Question

IS/LM ALGEBRA Showing your work, solve for the equilibrium interest rate and output level given the following: C = 400 + 0.5(Y-T) I = 800 – 100r G = 300 T = 200 (M/P)d = Y – 750r (M/P)s = 1000 Now let government expenditures (G) fall to 200 to balance the budget. Re-compute equilibrium r and Y. Illustrate with IS/LM graph including the original equilibrium conditions. Label everything on your graph.

Answer 1

Equation for IS depicts goods market equilibrium

Y = C + I + G

Y =  400 + 0.5(Y - 200) + 800 – 100r + 300

0.5Y = 1400 - 100r

Y = 2800 - 200r

Equation for LM shows money market equilibrium

Y – 750r = 1000

Y = 1000 + 750r

Solve for equilibrium r and Y

2800 - 200r = 1000 + 750r

1800 = 950r

r = 1.895%

Y = 2421.053

Now government expenditures (G) fall to 200 so that New G is 200

New IS is reduced by 100* multiplier = 100*2 = 200

Y = 2600 - 200r and LM is same Y = 1000 + 750r

2600 - 200r = 1000 + 750r

1600 = 950r

New r = 1.68%

New Y = 2263.158