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Equations of the IS and LM Curves

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.

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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