5. [IS-LM Model] Assume the following model of a closed economy in the short run, with the

Question

price level, P, fixed at 3.0:
𝑪 = 𝟓𝟎 + 𝟎. 𝟕𝟓(𝒀 − 𝑻 ) − 𝑪𝒐𝒏𝒔𝒖𝒎𝒑𝒕𝒊𝒐𝒏 𝒇𝒖𝒏𝒄𝒕𝒊𝒐𝒏
𝑰 = 𝟐𝟎𝟎 − 𝟐𝟓𝒓 − 𝑰𝒏𝒗𝒆𝒔𝒕𝒎𝒆𝒏𝒕 𝒇𝒖𝒏𝒄𝒕𝒊𝒐𝒏
𝑮 = 𝟑𝟓𝟎𝟎, 𝑻 = 𝟑𝟎𝟎𝟎 − 𝑬𝒙𝒐𝒈𝒆𝒏𝒐𝒖𝒔 𝑭𝒊𝒔𝒄𝒂𝒍 𝒑𝒐𝒍𝒊𝒄𝒚 𝒗𝒂𝒓𝒊𝒂𝒃𝒍𝒆𝒔
(𝑴/𝑷 )
𝒅 = 𝟎. 𝟓𝒀 − 𝟏𝟓𝟎𝒓 − 𝑴𝒐𝒏𝒆𝒚 𝒅𝒆𝒎𝒂𝒏𝒅 𝑭𝒖𝒏𝒄𝒕𝒊𝒐𝒏
𝑴𝑺 = 𝟔𝟎𝟎𝟎 − 𝑵𝒐𝒎𝒊𝒏𝒂𝒍 𝒎𝒐𝒏𝒆𝒚 𝒔𝒖𝒑𝒑𝒍𝒚
A. Write a numerical formula for the IS curve?
B. Write a numerical formula for the LM curve?
C. Find the equilibrium interest rate 𝑟 and the equilibrium level of income Y in this 𝐼𝑆 − 𝐿𝑀
model?
D. Now, suppose that the monetary authority increases the money supply from 6000 𝑡𝑜 6600.
Determine the new short-run equilibrium national income, Y (Hint: Use the 𝐼𝑆 − 𝐿𝑀 model
and support your computation with graphical presentation)?�

Answer 1

A. The IS curve is represented by the equation Y = 𝑪 + 𝑰 + 𝑮, so substituting in the given values:

Y = 50 + 0.75(Y - 3000) - 150r + 200 - 25r + 3500

Simplifying, we get: Y = 2350 + 0.5Y - 175r

B. The LM curve is represented by the equation M/P = L(r, Y), so substituting in the given values:

6000 = 600 + 0.5Y - 150r

C. To find the equilibrium interest rate and level of income, we set the IS curve equal to the LM curve:

2350 + 0.5Y - 175r = 600 + 0.5Y - 150r

Solving for r, we get r = 0.04

Substitute r back into the IS curve to find Y:

Y = 2350 + 0.5Y - 175(0.04)
Y = 2400

Therefore, the equilibrium interest rate is 4% and the equilibrium level of income is 2400.

D. When the money supply increases to 6600, the LM curve shifts downwards. The new equilibrium interest rate (r) will be lower and the new equilibrium level of income (Y) will be higher. By solving the new equations for IS and LM, we can find the new values for Y and r. This shift can be shown graphically by plotting the new LM curve below the old LM curve and finding the intersection with the IS curve to determine the new equilibrium income level.