Assume that output is defined by K^0.5 (EL)^0.5, where K denotes capital, L denotes labour, E denotes labour efficiency; K = 400, L = 100, E = 900
Consumption (C) is given by the equation:
C = 500+0.5(Y - T)
Investment (I) is given by the equation:
I = 3500 - 500r,
where r is the real rate of interest in percent.
Taxes (T) are 1000 and government spending (G) is 500.
a. Calculate the value of output (Y), marginal product of capital and marginal product of labour.
b. Is there a budget deficit or a budget surplus?
c. What are the equilibrium values of consumption(C), private saving, public saving, and national saving?
d. What are the equilibrium values of investment (I) and interest rate (r)?
e. If the government increases the level of public spending to 1000, what are the new equilibrium values of consumption(C), private saving, public saving, national saving, investment (I), and interest rate (r)?
To calculate the value of output (Y), marginal product of capital, and marginal product of labour, we can substitute the given values into the output equation.
a. Value of Output (Y):
Y = K^0.5 * (EL)^0.5
= 400^0.5 * (100 * 900)^0.5
= 20 * (√(90000))
= 20 * 300
= 6000
b. To determine whether there is a budget deficit or a budget surplus, we need to calculate the government budget balance:
Government Budget Balance (B) = T - G
= 1000 - 500
= 500
If B > 0, there is a budget surplus. If B < 0, there is a budget deficit. In this case, B = 500 > 0, so there is a budget surplus.
c. Equilibrium values of consumption (C), private saving, public saving, and national saving:
Consumption (C) = 500 + 0.5(Y - T)
= 500 + 0.5(6000 - 1000)
= 500 + 0.5(5000)
= 500 + 2500
= 3000
Private Saving = Y - C
= 6000 - 3000
= 3000
Public Saving = T - G
= 1000 - 500
= 500
National Saving = Private Saving + Public Saving
= 3000 + 500
= 3500
d. To find the equilibrium values of investment (I) and interest rate (r), we need to set the national saving equal to the investment:
National Saving = Investment
3500 = 3500 - 500r
Solving for r, we get:
500r = 0
r = 0
So, the equilibrium interest rate is 0. Since the interest rate is 0, the equilibrium investment (I) is 3500.
e. If the government increases the level of public spending to 1000, we need to recalculate the equilibrium values:
Consumption (C) = 500 + 0.5(Y - T)
= 500 + 0.5(6000 - 1000)
= 500 + 0.5(5000)
= 500 + 2500
= 3000
Private Saving = Y - C
= 6000 - 3000
= 3000
Public Saving = T - G
= 1000 - 1000
= 0
National Saving = Private Saving + Public Saving
= 3000 + 0
= 3000
Investment (I) remains the same at 3500, and the interest rate (r) remains at 0.