Macroeconomics
William Scarth
Chapter 2 Questions
1. Consider the following model economy:
aggregate demand
y   (m  p) p  g
g  a   ( y  y)
fiscal policy
monetary policy
m  x   ( p  x)
p   ( y  y )  x
aggregate supply
The notation is standard; all parameters are positive, and x and its time
derivative are zero. Derive the expressions for the impact effect on output,
and the cumulative (undiscounted) output loss, following a permanent fall in
autonomous spending (parameter a). Explain whether either monetary or
fiscal policy represents a ‘built-in stabilizer’. This analysis can be
accomplished by considering how the output response expressions are
affected by variations in the size of parameters  and .
2. Consider the following model:
y  g   (i  p )
i  r  x   ( p  x)
p  w  i
w   ( y  y )  x
All variables except the nominal interest rate, i, are logarithms. All slope
coefficients (the Greek letters) are positive, and the monetary policy
target variables, x and its time derivative, are zero. The first equation is
the standard descriptive IS relationship, and the second defines
monetary policy: the central bank raises the nominal interest rate
whenever the price level is above target. The third equation allows for
the fact that firms often have to pay their wage bill before receiving
their sales revenue. In this case, firms must take out a loan, so the selling
price of goods must be set to cover both wage costs and the interest
costs of the loan. If no loan is needed, coefficient  in the third equation
is zero. If a loan equal to the entire wage bill for one whole period is
required,  is unity. We assume that  is a fraction in this question. The
wage rate is sticky at each point in time; it adjusts gradually through
time according to a Phillips curve relationship (the fourth equation).
Use this model to derive the cumulative output effect of a once-for-all
drop in autonomous demand, g. Explain your reasoning fully, and use
your analysis to assess whether a more aggressive price-targeting policy
(a larger value for parameter ) is supported.
3. Consider the following model of a small open economy:
y  g  r   ( f  p  e)
p   ( y  y )
The first equation is the IS relationship, with demand depending
positively on autonomous spending, negatively on the interest rate, and
positively on the relative price of foreign goods.
g, f, p and e are the logarithms of autonomous spending, the foreign
price of foreign-produced goods, the domestic price of domestically
produced goods, and the exchange rate (defined as the foreign price of a
unit of domestic currency). Both f and r are exogenous constants: items
that are determined in the rest of the world and therefore are
unaffected by developments in this economy. (For simplicity we can set
f equal to zero.) The second equation is a dynamic supply relationship: a
Phillips curve.
You are to consider two exchange-rate regimes. Fixed exchange rates
are involved when e is taken as an exogenous constant (and the two
equations determine y and p in the short run and y and p in full
equilibrium). The price level adjusts only through time. With flexible
exchange rates, the central bank is free to pursue a domestic objective,
and in this case the bank keeps the overall consumer price index
constant. The overall price index is a weighted average of the price of
domestically produced goods and the price of imports. So in this case
there is a third equation (that p  (1   )( f  e) is constant), and the
model determines y, e and p in the short run and y, e and p in full
equilibrium).
Consider a once-for-all drop in g under both exchange-rate regimes, and
determine the undiscounted cumulative output loss in both cases. Under
which exchange-rate regime is the output loss smaller? Does this
analysis support the oft-cited proposition that a flexible exchange rate
acts as a shock absorber?