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Equations of the IS and LM Curves

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Consider the following numerical version of the IS-LM model in a closed economy:

C=400+0.5Yd; I=700-4000r+0.1Y; G=200; TP=200; Yd=Y-TP

RLMD=0.5Y-7500r; RLMS =500; X=M

A) Find the equations for the IS curve and LM curve.

B) Solve for equilibrium real output (Y), interest rate (r), consumption (C), and Investment (I).

C) If government spending increased to 700, solve again for the equilibrium Y, r, C, and I.

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Solution Preview

A) IS curve:
Y = C + I + G + (X - M)
Y = (400 + 0.5Yd) + (700 - 4000r + 0.1Y) + 200 + 0
Y = 400 + 0.5(Y - TP) + 700 - 4000r + 0.1Y + 200
Y = 400 + 0.5Y - 0.5(-200) + 700 -4000r + 0.1Y + 200
Y = 0.5Y + 0.1Y + 400 - 100 + 700 + 200 - 4000r
Y - 0.5Y - 0.1Y = 1200 - 4000r
0.4Y = 1200 - 4000r
Rearranging:
4000r = 1200 - 0.4Y
Solving for r gives us the equation of the IS curve:
r = 0.3 - ...

Solution Summary

This solution shows how to find the equations of the IS and LM curves and how to use them to find equilibrium output (Y), interest rate (r), consumption (C), and investment (I). Then the equilibrium is recalculated if government spending (Q) increases.

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See Also This Related BrainMass Solution

IS LM curves

Difficulty identifying formulas for use. also, do multipliers and autonomous spending have to be calculated for item 1/IS curve? For the last item, does autonomous consumption and investment have to be computed to derive?

Assume following (equations) summarize/represent structure of economy. If:

C=Ca + 0.75(Y-T)
Ca=800-25r
T=400+0.2Y
Ip=600-25r
G=1200
(M/P)^d = 0.2Y-20r
M^s/P=700

1. What are equations for IS and LM curves? What is equilibrium level of income and interest rate? What if mix of fiscal and monetary policies is changed. Te money supply is increased by 100 while government spending reduced by 250:
2. Does investment increase, decrease or remain unchanged? Why/calculate.
3. Does consumption increase, decrease or remain unchanged? Why/calculate.

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