Download Document

Chapter 17: Unemployment, Inflation, and Growth
Instructor’s Manual
Chapter 17: Unemployment, Inflation, and Growth
Problem 1
Productivity is defined as output per worker hour. As can be seen from Box 17.1 in the text,
although there is a strong positive trend in productivity, its growth is not constant. Notably,
productivity growth slowed between 1974-1994, but sped up following 1994.
Problem 2
The dynamic AD curve slopes downward because a given growth rate of the money stock implies
a unique growth rate of nominal GDP consistent with equilibrium. In other words, at any given
rate of money creation (M/M), an increase in the GDP growth rate (Y/Y) has to decrease the
price inflation rate (P/P), in order that the propensity to hold money balances remains constant.
An increase in the rate of money creation shifts the dynamic AD curve to the right -- at every
rate of price inflation, the growth rate of output demand is higher. Given the rate of price
inflation, as the rate of money creation increases, it increases the growth rate of real money
balances in the economy. In the classical theory of money demand, demand for real money
balances is proportional to real output. Hence, the increase in real balances has to be matched by
a corresponding increase in the growth rate of output demand.
Problem 3
According to the classical model, the real wage and output both grow at the rate of productivity
growth, g, in both the short run and the long run. According to Box 17.1 in the text, this is a very
good assumption in the long run as the real wage and productivity move closely together over
time. However, over shorter periods of time, for example, the 1974-1994 period, changes in the
growth of real wages can be different from the growth rate of productivity. This is consistent
with the new-Keynesian wage equation.
Problem 4
According to the classical dynamic aggregate supply curve, output growth is constant and equal
to the rate of productivity growth, g, regardless of the level of inflation. As a result, the classical
dynamic aggregate supply curve is simply a vertical line that is consistent with an output growth
rate of g. In the new-Keynesian model, the real wage can grow faster or slower than the rate of
productivity growth. As a result, output and employment can differ from their natural rates as
well based on changes in price and wage inflation. For example, the new-Keynesian dynamic
aggregate supply curve indicates that if price inflation exceeds wage inflation, real wages must be
growing at a rate less than g which will increase employment and output growth above the rate of
g in the short run. Thus, the new-Keynesian dynamic aggregate supply curve indicates that there
is a positive relationship between price inflation and output growth in the short run.
195
Instructor’s Manual
Chapter 17: Unemployment, Inflation, and Growth
Problem 5
If the real wage is growing faster than productivity growth, it must be true given our newKeynesian wage equation (equation 17.5) that unemployment is above its natural rate and
employment is below its natural rate. See Figure 17.4 in the text for graphs of the labor market
and production function in this case. The new-Keynesian dynamic aggregate supply curve in
equation 17.4 indicates that if wages are growing at 4%, which is faster than g = 3%, then output
must be growing at less than 3%, holding price inflation constant. Thus, the economy must be on
its short run dynamic aggregate supply curve but to the left of the long run dynamic aggregate
supply curve at a level of output growth less than g.
Problem 6
The neoclassical wage equation is
w
P E
g
 c(U  U * ) .
w
P
Since expected price inflation is fixed at 2%, the natural rate of unemployment is 5% and the
natural rate of productivity growth is 3%, the parameters of the neoclassical wage equation are:
g = 3%, U* = 5%, PE/P = 2%, c = 2.
Therefore, we can determine the unemployment rate consistent with zero wage inflation:
0 - 3% = 2% - 2(U - 5%)  U = 7.5%.
To obtain the rate of unemployment consistent with zero price inflation, first note that from
the dynamic aggregate supply equation
P  w
  Y


 g   b
 g  . Since output is
P  w
Y
 

growing at the rate g, the nominal wage inflation rate required for zero price inflation is also g =
3%. Substituting this number into the neoclassical wage equation, we find that the rate of
unemployment consistent with zero price inflation is 6%.
Problem 7
By assumption, output is growing at its natural rate. This means that the rate of growth of output
is the same as the productivity growth rate:
Y Y *
 * 3
Y
Y
The actual inflation rate is P/P = 4%. Hence, from the classical dynamic aggregate demand
equation, the rate of money creation is:
M Y P


