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 interest-rate-sensitive -- autonomous
consumption and investment. The interest-sensitive 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.