Department of Economics
Intermediate Macroeconomics
Fall 2006
Problem Set #2
Alexander
The model is: TE = C + I + G
C = a + b ( Y - t Y + TR )
I = c - d i + eY
L = f Y - g i
|
Where |
a = 200 |
e = .15 |
G = 500 |
|
|
b = .8 |
f = .12 |
TR = 400 |
|
|
c = 500 |
g = 2000 |
M/P = 500 |
|
|
d = 1000 |
t = .25 |
|
a. What is the equation that describes the IS curve?
The IS curve shows equilibrium in the goods market at various interest rates.
What is the definition of the IS curve?
The IS curve shows the various
combinations of i (interest rate) and Y (output
level) for which the goods market is in equilibrium.
b. What is the equation that describes the LM curve?
The LM
curve shows equilibrium in the money market at various income levels.
Plugging in the values of the
parameters yields:
i = 0.00006*Y – 0.25
What is the definition of the LM curve?
The LM
curve shows the various combinations of interest rate and income levels for which
the money market is in equilibrium.
c. What are the equilibrium values for Y and i?
To find
the equilibrium values for Y and i, you solve the IS
and LM equations together. Each equation, individually, is an equation in two
unknowns: i and Y. You can solve these two equations
together by inserting the equation for the LM curve into the IS equation:
Y = 6080
– 4000* i
Y = 6080 – 4000 { .00006*Y
- .25)
Y = 6080
- .24*Y + 1000
Y +
.24*Y = 7080
1.24 *Y
= 7080
Y = 7080
/ 1.24 =5,709.68
Since Y
= 5,709.68, i = .00006*Y - .25 = .0925
d. To satisfy a recent election-year promise, Congress decides to reduce taxes. Assume that the tax rate is reduced by .05 (Dt = -.05). What will be the changes in the equilibrium values for Y and i? Show all work!
The key to doing this part of the
problem is to look at the changes in Y and i that
will result from the change in the tax rate. The “changes” necessitate the
total differential. Thus, we want to look at the changes in the goods market
(which causes a change in Y) and also the changes in the money market (since
the change in Y will cause a change in i). The result
will be two equations in two unknowns: ∆Y and ∆i.
We now have two equations in two
unknowns:
We can solve these two equations
together to find the change in Y and the change in i:
With this change in Y, we can easily
figure the change in i (from the money market
differential):
Here, we want to use the “circle”
analysis to motivate the description:
↓t → ↑YD → ↑C → ↑TE →
↑Y (join the circle here—we want to go all the way around the circle until
we come back to this point) → ↑L
→ ↑i → ↓I → ↓TE →
↓Y (somewhat offsetting the
original ↑Y (where we entered
the circle)).
Here’s the graph:
f. The increase in the Government's budget deficit creates worries on Wall
Street. Investors decide that the economy is overheating and that the budget
deficit is out of control. Assume that these pessimistic sentiments lead to a
reduction in the income responsiveness of investment demand (De = -.05).What will be the changes in the
equilibrium values for Y and i? Show all
work!
This problem is done in exactly the same manner as the one above involving the change in the tax rate:
We have, as above, two
equations in two unknowns (we don’t know ∆Y and we don’t know ∆i):
We solve these two equations in two
unknowns together:
Once again, given this change in Y we
can easily compute the change in the interest rate by plugging this value into
the “change” equation from the money market:
g. Describe and graphically depict the effect of the change in e on the goods and the money markets (I want a 3 quadrant diagram and an explanation).
Here, again, we want to use the
“circle” analysis to motivate the description:
↓e → ↓I (join the circle here) → ↓TE → ↓Y → ↓L → ↓i → ↑I (we
have now gone full-circle; however, since I am primarily interested
in the effects on output and the interest
rate—Y and i, I continue around the circle until I
see the final effect on Y: the top of the
circle in this case) → ↑TE → ↑Y . That’s the end of the story!
Here’s the graph:
