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Answer to Question #62426 in Macroeconomics for HSG

Question #62426
Compute the equilibrium interest rate (do NOT type the solution as a percent) in the closed IS-LM model economy when G = 100, autonomous investment IA = 50, M = 100, c = 0.5, the interest rate coefficient b = 0.1, parameters in the money demand function k = 1 and h = 2
Expert's answer
If in the closed IS-LM model economy G = 100, autonomous investment IA = 50, M = 100, c = 0.5, the interest rate coefficient b = 0.1, parameters in the money demand function k = 1 and h = 2, then:
Y = G + c*Y + (IA - b*i),
i = 1/h*(k*Y - M), so
Y = 100 + 0.5Y + 50 - 0.1i
i = 0.5*(Y - 100)
Y = 150 + 0.5Y - 0.05Y + 5,
0.55Y = 155,
Y = 281.82
I = 0.5*(281.82 - 100) = 90.9

the equilibrium interest rate

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