# 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

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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