Question

Suppose that the economy is characterized by the following behavioral equations: C = 160 + 0.6Yd, I = 150 + 0.25Y, G = 150, T = 100. Solve for the following.
a. Equilibrium GDP (Y) and disposable income (Yd)
b. Consumption spending (C)
c. Compute the multiplier
d. If government spending doubles, what will happen to AD and Y? Compute the public and private saving. Explain what private and public savings are. Give a brief explanation of total savings in the AD model.

Answer 1

C = 160 + 0.6Yd, I = 150 + 0.25Y, G = 150, T = 100. Solve for the following.
a. Equilibrium GDP (Y) and disposable income (Yd):
Yd = Y - T, Y = C + I + G, so:
160 + 0.6(Y - 100) + 150 + 0.25Y + 150 = Y,
0.15Y = 400,
Y = 400/0.15 = 2,666.67.
Yd = Y - T = 2,666.67 - 100 = 2,566.67.
b. Consumption spending (C):
C = 160 + 0.6*2,566.67 = 1,700.
c. Compute the multiplier
The multiplier is m = 1/(1 - c) = 1/(1 - C/Y) = 1/(1 - 1,700/2,666.67) = 2.76.
d. If government spending doubles, AD will increase and Y will increase too.
Public saving = T - G = 100 - 150 = -50, private saving = (Y - T) - C = (2,666.67 - 100) - 1,700 = 866.67.
Total saving = public saving + private saving = -50 + 866.67 = 816.67.