Question

An economy has full-employment output of 1500. Suppose desired consumption and desired investment are ? ? = 125 + 0.75(? − ?) − 400? ? ? = 200 − 100?

G is the level of government purchases, and T=100 1.

Goods market and the IS curve section.

a) Derive desired saving with respect to Y and r if the government spending, G, is 150.

b) Find the goods market clearing real interest rate if the full-employment output is 1500 and the government spending, G, is 150.

c) Derive the IS curve based on part (a) and (b).

d) Now, the government decided to use the expansionary fiscal policy. The government increases the government spending by 50 (so, G=200) but did not change the taxes, T (T=100). The full employment output is still 1500. Find the goods market clearing real interest rate, the amount of desired saving and investment.

e) Based on the part d), Find the IS curve. f) Draw the desired saving curves and the desired investment curve from part (b) and (d). Show the real interest rate and the amount of desired saving (or the investment) at each equilibrium of the goods market.

g) Graph IS curve from part (c) and part (e). (Mark the label of the IS curve with IS1(G=150) and IS2(G=200)

2 - Money demand is ?? ? = 0.8? − 2000(? + ? ? ) where the expected rate of inflation, ? ? , is 0.05. The nominal supply of money M = 2000.

2. Asset market equilibrium and the LM curve.

h) Find the price level that clears the asset market if the real interest rate, r, is equal to the goods market equilibrium real interest rate in part (1-a) [Hint: Use the answer in part (1-a) for r]

i) Derive the LM curve when the price level is equal to the solution in part (h) [Hint: Use the price level from the part (2-h) to get the real money supply]

j) When the government use the expansionary fiscal policy with G=200, the goods market equilibrium real interest rate was changed (in the part (1-d).

If the money market also have this real interest rate at new equilibrium, how does the price change? Show the price level to get the real interest rate from the part 1-d) as the new money market equilibrium. [Hint: use the part (1-d) real interest rate to get the new price level.]

k) Graph the money market equilibrium from the part (2-h) and (2-j) with the real money demand curve and the real money supply curve.

l) In the part (2-j), the price is changed so it causes a change in LM curve. Derive the LM curve with the new price level from (2-j)

3. General equilibrium with the change in the government spending.

g) Draw the IS curves, LM curves and FE curve when the full employment output of 1500 on the Y-r

You need to draw two IS curves (from the part (1-c) when G=150 and the part (1-e) when G=200), two LM curves (from the part (2-i) with the price level if G=150 and the part (2-l) with the new price level) and one FE curve with the full employment level.

Answer 1

a) ? ? = 125 + 0.75(? − ?) − 400?

? ? = 200 − 100?

G is the level of government purchases, and T=100

Saving= Y-Cd-G

S= Y-(125 + 0.75(? − ?) − 400?)-150

S= 0.25Y+400r-125+0.75(100)-150=0.25Y+400r-200

b)  The goods market clearing condition:

Y=Cd+Id+G

Y= 125 + 0.75(? − ?) − 400?+200 − 100?+150

Y= 125 + 0.75(? − 100) − 400?+200 − 100?+150

Y=475+0.75Y-75-500r

0.25Y= 400-500r

Y=1500(given)

0.25(1500)=400-500r

375-400=-500r

0.05 = r

c) Derive the IS curve:

Y=Cd+Id+G

Y= 125 + 0.75(? − ?) − 400?+200 − 100?+150

Y= 125 + 0.75(? − 100) − 400?+200 − 100?+150

Y=475+0.75Y-75-500r

0.25Y= 400-500r

Y=1600-2000r IS curve equation

d) If government spending increases to 200, then

S= Y-(125 + 0.75(? − ?) − 400?)-200

S= 0.25Y+400r-125+0.75(100)-200=0.25Y+400r-250

The goods market clearing condition:

Y=Cd+Id+G

Y= 125 + 0.75(? − ?) − 400?+200 − 100?+200

Y= 125 + 0.75(? − 100) − 400?+200 − 100?+200

Y=525+0.75Y-75-500r

0.25Y= 450-500r

Y=1500(given)

0.25(1500)=450-500r

375-450=-500r

0.15 = r

e)Derive the IS curve:

Y=Cd+Id+G

Y= 125 + 0.75(? − ?) − 400?+200 − 100?+200

Y= 125 + 0.75(? − 100) − 400?+200 − 100?+200

Y=525+0.75Y-75-500r

0.25Y= 450-500r

Y=1800-2000r IS curve equation