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# IS/LM model in economics

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Consider this economy

1. The consumption function is given by C = 200 + 0.75(Y − T ). The investment function is I = 200 − 25r, where r is the real interest rate. Government purchases and taxes are both 100. Inflation expectation πe
= 0. For this economy, graph the IS curve for i ranging from 0 to 8. Interpret the IS curve intuitively.

2. The money demand function in Bocconia is (M/P)d = Y − 100i. The money supply M is 1000 and the price level P is 2. For this economy, graph the LM curve for i ranging from 0 to 8. Interpret the LM curve intuitively.

3. Find the equilibrium interest rate i and the equilibrium level of income Y .

4. Suppose that government purchases are raised from 100 to 150. How much does the IS curve shift? What are the new equilibrium interest rate and level of income? Explain intuitively.

5. Suppose instead that the money supply is raised from 1000 to 1200. How much does the LM curve shift? What are the new equilibrium interest rate and level of income? Explain.

6. With the initial values for monetary and fiscal policy, suppose that the price level rises from 2 to 4 but πe still equals 0. What happens? What are the new equilibrium interest rate and level of income? Explain in words.

7. Derive and graph an equation for the aggregate demand curve. What happens to this aggregate demand curve if fiscal or monetary policy changes, as in parts (4) and (5). Explain in words.

##### Solution Preview

1. The consumption function is given by C = 200 + 0.75(Y − T ). The investment function is I = 200 − 25r, where r is the real interest rate. Government purchases and taxes are both 100. Inflation expectation is 0. For this economy, graph the IS curve for i ranging from 0 to 8. Interpret the IS curve intuitively.
C = 200 + 0.75(Y − T)
I = 200 − 25r
First of all we need to write our equation:
Y= C + I + G
If we plug in our consumption and investment functions in our formula:
Y= 200+0.75*(Y-T) + 200-25*r +G
Now if we write the expression above with r as a function of Y, G and T our formula would be:
25r= 400- 0.75T +0.75Y + G
r=16-0.03*T-0.01*Y+0.04*G
Since government purchases and taxes are both 100:
G=T=100
r=16-0.03*100-0.01*Y+0.04*100
Then our formula and the function of IS curve at the same time would be:
r=17-0.01*Y

(See attached)

2. The money demand function in Bocconia is (M/P)d = Y − 100i. The money supply M is 1000 and the price level P ...

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• BSc, Dokuz Eylul University
• MBA, Texas A&M University-Kingsville
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