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C = 200 + 0.25Y, I = 150 + 0.25Y – 1,000i G = 250 T = 200 (M/P)ª = 2Y – 8,000i M/P = 1,600 a. Derive the IS relation. (Hint: You want an equation with Y on the left side and everything else on the right.) b. Derive the LM relation. (Hint: It will be convenient for later use to rewrite this equation with i on the left side and everything else on the right.) c. Solve for equilibrium real output. (Hint: Substitute the expression for the interest rate given by the LM equation into the IS equation and solve for output.) d. Solve for the equilibrium interest rate. (Hint: Substitute the value you obtained for Y in part (c) into either the IS or LM equation and solve for i.) e. Solve for the equilibrium values of C and I, and verify the value you obtained for Y by adding C, I, and G. f. Now suppose that the money supply increases to M/P = 1,840. Solve for Y, i, C, and I, and describe in words the effects of an expansionary monetary policy. g. Set M/P equal to its initial value of 1,600. Now suppose that government spending

C = 200 + 0.25Y, I = 150 + 0.25Y – 1,000i G = 250 T = 200 (M/P)ª = 2Y – 8,000i M/P = 1,600 a. Derive the IS relation. (Hint: You want an equation with Y on the left side and everything else on the right.) b. Derive the LM relation. (Hint: It will be convenient for later use to rewrite this equation with i on the left side and everything else on the right.) c. Solve for equilibrium real output. (Hint: Substitute the expression for the interest rate given by the LM equation into the IS equation and solve for output.) d. Solve for the equilibrium interest rate. (Hint: Substitute the value you obtained for Y in part (c) into either the IS or LM equation and solve for i.) e. Solve for the equilibrium values of C and I, and verify the value you obtained for Y by adding C, I, and G. f. Now suppose that the money supply increases to M/P = 1,840. Solve for Y, i, C, and I, and describe in words the effects of an expansionary monetary policy. g. Set M/P equal to its initial value of 1,600. Now suppose that government spending

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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part g

### IS-LM Model Problem Consider the following IS-LM model: **Equations:** - \( C = 200 + 0.25Y_d \) - \( I = 150 + 0.25Y - 1,000i \) - \( G = 250 \) - \( T = 200 \) - \( (M/P)^d = 2Y - 8,000i \) - \( M/P = 1,600 \) **Tasks:** a. **Derive the IS relation.** - Hint: You want an equation with \( Y \) on the left side and everything else on the right. b. **Derive the LM relation.** - Hint: It will be convenient for later use to rewrite this equation with \( i \) on the left side and everything else on the right. c. **Solve for equilibrium real output.** - Hint: Substitute the expression for the interest rate given by the LM equation into the IS equation and solve for output. d. **Solve for the equilibrium interest rate.** - Hint: Substitute the value you obtained for \( Y \) in part (c) into either the IS or LM equation and solve for \( i \). e. **Solve for the equilibrium values of \( C \) and \( I \),** and verify the value you obtained for \( Y \) by adding \( C \), \( I \), and \( G \). f. **Increase in Money Supply:** - Suppose the money supply increases to \( M/P = 1,840 \). Solve for \( Y \), \( i \), \( C \), and \( I \), and describe in words the effects of an expansionary monetary policy. g. **Fiscal Policy Changes:** - Set \( M/P \) equal to its initial value of 1,600. Now suppose that government spending increases to \( G = 400 \). Summarize the effects of an expansionary fiscal policy on \( Y \), \( i \), and \( C \).
Transcribed Image Text:### IS-LM Model Problem Consider the following IS-LM model: **Equations:** - \( C = 200 + 0.25Y_d \) - \( I = 150 + 0.25Y - 1,000i \) - \( G = 250 \) - \( T = 200 \) - \( (M/P)^d = 2Y - 8,000i \) - \( M/P = 1,600 \) **Tasks:** a. **Derive the IS relation.** - Hint: You want an equation with \( Y \) on the left side and everything else on the right. b. **Derive the LM relation.** - Hint: It will be convenient for later use to rewrite this equation with \( i \) on the left side and everything else on the right. c. **Solve for equilibrium real output.** - Hint: Substitute the expression for the interest rate given by the LM equation into the IS equation and solve for output. d. **Solve for the equilibrium interest rate.** - Hint: Substitute the value you obtained for \( Y \) in part (c) into either the IS or LM equation and solve for \( i \). e. **Solve for the equilibrium values of \( C \) and \( I \),** and verify the value you obtained for \( Y \) by adding \( C \), \( I \), and \( G \). f. **Increase in Money Supply:** - Suppose the money supply increases to \( M/P = 1,840 \). Solve for \( Y \), \( i \), \( C \), and \( I \), and describe in words the effects of an expansionary monetary policy. g. **Fiscal Policy Changes:** - Set \( M/P \) equal to its initial value of 1,600. Now suppose that government spending increases to \( G = 400 \). Summarize the effects of an expansionary fiscal policy on \( Y \), \( i \), and \( C \).
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