 3  4  7%
M
Y
P
Thus, the rate of money creation consistent with price inflation of 4% and output growth at its
natural rate is 7%.
196
Instructor’s Manual
Chapter 17: Unemployment, Inflation, and Growth
From the short-run dynamic aggregate supply equation
P  w
  Y


 g   b
 g ,
P  w
  Y

we see that the rate of wage inflation in this scenario is also 7%:
w
P
g
 7%.
w
P
Problem 8
If the Fed raised the rate of money creation, at first workers will be "surprised." The real wage
would decrease because the actual inflation rate would be higher than the expected rate. This, in
turn, would drive employment and output to increase above their natural rates. But soon people
would learn that the actual inflation rate is higher than what they had expected, so they will revise
their expectations upwards. Subsequently, the rate of growth of the output and the rate of growth
of the real wage would return to their natural rates, but the inflation rate and the rate of growth of
nominal wage will be higher.
Problem 9
If g = 0, the rate of unemployment compatible with zero wage inflation is lower and
equal to 6%. The unemployment rate compatible with zero price inflation is also 6%, since if
productivity does not grow at all, the nominal wage inflation rate is equal to zero (from the
dynamic aggregate supply equation).
Problem 10
a.
In the classical dynamic aggregate supply curve, inflation growth equals money growth
minus output growth, which is equal to productivity growth. In the classical wage
equation, nominal wage inflation equals productivity growth plus price inflation. Thus,
(i) inflation equals 5% - 3% = 2%,
(ii) output growth equals productivity growth which is 3%,
(iii) nominal wages grow at the rate of productivity growth plus inflation, or
2% + 3% = 5%,
(iv) real wages grow at the rate of productivity growth, 3%.
b.
Now,
(i) inflation equals –1%,
(ii) output growth equals 6%,
(iii) nominal wages grow at 5%,
(iv) real wages grow at 6%.
197
Instructor’s Manual
Chapter 17: Unemployment, Inflation, and Growth
Problem 11
In the new-Keynesian model, the short run aggregate supply curve is equal to
P  w
  Y


 g   b
 g
P  w
  Y

If real wage growth is 3%, productivity growth is 1%, and inflation is 1%, then from this equation
we see that 1% = (3%-1%) + .5(
Y
Y
-3%), or
=1%.
Y
Y
Problem 12
The Phillips curve is the negative relationship between unemployment and nominal wage
inflation that A.W. Phillips observed in U.K. data. Panel A of Figure 17.7 illustrates the Phillips
curve for the U.S. between 1949-1959 in which there is also a strong negative relationship
between these two variables. However, we see in the new-Keynesian wage equation (equation
17.5) that a negative relationship may only hold between nominal wage inflation and
unemployment if (1) the expected price level is constant, and (2) the rate of productivity growth
is constant. If one of these two variables change, then it will necessarily change the relationship
between nominal wages and unemployment. Specifically, and increase in productivity or a lower
expected price level shifts the Phillips curve downward and reduces the level of nominal wage
inflation for a given level of unemployment.
Problem 13
A class discussion is helpful here.
a.
An increase in the price of oil reduces the productivity of much of the existing capital
stock and, as a result, reduces g. This would shift the short run new-Keynesian aggregate
supply curve to the left, increasing price inflation and reducing output growth for a given
level of aggregate demand.
b.
The Fed cut the federal funds interest rate by 1%, meaning it increased the rate of money
growth. This will shift the dynamic aggregate demand curve to the right and increase
both price inflation and output growth in the short run. However, in the long run this
monetary policy action will have no effect on the output growth rate, which is determined
only by the rate of productivity growth. As a result, the long run effect of this action is
only to increase the price inflation rate.
c.
In the short run, there is a tradeoff between price inflation and output growth. However,
this tradeoff only exists in the short run and is not stable but can change based on changes
in productivity or the expected inflation rate.
Problem 14
Answers will vary.
198