ECON 3012
PROBLEM 5
Answers
I.
A. IS: Y = b2 i = 21250 – 225i = 2500 – 50i ; LM: i = (d1/d2)Y (1/d2)M/1.0 =
(0.2/10)Y – (1/10)300 = 0.02Y – 30
Y = 2500 – 50(0.02Y – 30)  Y = 2500 – Y + 1500  2Y = 4000  Y0 = 2000; i =
0.022000 – 30  i0 = 40 – 30 = 10; I0 = 400 – 2510 = 400 – 250 = 150
B. New LM: i = 0.02Y – (1/10)250 = 0.02Y – 25
Y = 2500 – 50(0.02Y – 25)  Y = 2500 – Y + 1250  2Y = 3750  Y1 = 1875; i =
0.021875 – 25  i0 = 37.5 – 25 = 12.5; I1 = 400 – 2512.5 = 400 – 312.5 = 87.5.
Action: In the Financial Sector, the nominal money stock is reduced; speculators have
less money and try to get more by selling bonds. Simultaneously, the Central Bank is
selling bonds to reduce the money stock. Both increase the supply of bonds on the
market, lowering bond prices and raising the interest rate.
Reaction: In the Real Sector, the higher interest rate reduces private Investment, which
through the multiplier process, reduces income/output, Y.
Feedback: The reduced income reduces transactions demand which reduces the interest
rate. But it must ALWAYS be true that Feedback effects are less than Action effects, so
the net result is a higher interest rate and a lower income/output.
C. New IS: Y = 21300 – 225i = 2600 – 50i
1. Y = 2600 – 50(0.02Y – 30)  Y = 2600 – Y + 1500  2Y = 4100  Y2 = 2050; i
= 0.022050 – 30  i2 = 41 – 30 = 11; I2 = 400 – 2511 = 400 – 275 = 125
Action: In the In the Real Sector, the increase in Government spending, through the
multiplier process, increases income/output, Y.
Reaction: In the Financial Sector, higher income increases transactions demand which
increases the interest rate: speculators have less money and try to get more by selling
bonds. This increases the supply of bonds on the market, lowering bond prices and
raising the interest rate.
Feedback: The higher interest rate reduces private Investment, which through t he
multiplier process, reduces income/output. This reduction is the “crowding out” effect.
But it must ALWAYS be true that Feedback effects are less than Action effects, so the
net result is a higher income/output and a higher interest rate.
2. I2 – I0 = 100 – 125 = -25. 25 in Investment was crowded out.
3. This is a little tricky and don’t worry, you won’t see anything like this on the exam.
First, i3 must equal i0 = 10. So, from the IS curve: Y3 = 2600 – 5010 = 2600 – 500 =
2100.
NOTE: this is higher than Y2 above because the interest rate hasn’t risen and there has
been no crowding out.
Now substitute the values of Y3 and i3 into the equation for LM curve and solve for M:
10 = 0.022100 – M/10  M/10 = 42 – 10 = 32  M = 320
D. This is similar to the above, but a little easier. You just might see something like
this on the exam. Note that you are now given the two unknowns: Y and i.
Substitute into the equation for the LM curve just as above and solve for M: 8 =
0.022150 – M/10  M/10 = 43 – 8 = 35  M = 350. Now just do the same thing
with the IS curve and solve for A: 2150 = 2A – 508  2A = 2150 + 400 = 2550 
A = 1275. A = 950 + G  1275 – 950 = 375
II.
1. Rewrite the IS and LM curves above: IS: Y = Ai; LM: i = 0.02Y –
(1/10)M(1/P).
Now solve for reduced form in Y: Y = 2·A – 50[0.02Y – (1/10)M(1/P)]  Y = 2·A – Y +
50(1/10)M(1/P)  2Y = 2·A + 5M(1/P)  Y = 1·A + 2.5M(1/P). Since the general form
of the AD curve is Y = A + M(1/P),  = 1 and  =2.5. The AD curve with numbers is:
Y = 1·1250 + 2.5·300(1/P) = 1250 + 750(1/P)
2. Y0 = 1250 + 750(1/1) = 2000; i0 = .02·2000 – 30(1/1) = 40 – 30 = 10; I0 = 400 –
25·10 = 150
3. Y1 = 1250 + 750(1/1.25) = 1250 + 600 = 1850; i1 = .02·1850 – 30(1/1.25) = 37 – 24
= 13; I1 = 400 – 25·13 = 75
4. Y2 = 1250 + 750(1/0.83) = 1250 + 900 = 2150; i2 = .02·2150 – 30(1/0.83) = 43 – 36
= 7; I1 = 400 – 25·7 = 225
5.
P
1.25
1.0
0.83
1850
2000
2150
1950 2075
6. AD curve: Y = ·A + ·M(1/P). New M = 330; new AD curve: Y = 1250 +
825(1/P). With P = 1.0, Y = 1250 + 825 = 2075
7. AD curve: Y = ·A + ·M(1/P). New A = 1200; new AD curve: Y = 1200 +
750(1/P). With P = 1.0, Y = 1200 + 750 = 1950.
Y