5000-1000) ) -1000 = 750$

$Private\; savings=Y-T-C$

$=5000-1000-(250+0.75(5000-1000) ) = 750$

$Public\; savings = T-G$

$=1000-1000 = 0$

b.). Find the equilibrium interest rate:

Find Total Savings (S):

$S = Private \; saving+Public\; saving$

$=750+0 = 750$

S = I

$750=1000-50r$

$50r = 1000-750$

$50r=250$

$r=\frac{250}{50} = 5$

The equilibrium interest rate (r) = 5

c.). Now suppose that G rises to 1,250. Compute private saving, public saving, and national saving.

$National \; savings=Y-C-G$

$=5000-(250+0.75(5000-1000) ) -1250 = 500$

$Private \; savings=Y-T-C$

$=5000-1000-(250+0.75(5000-1000) ) = 750$

$Public\; savings = T-G$

$=1000-1250 = -250$

d.). Find the new equilibrium interest rate:

$Total \; Savings (S) = Private\; savings+Public \; savings$

$=750+(-250) = 500$

S = I

$500 = 1000 -50r$

$50r=1000-500$

$50r=500$

$r= \frac{500}{50} = 10$

The new equilibrium interest rate = 10