Question

Let the money demand function be: L(r,Y) = 50 - 25r + 5Y

the consumption function be : C = 10 + 0.5(Y-T)

and the investment function be: I = 17 - r

where T denotes taxes, G denotes government expenditures, P denotes the price level and M^S denotes the money supply. Suppose T = 10, G = 5, P = 2, and  M^S = 500.

In this economy

1. Public Savings equal  

2. Private Savings equal

3. Output is equal to

4. The real interest rate equals

5. Consumption is equal to  and

6. Investment is equal to .

Answer 1

First find the equilibrium interest rate and income

AD = Y and MD = MS

C + I + G = Y and MD = MS

10 + 0.5*(Y – 10) + 17 – r + 5 = Y and 50 – 25r + 5Y = 500/2

10 + 0.5Y – 5 + 17 – r + 5 = Y and 50 – 25r + 5Y = 250

27 – r = 0.5Y and 5Y = 200 + 25r

Y = 54 – 2r and Y = 40 + 5r

This gives

54 – 2r = 40 + 5r

14 = 7r

r = 2% and Y = 50

Public saving = T – G = 10 – 5 = $5

Private saving = Y – T – C = 50 – 10 – 10 – 0.5*(50 – 10) = $10

Output = $50

Real interest rate = 2%

Consumption = 10 + 0.5*(50 – 10) = $30

Investment = 17 – 2 = $15.