ECO 202, Lyons
Fall 2010
PROBLEM SET IV DISCUSSION SHEET
CHAPTER 12
Problem 1:
Begin, as usual, by finding PAE, given the information in the problem, remembering to plug in
the interest rate as a decimal fraction (0.10, rather than 10%).
PAE = C + Ip + G + NX
= [2,600 + 0.8(Y  3,000)  10,000•0.10] + [2,000  10,000•0.10] + [1,800] + [0]
= [2,600 + 0.8Y 2,400  1,000] + [2,000  1,000] + [1,800]
= 2,000 + 0.8Y
Solve for equilibrium (i.e., where PAE = Y):
PAE = Y = 2,000 + 0.8Y
=> 0.2Y = 2,000, so PAE = Y =
10,000
.
Graphically, you will observe that a plot of the expenditure line PAE = 2,000 + 0.8Y, crosses the
equilibrium line (PAE = Y) where Y = 10,000.
Problem 2 (a & b):
a)
Given the results of problem 1, if potential output, Y*, is equal to 12,000, then the economy is
suffering a recessionary gap, and monetary policy should be expansionary, which means acting
to lower the real (and nominal) interest rate.
There are two ways to proceed:
i) The recessionary gap is
2,000, so the Fed must lower the interest rate by enough to
increase autonomous expenditures by 400 (that is, given the expenditure multiplier of 5 derived
from the mpc of 0.8).
Two components of expenditure are interestratesensitive  autonomous
consumption and investment. The interestsensitive components are 10,000•
r
in each case, so
together the impact of
r
is –20,000•
r
.
We want
∆
PAE = 400 = 20,000•
∆
r
, so
∆
r
= –0.02.
That
is, the interest rate must be reduced by two percentage points from 10% to
8%
.
ii) Solve the equation in problem 6 for
r
after substituting Y* = 12,000 for Y:
Y*= 12,000 = PAE = [2,600 + 0.8(12,000 3,000) 10,000•
r
] + [2,000  10,000•
r
] + [1,800] + [0]
12,000 = [2,600 + 7,200  10,000•
r
] + [2,000 10,000•
r
] + [1,800]
20,000•
r
= 2,600 + 7,200 + 2,000 + 1,800  12,000 = 13,600  12,000 = 1,600
Thus,
r
= 1,600/20,000 = 0.08, or 8%.
* Lowering the real interest rate by 2% is correct policy.
b)
If Y* = 9,000, the Fed should raise the interest rate to eliminate the expansionary gap.
Using
the method of a) i) above:
Since the gap is 1,000 and the multiplier is 5, autonomous
expenditures must fall by 200.
A
1% increase
in the interest rate will accomplish this end, since
–20,000•0.01 = –200.
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ECO 202, Lyons
Problem Set IV Discussion, page 2
10th December, 2010
CHAPTER 13
Problem 1:
Refer to Figure 13.12 on page 401 in the textbook for parts a), b), c), and e).
Figure 13.13 on
page 404 can be used for part d). Notice that each response assumes (for convenience) that the
economy begins at longrun equilibrium, and that there is no change in monetary or fiscal policy.
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 Spring '08
 NORMMILLER
 Inflation, Inflation rates

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