Consumption=2000+0.9y-100000r-g

Question

Investiment=1000-4500r
Real money demand=y-6000i
Inflation=0.03
G=500
Full employment=1000
M=2100
Find equilibrium values of the real interest rate, consumption,investment,price level

Answer 1

To find the equilibrium values of the real interest rate, consumption, investment, and price level, we need to set the supply of savings equal to the demand for savings.

First, we'll find the supply of savings:

S = Y - C

Given that Consumption (C) is equal to 2000 + 0.9Y - 100000r - G, we have:

S = Y - (2000 + 0.9Y - 100000r - G)
S = Y - 2000 - 0.9Y + 100000r + G
S = 8000 + 99900r

Now, we'll find the demand for savings, which is equal to investment (I):

I = 1000 - 4500r

Equating the supply and demand for savings:

8000 + 99900r = 1000 - 4500r

Rearranging the equation:

104400r = -7000

Dividing by 104400:

r = -7000 / 104400
r ≈ -0.067

Since the real interest rate cannot be negative, this result is not feasible. Therefore, there is no equilibrium in the real interest rate for this model.

Next, we'll find the equilibrium values for consumption, investment, and the price level:

Given the equation for consumption:

C = 2000 + 0.9Y - 100000r - G

Substituting the given values for G and r:

C = 2000 + 0.9Y - 100000(-0.067) - 500
C ≈ 2000 + 0.9Y + 6700 - 500
C ≈ 9200 + 0.9Y

To find the equilibrium value for investment, we need to plug in the equilibrium value of the real interest rate (r ≈ -0.067) into the investment equation:

I = 1000 - 4500(-0.067)
I ≈ 1000 + 301.5
I ≈ 1301.5

Finally, to find the equilibrium price level, we can use the inflation equation:

π = 0.03 = (P - P_0) / P_0

Where P_0 is the initial price level. We're given that the initial money supply (M) is equal to 2100, which is also equal to P_0 * Y.

2100 = P_0 * Y

Therefore, the initial price level (P_0) is:

P_0 = 2100 / Y

Substituting this into the inflation equation:

0.03 = (P - (2100 / Y)) / (2100 / Y)
0.03 = (P * Y - 2100) / 2100

Rearranging the equation and substituting the given full employment value (Y = 1000):

P * 1000 = 0.03 * 2100 + 2100
P * 1000 = 63 + 2100
P * 1000 = 2163
P ≈ 2.163

Therefore, the equilibrium values are approximately:

Real interest rate (r): Not feasible (no equilibrium)
Consumption (C): 9200 + 0.9Y
Investment (I): 1301.5
Price level (P): 2.163