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Unformatted text preview: ISLM Model Example Given the following information, derive the equations for the IS and LM curves. C = 200 + 0.25 YD I = 150 + 0.25 Y – 1000 r G = 250 T = 200 YD = Y – T d (M/P) = 2 Y – 8000 r M/P = 1,600 (A) (B) (C) (D) (E) (F) (G) You can use equations (A) through (E) to determine the equation for the IS curve. Please note that this is the long way to do it. Many steps can be skipped here, but it is important to understand that this is the same process used in developing the simple Keynesian model, which was introduced in chapter 10. E=C+I+G E = 200 + 0.25 YD + 150 + 0.25 Y – 1000 r + G E = 200 + 0.25 (Y – T) + 150 + 0.25 Y – 1000 r + G Recall that in equilibrium E = Y, therefore rewrite above equation: Y = 200 + 0.25 (Y – T) + 150 + 0.25 Y – 1000 r + G Y = 200 + 0.25Y – 0.25 T + 150 + 0.25 Y – 1000 r + G Group all the Y’s on the left side of the equation. Y – 0.25 Y – 0.25 Y = 200 – 0.25 T + 150 – 1000 r + G 0.5 Y = 200 – 0.25 T + 150 – 1000 r + G Since G = 250 and T = 200, substitute these into the above equation. 0.5 Y = 200 – 0.25 (200) + 150 – 1000 r + 250 0.5 Y = 200 – 50 + 150 – 1000 r + 250 0.5 Y = 550 – 1000 r Y = [1/0.5] * [ 550 – 1000 r ] Notice that the multiplier is [1/0.5] or 2 Y = 1100 – 2000 r [IS Curve] To determine the LM Curve you can use equations (F) and (G). Money Supply = Money Demand d M/P = (M/P) 1,600 = 2 Y – 8000 r 2 Y = 1,600 + 8000 r Y = 800 + 4000 r [LM Curve] Now, you have both the IS equation and LM equation. Now, you can determine both the equilibrium real output and the equilibrium interest rate. Set the IS curve and LM curve equal to each other. Equilibrium condition. 1100 – 2000 r = 800 + 4000 r 6000 r = 300 r = 300 / 6000 r = 0.05 or 5% [Equilibrium interest rate] By substituting r = 5% in either the IS or LM equation, you obtain equilibrium real output (Y). Y = 1,100 – 2,000 (0.05) = 1,100 – 100 = 1,000 Y = 1000 _____________________________________ ...
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This note was uploaded on 11/17/2009 for the course ECO 121212 taught by Professor Smith during the Spring '09 term at CulverStockton.
 Spring '09
 Smith
 Macroeconomics, ISLM Model

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