You will type answers to questions in Word as much as possible. If an answer requires graphs or
equations you will handwrite those two parts of an answer. Be careful to graph things clearly and in
detail. Handwritten equations should be clearly and carefully written
1.
A. Using the IS-MP-FE and AD-A-LRAS model, GRAPH an economy operating at a point
where output is at its full employment level (Y=YFE), the real rate of interest is at its natural rate
(r=rN) and is at the desired rate of inflation (Hint: This is a point of GE, general equilibrium)
B. Starting from a position of GE, suppose the economy is hit by excessive optimism. In other
words, people expect higher future income and firms expect higher future marginal product of
capital. However, the central bank recognizes that there was no change in the level of full
employment output or in their target for inflation. What would the central bank do to keep
these variables operating at these desired levels? Illustrate your answer to this question with a
new graph which shows the initial GE, what excessive optimism does to the graph, and how the
central banks response keeps output and inflation at desired levels.
C. Starting from a position of GE, assume there is a technological improvement. Suppose the
central bank recognizes precisely the change in the level of full employment output that has
occurred, and there is no change in the target for inflation. What would the central bank do to
keep these variables operating at these desired levels? Illustrate your answer to this question
with a new graph which shows the initial GE, what the change in technology does to the graph,
and how the central banks response keeps output and inflation at the desired levels.
2. An inflation targeting policy would attempt to keep inflation at some constant desired rate and
not be concerned about anything else. Correct answers to Parts B and C of Question 1 illustrate
possible reasons why many central banks across the world have opted to target inflation. These
two analytical results imply that targeting inflation will keep output at its full employment level
in response to some of the most important shocks to an economy. This is a significant result
because even if the central bank didnt know the actual level of full employment output it would
still be able to achieve that level of output simply by holding inflation at a constant rate.
A. What difficulties does a central bank face in trying to implement a policy of attempting to
control the rate of inflation? (for this part of the question ignore the effects of unexpected
movements in the marginal product of labor, as these will be dealt with later)
B. Supply shocks, that is unexpected movements in the marginal product of labor, also affect
the economy. Explain a particular sort of event could happen to an economy that makes the
marginal product of labor higher than it was expected to be.
C. Using the assumption from part B and the AD-A-LRAS model, GRAPH and explain what
happens to output when that shock occurs. In this case, does implementing an inflation
target a monetary policy that keeps inflation keeping it constant at the target rate – make
it easy, somewhat difficult, or impossible to maintain output at its full employment level?
3. A linear version of the IS Curve can be algebraically written as:
Y = A br
where A represents all the things that shift the IS Curve (factors other than real output, Y, and
the real interest rate, r, for Cd
, Id
, NXd
, and G), and b is the interest sensitivity of spending, arising
from interest sensitivities of each component in desired spending.
The MP curve can be written as:
r = Q + cY + d
The real rate reacts to real output and the inflation rate (), with c and d being positive
parameters, and Q summarizes the effects on r of all target variables in the central bank interest
rate rule.
A. Derive algebraically an equation for the aggregate demand curve. Does inflation have a
negative effect on output in this equation (as it does in our lecture slides discussion of
aggregate demand)?
B. In a liquidity trap, the central bank has lowered the nominal interest rate to zero. Combining
this with the Fisher Equation you get: r = – (technically it is expected inflation, but to
simplify we will drop the expectation). Derive the aggregate demand curve equation under
this assumption.
C. Using the aggregate demand curve implied in Part B, draw the AD-A-LRAS graph assuming
the economy starts off in GE (at full employment). In your graph, the slope of the aggregate
demand curve is quantitatively larger (hence should be drawn steeper) than the slope of the
inflation adjustment curve. Suppose that for some reason the aggregate demand curve
shifts to the left. Show that shift in your graph. Is the economy in recession? When inflation
begins to adjust will this push output in the direction of full employment or will output be
pushed further away from full employment? Please illustrate clearly in your graph.
D. What sort of macroeconomic policy could work for the situation in Part C to bring the
economy back to GE? Monetary policy, fiscal policy, or both could be used? Simulative or
contractionary policy? (Hint: Look at the graph and think about the derivation). Explain how
you justify your policy recommendation.
4. A common assumption in macroeconomics is that the natural rate of unemployment and the full
employment level of output are unaffected by inflation. However, there are numerous theories
for which higher inflation may raise output and lower unemployment in the long run, and some
empirical evidence to support these effects. One such theory assumes nominal wages are
downwardly rigid. In other words, firms may be in a position to want to lower nominal wages
but there is some market force that does not allow them to. In fact there is ample empirical
evidence that labor markets behave in this way.
A. To get a sense of this mechanism, first GRAPH a Classical labor market model with a labor
supply curve, a labor demand curve, and a unique equilibrium point.
B. Suppose for some reason the real wage is above equilibrium. Combine our earlier
assumption that the nominal wage cant fall with the assumption that the price level cant
rise and GRAPH the resulting real wage line. How do these quantities of employment, labor
supply, and unemployment relate to those quantities when the labor market is in the
Classical equilibrium (for each one is it higher, lower, the same, ambiguously related)?
C. This analysis can be extended to when the price level rises. With fixed nominal wages, the
more price rises the lower is the real wage. Therefore unemployment is lower. The faster
price rises the greater the rate of inflation. Hence, this theory yields an inverse relationship
between unemployment and inflation in equilibrium (or the long run).
Can our equilibrium labor market model that we derived from wage setting and price
setting explain this effect? For that model, (see the slides) the natural rate of
unemployment is linearly related to the markup (mu) and factors that affect wage
bargaining (z) and a positive parameter (a) as follows:

Assume wage bargaining power is negatively related to the inflation rate:
z = H – e
where e is a positive parameter. H represents all other factors that positively affect the
wage bargaining power of workers.
We could show, using the production function (in logarithmic form) and an identity
between labor supply, employment and the unemployment rate that output (y) can be
written as a negative function of the unemployment rate:
y = J (1-)u
with J representing all other factors in the production function (capital, labor supply, and
productivity) and is the parameter from the Cobb-Douglas production function. Full
employment output occurs when unemployment is equal to its natural rate.
How does an increase in inflation affect the natural unemployment rate and full
employment output? (positive, negative, zero, or ambiguous). For each of these you must
derive relevant expressions and discuss them. And finally, does the real wage decline with
higher inflation as our first graphical analysis suggests it should? (Hint: to answer this very
last question use economic reasoning. Deriving an equation is tedious and unnecessary)