QUESTION
Consider an economy described by the following equations:
Y=C+I+G
Y=500
G=1,000
T=1,000
C=250+0.75(Y-T)
I=1,000-50r
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 rate.
(a) By conventional macroeconomic definitions,
Private saving is equal to (Y – T – C)
Public saving is equal to (T – G)
National saving is the sum of the two, (Y - C - G).
I am assuming that r is the interest rate in %
(b) If you set Y = C + I + G, you can solve for r.
500 = 250 + 0.75(500-1000) + 1000 - 50r +1000
50 r = 2250 -375 -500 = 27.5%
(c and d) Repeat with the new value of G.
THANK YOU, you are GREAT, its a review quest. and i do not have the book.
41570
C
To find the private saving, public saving, and national saving, we'll follow these steps:
a. Computing private saving, public saving, and national saving:
Private saving (Sprivate) is the income that households save, which is the difference between disposable income (Y - T) and consumption (C).
Public saving (Spublic) is the difference between government revenues (T) and government spending (G).
National saving (Snational) is the sum of private saving (Sprivate) and public saving (Spublic).
Given the following equations:
Y = C + I + G
Y = 500
G = 1,000
T = 1,000
C = 250 + 0.75(Y - T)
I = 1,000 - 50r
We can substitute the given values into the equations to compute the desired values.
1. Private Saving (Sprivate):
Sprivate = (Y - T) - C
Sprivate = (500 - 1,000) - (250 + 0.75(500 - 1,000 - 1,000))
Sprivate = -500 - (250 + 0.75(-500))
Sprivate = -500 - (250 - 375)
Sprivate = -500 - (-125)
Sprivate = -375
2. Public Saving (Spublic):
Spublic = T - G
Spublic = 1,000 - 1,000
Spublic = 0
3. National Saving (Snational):
Snational = Sprivate + Spublic
Snational = -375 + 0
Snational = -375
b. Finding the equilibrium interest rate:
To find the equilibrium interest rate (r), we need to equate investment (I) and national saving (Snational).
Given: I = 1,000 - 50r
Snational = -375
Setting both equations equal to each other:
1,000 - 50r = -375
Solving for r:
50r = 1,375
r = 27.5
Therefore, the equilibrium interest rate is 27.5.
c. Computing private saving, public saving, and national saving when G rises to 1,250:
Using the updated value of G, we can repeat the calculations for private saving (Sprivate), public saving (Spublic), and national saving (Snational).
1. Private Saving (Sprivate):
Sprivate = (Y - T) - C
Sprivate = (500 - 1,000) - (250 + 0.75(500 - 1,000 - 1,250))
Sprivate = -500 - (250 + 0.75(-500))
Sprivate = -500 - (250 - 375)
Sprivate = -500 - (-125)
Sprivate = -375
2. Public Saving (Spublic):
Spublic = T - G
Spublic = 1,000 - 1,250
Spublic = -250
3. National Saving (Snational):
Snational = Sprivate + Spublic
Snational = -375 + (-250)
Snational = -625
d. Finding the new equilibrium interest rate:
Using the updated values of G and Snational, we can find the new equilibrium interest rate (r).
Given: I = 1,000 - 50r
Snational = -625
Setting both equations equal to each other:
1,000 - 50r = -625
Solving for r:
50r = 1,625
r = 32.5
Therefore, the new equilibrium interest rate is 32.5.