## Econ 302 Exercise Set 5

Course Instructor: Leigh Tesfatsion
Date Assigned: 2 April 1996

```FIFTH TAKE-HOME EXERCISE SET [12 Points Total]       L. Tesfatsion
DUE DATE:  Thursday, April 11, 9:30 A.M.        Econ 302/Spring 96
**PLEASE NOTE: As always, no late assignments will be accepted.

Each exercise below concerns a Hall and Taylor Chapter 8 economy
satisfying the following six properties UNLESS OTHERWISE
SPECIFIED:
(1) The economy exists over time periods T=0,1,...;
(2) Potential GDP is given by a **constant** value Y* in each period;
(3) Money demand is given by M^D/P = kY - hR, implying that the
expected inflation rate does **not** affect money demand.
(4) At the beginning of period 0 the economy is in internal balance;
(5) the actual inflation rate INF(0,1) from period 0 to 1 is zero;
(6) The expected inflation rate satisfies

(*)          INF^e(T,T+1)  =  0.6 x INF(T-1,T)  ,  T = 1,2,... .

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EXERCISE 5.1  [4 Points Total; 2 points for each part]. [HINT:
For some parts of this exercise, use the HT6 formula

[1 + q^2 +  q^3 + ... ]  = 1/[1-q],

which holds for any number q with absolute value less than 1.]

Part (a):  Suppose that GDP Y(1) for period 1 rises above the
potential GDP level Y*, but that Y(T) = Y* in all subsequent
periods T = 2, 3,... .  Using the Hall and Taylor
expectations-augmented Phillips curve, determine what happens to
the **actual** inflation rate over periods T = 2, 3, ...  How
were changed to 1.5?  #Be sure to justify your assertions#.

Part (b):  Suppose, instead, that GDP Y(1) for period 1 rises to
a level Y' that is higher than Y*, and that Y(T) **remains** at
the higher level Y' in all subsequent periods T = 2, 3,...  Using
the Hall and Taylor expectations- augmented Phillips curve,
explain what happens to the **actual** inflation rate over
periods T = 2, 3, ...  How would your answer change if, in
relation (*), the constant 0.6 were changed to 1.5?  #Be sure to

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EXERCISE 5.2  [4 Points Total; 2 points for each part]. Hall and
Taylor, Chapter 8, ANALYTICAL exercise 4, page 226-227. #Be sure
NOTE: For each part of this exercise, assume that the
government increase in defense spending occurs suddenly at the
beginning of period 1, disrupting the internal balance of the
economy. In the first part, assume [instead of relation (*)] that
expectations of inflation remain at zero.  In the second part,
assume that expectations of inflation satisfy relation (*).
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EXERCISE 5.3 [4 Points Total; 2 points for each part]. Hall and
Taylor, Chapter 8, MACROSOLVE exercise 4, page 228.
NOTE: For part a, explore at least **three different
combinations** of expansionary fiscal policy and tight monetary
policy to check the robustness of your policy conclusions.  For
part b, you might first want to review some of the U.S. data
presented by Hall and Taylor in Chapters 1 through 3.

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```