Consider a closed economy with the following equations and values:Y=C+I+GY=6,000G=2,000T=2,000C=300+0.5(Y-T)I=2,000-6,000rWhat is the equilibrium real interest rate(r)?
Question
Consider a closed economy with the following equations and values:Y=C+I+GY=6,000G=2,000T=2,000C=300+0.5(Y-T)I=2,000-6,000rWhat is the equilibrium real interest rate(r)?
Solution
In a closed economy, the equilibrium condition is that the total output (Y) equals the total spending, which is the sum of consumption (C), investment (I), and government spending (G).
Given the equations:
C = 300 + 0.5(Y - T) I = 2000 - 6000r
We can substitute Y, G, and T into the consumption function:
C = 300 + 0.5(6000 - 2000) = 300 + 0.5(4000) = 300 + 2000 = 2300
Now we can substitute C, I, and G into the equilibrium condition Y = C + I + G:
6000 = 2300 + I + 2000 6000 = 4300 + I I = 6000 - 4300 = 1700
Now we can substitute I into the investment function to solve for r:
1700 = 2000 - 6000r 6000r = 2000 - 1700 6000r = 300 r = 300 / 6000 = 0.05
So, the equilibrium real interest rate (r) is 0.05 or 5%.
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