Week 6
EC301
2
011
Problem 14-1 (a-f)
1. a. Given that the interest rate has been 4 percent for the last ten quarters, then for
IS
curve I, real
GDP equals 8,800 - 25(4) - 25(4) - 25(4) - 25(4) - 20(4) - 20(4) - 20(4) - 15(4) - 15(4) - 10(4)
=
8,000. For
IS
curve II, real GDP equals 8,400 - 5(4) - 5(4) - 5(4) - 5(4) - 10(4) - 15(4) - 15(4)
- 15(4) - 20(4)
=
8,000.
b. For
IS
curve I, real GDP in the first quarter equals 8,800 - 25(3) - 25(4) - 25(4) - 25(4) - 20(4)
- 20(4) - 20(4) - 15(4) - 15(4) - 10(4)
=
8,025. Using the same
IS
curve, it is easy to show that for
quarters two through ten, real GDP equals 8,050, 8,075, 8,100, 8,120, 8,140, 8,160, 8,175, 8,190, and
8,200, respectively. For
IS
curve II, real GDP in the first quarter equals 8,400 - 5(3) - 5(4) - 5(4)
- 5(4) - 5(4) - 10(4) - 15(4) - 15(4) - 15(4) - 20(4)
=
8,005. Using the same
IS
curve, it is easy to
show that for quarters two through ten, real GDP equals 8,010, 8,015, 8,020, 8,025, 8,035, 8,050,
8,065, 8,080, and 8,100, respectively.
c. Real GDP increases by 200 billion for
IS
curve I. The increase in real GDP for
IS
curve II equals
100 billion.
d. For
IS
curve I, it takes four quarters for real GDP to increase by 100 billion or one-half of the total
increase in real GDP. For
IS
curve II, it takes seven quarters for real GDP to increase by 50 billion or
one-half of the total increase in real GDP.
e.
IS
curve I resembles the economy’s response prior to 1991. The increase in output in response to a
decline in the interest rate is larger than for
IS
curve II and one-half of the total increase in output
occurs much sooner with
IS
curve I as compared to
IS
curve II.
IS
curve II resembles the economy’s
response to a change in the interest rate since 1991.
The reasons why
IS
curve I resembles the economy’s response prior to 1991 is that its interest rate
parameters for the first six quarters are larger than those of
IS
curve II, and it is only for that last
quarter that
IS
curve I has a smaller interest rate parameter than that of
IS
curve II. These parameters
reflect the fact that since 1991, the monetary policy effectiveness lag has been longer and the interest-
rate multiplier has been smaller.
f. The answers to Parts b through d indicate that for