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```ECON 3312
Mid-term Exam
Answer two of the three questions. Neatness counts.
1. Using the three-graph IS-LM model, analyze the effects of an increase in lump-sum
taxes.
2. Demonstrate that government fiscal policy (both spending and taxes) has no effect on
aggregate demand in the classical model.
3. Derive the Classical aggregate supply. Include the labor market and aggregate
production function.
Extra Credit (10 points) - Demonstrate that the crowding out effect is larger when Ir is
larger (in absolute value) and smaller when Lr is larger (in absolute value). Hint: Derive
an expression for the crowding effect.
Q1.
AE
450
Initial Equilibrium
AE(A0, T0, r0)
A
Y0
Ms
Y
r
r
LM(M0)
A
r0
A
r0
Md(Y0)
IS(A0, T0)
Y0
Y
M0
M
AE
450
T↑→ESG (pt. B)→ inventories↑→Y↓ (pt. C)→
Md↓→ESM↔EDB→PB↑→r↓ →(point D)→
I↑→EDG→inventories ↓ →Y ↑(point E)→
AE(A0, T0, r0)
AE(A0, T0, r1)
A
E
B
C
Y0
LM(M0)
A
C
r3
r
r0
r2
r1
F
E
D
Ms
Y
r
r0
r2
r1
I↓→ESG→ …Y*↓ and r* ↓
AE(A0, T1, r0)
D
Y1 Y2
Md↑→EDM↔ESB→PB↓→r↑ →(point F)→
C
A
F
D
IS(A0, T0)
Y2 Y0
Y
Md(Y0)
Md(Y1)
IS(A0, T1)
Y1
E
M1
M0
Md(Y2)
M
We know that the equation describing the IS curve can be found
by solving for equilibrium in the goods market and is given as:
Similarly we can describe the LM curve by solving for
equilibrium in the money market:
Joint equilibrium in the IS-LM model can then be
found by setting the LM equation equal to the IS
and solving for Y* and r*:
We can now use the two equilibrium equations to
find out what happens to Y* and r* when taxes
rise:
When the taxes rise Y* and r* decreases.
Q2.
i
S = Savings
A
i0
D = Investment + G-T
Q0
Initial equilibrium in the loanable funds market
yields interest rate i0 and Q0.
Q\$
i
S = Savings
B
A
i0
D = Investment + G-T
D’ = Investment - ΔT
Q1
Q0
Q\$
The increase in taxes shifts the demand for loanable funds to the left (smaller deficit, less gov’t borrowing).
i
S = Savings
B
A
i0
C
i1
D = Investment + G-T
D’ = Investment - ΔT
Q1
Q2
Q0
Q\$
If we assume that the tax increase caused consumption to decline (as opposed to savings decline) then the new equilibrium is at
point C and ΔT = -ΔC = Q0 – Q1. Since interest rate is lower at the new equilibrium (pt. C), investment increases Q2 – Q1 and
savings declines Q0 – Q2. But a savings decline is the same as a consumption increase. So the net effect is the consumption
declines by Q2 – Q1 but investment increases by the same amount so there is no net change in total spending.
S’ = Savings - ΔT
i
S = Savings
B
A
i0
D = Investment + G-T
D’ = Investment - ΔT
Q1
Q0
Q\$
If we assume that the tax increase caused savings to decline, ΔT = -ΔS, then the supply will shift leftward the same amount as
the demand curve shifts and there is no change in the interest rate. Since the interest rate has not changed, investment and
savings will stay the same and there will be no change in total spending.
S = Savings
i
i1
C
A
B
i0
D = Investment + ΔG
D = Investment
Q1
Q2
Q0
Q\$
The increase in government spending shifts the demand for loanable funds to the right. The ΔG = Q0 – Q1. The new equilibrium
is at point C. Since interest rate is higher at the new equilibrium (pt. C), investment decreases Q0 – Q2 and savings increase Q2 –
Q1. But a savings increase is the same as a consumption decrease. So ΔG = Q0 – Q1 and -ΔI = Q0 – Q2 and -ΔC = Q2 – Q1. No
change in total spending.
Q3.
Y
C
Y1
F1(N)
B
F0(N)
Y0
A
N0
N1
N
The initial equilibrium is at pt. A where employment is N0 as determined by the equilibrium in the labor market. This
translates into real output of Y0 and real wage of W0/P0. The increase in technology rotates the aggregate production
function upward. This increases the slope which is the same as the MPL. Since the MPL is the labor demand curve, Nd will
shift rightward. Note that price level has not changed. Labor demand is higher because workers are more productive. This
leads to higher equilibrium employment N1 which causes output to rise even more than it would with just the productivity
increase. The new equilibrium at pt. C has higher real wage of W1/P0.
W
Ns(P0)
C
W1
A
W0
Nd’(P0)
Nd(P0)
N0
N1
N
AS0
AS1
P
P0
A
Y0
C
Y1
Y
```
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