Question 02:
Consider an economy described by the following equations:
Y=C+I+G
Where, Y = 6,000, G = 2,000, T = 2,000
C = 300 + 0.50 (Y-T)
I = 2,000 – 60r
In this economy, compute:
a. Private saving
b. Public saving
c. National saving
d. The equilibrium interest rate
e. The amount of equilibrium level of investment
To compute the different parts of the economy described by the given equations, we can follow these steps:
a. Private saving:
Private saving represents the portion of income that households save. It can be calculated by subtracting consumption (C) from disposable income (Y-T).
Step 1: Calculate disposable income (Y-T)
Y-T = 6,000 - 2,000 = 4,000
Step 2: Calculate private saving
Private saving = Y - C = 4,000 - (300 + 0.50(4,000-2,000)) = 4,000 - (300 + 0.50(2,000)) = 4,000 - (300 + 1,000) = 2,700
Therefore, private saving is 2,700.
b. Public saving:
Public saving represents the difference between government revenue (T) and government spending (G). It can be calculated by subtracting government spending from government revenue.
Step 1: Calculate public saving
Public saving = T - G = 2,000 - 2,000 = 0
Therefore, public saving is zero.
c. National saving:
National saving is the sum of private saving and public saving, representing the total amount of income that is saved in the economy.
Step 1: Calculate national saving
National saving = Private saving + Public saving = 2,700 + 0 = 2,700
Therefore, national saving is 2,700.
d. Equilibrium interest rate:
To find the equilibrium interest rate, we need to equate investment (I) and national saving (S).
Step 1: Set I = S
2,000 - 60r = 2,700
Step 2: Solve for r
60r = 2,000 - 2,700
60r = -700
r = -700 / 60
r ≈ -11.67
Therefore, the equilibrium interest rate is approximately -11.67.
e. Equilibrium level of investment:
To find the equilibrium level of investment, we substitute the equilibrium interest rate (r) into the investment equation (I).
Step 1: Substitute r into I
I = 2,000 - 60(-11.67) = 2,000 + 700.2 = 2,700.2
Therefore, the equilibrium level of investment is approximately 2,700.2.