Solution Key: Homework 4,
Economics 101
Chapters 6
1. s/(s+f) = 0.02/(0.02+0.10) = 16.67 percent
2.
a. 39 million
b. (36/39)100 = 92.3 percent
c. 3x12+36 = 72 million(3/6)100 = 50 percent
Chapters 4
1. a) %M + %V = %P + %Y
so 9% + 0 = %P + 6% so %P = 3%,
r = i -  = 7% - 3% = 4%
b) now 8% + 0 = %P + 6% so %P = 2%
Since the real interest rate is determined by the real side of the economy, r is still
4%. (But the nominal interest rate will become i = r +  = 4% + 2% = 6%.)
2. The cut in money growth lowered the government’s revenue from seigniorage and
created a government deficit. People may have expected the government would need to
use seigniorage in the future to pay off the debt the government was accumulating. So
they expected the government to raise money growth in the future again, and this would
lead to an expectation of inflation and a rise in the CURRENT nominal interest rate.
Because money demand is a function of the nominal interest rate, these expectations
would lower current money demand, and require a rise in the price level today to equate
money demand with money supply. Hence, the government’s attempt to lower money
growth will not lower inflation.
3. The money demand function is given as
a. To find the average inflation rate the money demand function can be expressed in
terms of growth rates:
% growth Md – % growth P = % growth Y
The parameter k is a constant, so it can be ignored. The percentage change in
nominal money demand Md is the same as the growth in the money supply
because nominal money demand has to equal nominal money supply. If nominal
money demand grows 12 percent and real income (Y) grows 4 percent then the
growth of the price level is 8 percent.
b. From the answer to part (a), it follows that an increase in real income growth will
result in a lower average inflation rate. For example, if real income grows at 6
percent and money supply growth remains at 12 percent, then inflation falls to 6
percent. In this case, a larger money supply is required to support a higher level of
GDP, resulting in lower inflation.
c. If velocity growth is positive, then all else the same inflation will be higher. From
the quantity equation we know that:
% growth M + % growth V = % growth P + % growth Y
Suppose that the money supply grows by 12 percent and real income grows by 4
percent. When velocity growth is zero, inflation is 8 percent. Suppose now that
velocity grows 2 percent: this will cause prices to grow by 10 percent. Inflation
increases because the same quantity of money is being used more often to chase
the same amount of goods. In this case, the money supply should grow more
slowly to compensate for the positive growth in velocity.
Chapters 9
1)
a) The fall in velocity lowers demand in the economy (a leftward shift in the AD
curve in the short run). This would lower output and generate a recession. Since
price is fixed, inflation is not a problem in the short run. (Remember the AD
curve here is determined by the equation M V = P Y. A fall in velocity would
lower output for a given price level and money supply.) Since the shock to
velocity is only temporary, demand will return to normal on its own in the long
run. (AD shifts right in the long run back to its initial position. So there is no
effect on output and no inflation in the long run.)
b) To counteract the short-run effects of the shock, the Federal Reserve can increase
the money supply in the short run. This would shift the AD to the right, returning
it to its initial position. But it should reverse this policy in the long run. Otherwise
when the velocity returns to normal in the long run, the extra money supply would
generate inflation. The AD curve would be to the right of its initial position before
the velocity shock.(One might argue that the gains from policy intervention in this
case is not worth its side but that is a different issue) .