Assume that output is defined by K0.5 (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)?
a. To calculate the value of output (Y), we can use the given equation: Y = K^0.5 * (EL)^0.5. Substitute the given values: K = 400, L = 100, E = 900.
Y = 400^0.5 * (100 * 900)^0.5
Y = 20 * 30
Y = 600.
The marginal product of capital (MPL) is the change in output when capital increases by one unit, while holding other factors constant. In this case, MPL can be calculated as MPL = ∂Y/∂K = 0.5 * K^(-0.5) * (EL)^0.5.
Substituting the values: MPL = 0.5 * 400^(-0.5) * (100 * 900)^0.5
MPL = 0.5 * 0.25 * 30
MPL = 3.75.
Similarly, the marginal product of labor (MPL) is the change in output when labor increases by one unit, while holding other factors constant. In this case, MPL can be calculated as MPL = ∂Y/∂L = 0.5 * K^0.5 * (E * L)^(-0.5).
Substituting the values: MPL = 0.5 * 400^0.5 * (900 * 100)^(-0.5)
MPL = 0.5 * 20 * 0.05
MPL = 0.5.
b. To determine if there is a budget deficit or surplus, we need to calculate the difference between government spending (G) and taxes (T). If G - T is positive, there is a budget deficit, and if G - T is negative, there is a budget surplus.
Given G = 500 and T = 1000, the difference is:
G - T = 500 - 1000 = -500.
Therefore, there is a budget surplus of 500.
c. To find the equilibrium values of consumption (C), private saving, public saving, and national saving, we need to use the equations given:
C = 500 + 0.5(Y - T)
C = 500 + 0.5(600 - 1000)
C = 500 + 0.5(-400)
C = 300.
Private saving is equal to income minus consumption: Private Saving = Y - C = 600 - 300 = 300.
Public saving is equal to tax revenues minus government spending: Public Saving = T - G = 1000 - 500 = 500.
National saving is the sum of private and public saving: National Saving = Private Saving + Public Saving = 300 + 500 = 800.
d. To find the equilibrium values of investment (I) and the interest rate (r), we need to use the given equation:
I = 3500 - 500r.
Since the equilibrium occurs when investment (I) equals national saving, we can equate the two:
I = National Saving
3500 - 500r = 800
500r = 3500 - 800
500r = 2700
r = 2700/500
r = 5.4.
Therefore, the equilibrium values of investment (I) and the interest rate (r) are 800 and 5.4% respectively.
e. If the government increases the level of public spending to 1000, we need to recalculate the equilibrium values.
The new equation for consumption (C) becomes:
C = 500 + 0.5(Y - T)
C = 500 + 0.5(600 - 1000)
C = 500 - 0.5(400)
C = 500 - 200
C = 300.
The new public saving (Sg) becomes:
Public Saving = T - G = 1000 - 1000 = 0.
National saving (Sn) remains unchanged as it is the sum of private and public saving: Sn = 800.
Investment (I) remains unchanged as well: I = 800.
The new interest rate (r) also remains the same at 5.4%.