Chapter 10 Problem 5

# Chapter 10 Problem 5 - Y =[1 0.4[500 – 4 r Y = 1250 –...

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Chapter 10, Problem #5 , (6 th Edition) The objective of this problem is to find the equations for IS and LM and solve for equilibrium level of income and real interest rate. Equations used to solve for IS Curve (Goods Market Equilibrium) Y= C + I + G C = 170 + 0.60 (Y – T) I = 100 – 4 r G = 350 T = 200 Equations used to solve for LM Curve (Financial Market Equilibrium) (M/P) d = L = 0.75 Y – 6 r (Demand for Money) M s / P = 735 (Supply of Money) According to the Keynesian model, we know that equilibrium occurs somewhere along the 45-degree line (the slope of this line is 1). This is where Planned Expenditures (E) are equal to Actual Expenditures (Y). In addition to the mode given above, we also know that E = Y in equilibrium. E = C + I + G E = [ 170 + 0.6 (Y – T) ] + [ 100 – 4 r ] + [ 350 ] E = 170 + 0.6 (Y – 200) + 100 – 4 r + 350 E = 620 + 0.6 Y – 0.6 (200) – 4 r E = 500 + 0.6 Y – 4 r Since E = Y in equilibrium, then Y = 500 + 0.6 Y – 4 r Y – 0.6 Y = 500 – 4 r 0.4 Y = 500 – 4 r

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Unformatted text preview: Y = [1 / 0.4] [500 – 4 r] Y = 1250 – 10 r {This is the IS Curve} Solving for the LM Curve Money Demand = Money Supply (M/P) d = L = 0.75 Y – 6 r (Demand for Money) M s / P = 735 (Supply of Money) 0.75 Y – 6 r = 735 Y = 1/0.75 [735 + 6 r] Y = 980 + 8 r {This is the LM Curve} We can now combine the equations for IS and LM to determine the equilibrium income and interest rate in this model economy. IS : Y = 1250 – 10 r LM: Y = 980 + 8 r Setting IS equal to LM: 1250 – 10 r = 980 + 8 r - 10 r – 8 r = 980 – 1250 -18 r = - 270 r = 15% {Equilibrium Real Interest Rate } Substituting r = 15% into either the IS or LM curves will give you the value of Y. IS: Y = 1250 – 10 r = 1250 – 10 (15) = 1100 {Equilibrium Income} Checking our work by substituting into the LM will yield the same result. LM: Y = 980 + 8 r = 980 + 8 (15) = 1100 Once you have the equilibrium values of Y and r, it’s relatively easy to answer the remaining questions. Prof. Lopez-Calleja...
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Chapter 10 Problem 5 - Y =[1 0.4[500 – 4 r Y = 1250 –...

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