Problem 1 - IS/LM Model
Consider the following equations that define the IS - LM model:
C = 200 + 0.75 (Y-T)
I = 200 – 1000 i
G = 250
T = 200
MD = 2 Y- 8000 i
MS = 1600
Here, C is consumption, Y national income, I investment, i the interest rate, G government
spending, T taxes, MD the demand for money and MS the supply of money.
a. Derive the IS (Investment-Savings) relation. (Hint: You want an equation with Y on the
left side and everything else on the right.) For this first, derive public and private savings,
and then total savings. Thereafter, equate total savings to total investments
b. Derive the LM (Liquidity-Money) 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 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 equations and solve for i. If your algebra is correct, you
should get the same answer from both equations.)
e. Solve for the equilibrium values of C and I, and verify the value you obtained for Y by
adding up C, I, and G.
f. Now suppose that the money supply increases to MS = 2600. Solve for Y, i, C and I. Also
describe in words the effects of an expansionary monetary policy.
g. Return MS to its initial value of 1600. Now suppose that government spending increases
to G = 350. Summarize the effects of an expansionary fiscal policy on Y, i, C and I.
h. Contrast the differences in monetary versus fiscal stimulus on investment I.
Consider the following equations that define the IS - LM model:
C = 200 + 0.75 (Y-T)
I = 200 – 1000 i
G = 250
T = 200
MD = 2 Y- 8000 i
MS = 1600
Here, C is consumption, Y national income, I investment, i the interest rate, G government
spending, T taxes, MD the demand for money and MS the supply of money.
a. Derive the IS (Investment-Savings) relation. (Hint: You want an equation with Y on the
left side and everything else on the right.) For this first, derive public and private savings,
and then total savings. Thereafter, equate total savings to total investments
b. Derive the LM (Liquidity-Money) 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 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 equations and solve for i. If your algebra is correct, you
should get the same answer from both equations.)
e. Solve for the equilibrium values of C and I, and verify the value you obtained for Y by
adding up C, I, and G.
f. Now suppose that the money supply increases to MS = 2600. Solve for Y, i, C and I. Also
describe in words the effects of an expansionary monetary policy.
g. Return MS to its initial value of 1600. Now suppose that government spending increases
to G = 350. Summarize the effects of an expansionary fiscal policy on Y, i, C and I.
h. Contrast the differences in monetary versus fiscal stimulus on investment I.
