Chapter19 mechanical vibrations

Chapter 19 Homework Solutions
1. Suppose the money supply M has been growing at 10% per year and nominal GDP PY
has been growing at 20% per year. The data are as follows:
2004 2005 2006
M 100 110 121
PY 1000 1200 1440
Calculate the velocity in each year. At what rate is the velocity growing?
Use the quantity theory of money identity: M*V = P*Y  V = PY/M
2004: V = 1000/100 = 10
2005: V = 1200/110 = 10.91
2006: V = 1440/121 = 11.9
Growth rate in V is approximately 9.1% per year.
2. Calculate what happens to nominal GDP if velocity remains constant at 5 and the
money supply increases from $200 billion to $300 billion.
PY = M*V
Before: PY = $200 billion * 5 = $1 trillion
After: PY = $300 billion * 5 = $1.5 trillion
3. Calculate what happens to nominal GDP if the money supply grows by 20%, but
velocity declines by 30%?
M*V = P*Y  %ΔPY = %ΔM + %ΔV = 20% - 30% = -10%
A 20% increase in the money supply plus a 30% decrease in velocity will decrease
nominal GDP by 10%.
4. If credit cards were made illegal by congressional legislation, what would happen to
velocity?
Without credit cards, there would be increased demand for money since people would
have to hold more money to carry out the same amount of transactions.
V = PY/M  When M increases, V must fall.
Banning credit cards would reduce the velocity of money.

5. If velocity and aggregate output are reasonably constant (as the classical economists
believed), what happens to the price level when the money supply increases from $1
trillion to $4 trillion?
Again using the quantity equation, we have M*V=P*Y. Assuming constancy in both V
and in Y, then any increase in M will be met by a proportionate increase in price. In this
example, the money supply increases by 300%. If both V and Y are constants, then P
must also increase by 300% to restore full employment output.
9. In Keynes’ analysis of the speculative demand for money, what will happen to money
demand if people suddenly decide that the normal level of the interest rate has declined?
If people believe that the “normal” level of the interest rate has fallen, then they believe
that current interest rates are above normal. Therefore, they expect that interest rates
will fall in the future, prompting them to buy more bonds today. The demand for
money falls as people shift their wealth into bonds.
11. If interest rates on bonds go to zero, what does the Baumol-Tobin analysis suggest
Grant Smith’s average holdings of money should be?
Since bonds pay no interest, but do incur transactions costs (e.g. brokerage fees), Grant
should not hold any bonds. Thus, Grant will hold his entire income as money, which
according to the analysis presented suggests that his average cash balance will be equal
to half his income.
12. If brokerage fees go to zero, what does the Baumol-Tobin analysis suggest Grant
Smith’s average holdings of money should be?
Since bonds are now costless to hold and pay a higher return than money, Grant should
hold just enough money to make his purchases and no more. In other words, Grant
should always hold bonds and only convert bonds into money to make his purchases.
Grant never holds any cash balances (bonds are instantly converted to consumption), so
average cash balances equal zero.
13. “In Tobin’s analysis of the speculative demand for money, people will hold both
money and bonds, even if bonds are expected to earn a positive return.” Is this statement
true, false, or uncertain?
Tobin argued that people care about both the return and the risk of the assets they
hold. Since bonds are generally considered to be riskier than money, people will still
choose to hold money for diversification purposes.
14. Both Keynes’ and Freidman’s theories of the demand for money suggest that as the
relative expected return on money falls, demand for it will fall. Why does Friedman

think that money demand is unaffected by changes in interest rates? Why did Keynes
think that money demand is affected by changes in interest rates?
Keynes proposed that people held money to make transactions, in case a sudden need
for liquidity arose, and for speculation. In each of these cases, the demand for money is
inversely related to interest rates. As interest rates rise, the opportunity cost of holding
money increases as well.
Friedman does not disagree with Keynes’ analysis behind the motivation to hold money,
but argues that what we need to consider are excess returns. The opportunity cost of
holding money only increases if the return on bonds (or equities or goods) goes up
relative to the return on money. Friedman argued that excess returns were constant
since all interest rates tend to move in the same direction. Thus, an increase in the
return on bonds would be met by an increase in the return on money and there would
be no additional incentive to hold bonds over money.

Chapter19 mechanical vibrations

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