07 Jun Question ECN137 Macroeconomic Policy Post-class Assignment #2 (Due: Aug. 24, 2015)
Question
ECN137 Macroeconomic Policy
Post-class Assignment #2 (Due: Aug. 24, 2015)
Jae Wook Jung
[email protected]
1. Three equations are given for the short-run model.
The IS curve is described as
¯
Yt Y = at ¯ t r)
b(R
¯
¯
¯
where Yt is the output level in time t, Y is the long-run level of output (so Yt Y is
called output gap), Rt is the real interest rate in time t, and r is the long-run level of real
¯
interest rate. The term at is the aggregate demand shifter (or shock parameter) in time t.
¯ governs how sensitive the investment is to change in the real interest rate.
b
The simplest version of Taylor rule is given for the monetary policy rule:
it = ¯ + (m + 1)(πt π )
i
¯
¯
(1)
where it is the targeted nominal interest rate in time t, ¯ is the long-run level of nominal
i
interest rate, πt is the ination rate in time t, and π is the long-run level of ination rate
¯
and targeted level by the (ination targeting) monetary policy. m is a positive parameter
¯
that captures how much the Fed cares about the ination deviation from the long-run
level1 .
The last equation is Phillips curve given by:
¯
πt = πt1 + ν (Yt Y ) + ot
¯
where ν describes how sensitive the ination rate responses to the output gap, and ot
¯
captures shocks in the supply side of the economy in time t.
Answer the following questions:
(a) Derive the monetary policy equation for Rt and πt from the simple version of Taylor
rule (1) and Fishers equation it = Rt + πt (or, ¯ = r + π ).
i ¯ ¯
(b) What is the Aggregate Demand (AD) and Aggregate Supply (AS) curves for this
economy.
(c) Draw the AS and AD curves in the same graph. Label the axes as appropriate.
(d) In the long-run, what should be at and ot ? Explain why?
Now assume that up to period t = 2013 the economy has been resting at the long-run
equilibrium. Let π = 0.05. ¯ = 0.8, m = 0.5, and ν = 0.5. In period t = 2014, a
¯
b
¯
¯
supply shock o2014 = 0.03 hits the economy. The shock lasts for three periods, that is
o2014 = o2015 = o2016 = 0.03 and o2017 = 0..
(d) What is the AS curve equation in t = 2014?
1 The
¯
original version of Taylor rule is described by it = ¯ + 0.5(πt π ) + 0.5(Yt Y )
i
¯
1
ECN137 Macroeconomic Policy
Post-class Assignment #2 (Due: Aug. 24, 2015)
Jae Wook Jung
[email protected]
(e) Start with a graph that represents the long-run equilibrium. Draw the new AS curve
AS in t = 2014.
(f) What is the level of ination π2014 and actual output Y2014 in t = 2014?
(hint: Plug your AD curve equation into AS curve equation and nd π2014 rst. Then
plug it into AD curve equation to nd Y2014 .)
(g) What is the level of ination π2015 and actual output Y2015 in t = 2015?
(h) What is the level of ination π2016 and actual output Y2016 in t = 2016?
(i) Again, o2017 = 0. What is the level of ination π2017 and actual output Y2017 in
t = 2017?
(j) Draw the paths of ination πt and actual output Yt over time from t = 2013 until
t = 2018.
(k) Can you guess the level of ination π2100 and actual output Y2100 in t = 2100, i.e.,
the time when sucient time lasts after the shock disappears?
2
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