Velocity Equations
Money Supply Divided By Velocity Equals Real Gdp Equals
Physics Velocity Equations

Money supply × velocity of money = price level × real GDP. The left side of this equation is the product of two variables, the money supply and the velocity of money. The right side is likewise the product of two variables. Growth rate of the money supply + growth rate of the velocity of money = inflation rate + growth rate of output.
Money supply divided by velocity equals real GDP. Money supply multiplied by real output equals velocity. Money supply divided by velocity equals nominal GDP. Velocity multiplied by money supply equals real output times the price level. The Fed's purchase of U.S. Government securities constitutes.
Since (P x Y) is equal to the nominal GDP, then M x V = nominal GDP. Velocity (V) and Real GDP (Y) are effectively constant in the short run, therefore any changes in money supply (M), will cause a proportional change in the price level (P). Re-writing the equation, we get: P = (M x V) / Y.

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Economics 401 – Answers to Problems from Chapter 7

Review Questions
1. Money is the economist’s term for assets that can be used in making payments, such as cash and checking accounts. In everyday speech, people often use the term “money” to refer to their income or wealth, but in economics money means only those assets that are widely used and accepted as payment.
2. The three functions of money are (1) the medium of exchange function, which contributes to a better-functioning economy by allowing people to make trades at a lower cost in time and effort than in a barter economy; (2) the unit of account function, which provides a single, uniform measure of value; and (3) the store of value function, by which money is a way of holding wealth that has high liquidity and little risk.
3. The size of the nation’s money supply is determined by its central bank; in the United States, the central bank is the Federal Reserve System. If all money is in the form of currency, the money supply can be expanded if the central bank uses newly minted currency to buy financial assets from the public or directly from the government itself. To reduce the money supply, the central bank can sell financial assets to the public or the government, taking currency out of circulation.
4. The four characteristics of assets that are most important to wealth holders are (1) expected return, (2) risk, (3) liquidity; and (4) time to maturity. Money has a low expected return compared to other assets, low risk since it always maintains its nominal value, is the most liquid of all assets, and has the lowest (zero) time to maturity.
5. The expectations theory of the term structure of interest rates is the idea that investors compare bonds with different times to maturity and choose the ones that yield the highest return. In equilibrium, the theory implies that the expected rate of return on an N-year bond should equal the average of the expected rates of return on one-year bonds during the current year and the N–1 succeeding years.
The expectations theory is not sufficient because on average, long-term interest rates exceed short-term interest rates, in violation of the theory’s implications. To form a more accurate theory, a risk premium must be added to the analysis.
6. The macroeconomic variables that have the greatest impact on money demand are the price level, real income, and the nominal interest rate on other assets. The higher the price level, the higher the demand for money, since more units of money are needed to carry out transactions. The higher the level of real income, the higher the need for liquidity, and so the higher is money demand. When the nominal interest rate on other assets is high, money demand is low, because the opportunity cost of holding money (that is, the interest you forgo on other assets because you are holding money instead) is high.
7. Velocity is a measure of how often money “turns over” in a period. It is equal to nominal GDP divided by the nominal money supply. The quantity theory of money assumes that velocity is constant, which implies that real money demand is proportional to real income and is unaffected by the real interest rate.
8. Equilibrium in the asset market is described by the condition that real money supply equals real money demand because when supply equals demand for money, demand must also equal supply for nonmonetary assets. The aggregation assumption that is needed for this is that we can lump all wealth into two categories: (1) money and (2) nonmonetary assets.
9. In equilibrium, the price level is proportional to the nominal money supply; in particular it equals the nominal money supply divided by real money demand. Similarly, the inflation rate is equal to the growth rate of the nominal money supply minus the growth rate of real money demand.
10. Factors that could increase the public’s expected rate of inflation include a rise in money growth or a decline in income growth. With no effect on the real interest rate, the increase in the expected inflation rate would increase the nominal interest rate.
Numerical Problems
1. For a two-year bond, according to the expectations theory, the interest rate would be the average of the two one-year bonds, which is (6% + 4%)/2 = 5%. Adding the risk premium of 0.5% gives an interest rate on the two-year bond of 5.5%.
For the three-year bond, according to the expectations theory, the interest rate would be the average of the three one-year bonds, which is (6% + 4% + 3%)/3 = 4.33%. Adding the risk premium of 1.0% gives an interest rate on the three-year bond of 5.33%.
The yield curve would show the interest rate on a one-year bond of 6%, the interest rate on a two-year bond of 5.55%, and the interest rate on a three-year bond of 5.33%, so it would be downward sloping, which is called “inverted” in the market.

2. (a) Real money demand is
Md/P = 500 + 0.2Y – 1000i
= 500 + (0.2 ´ 1000) – (1000 ´ 0.10)
= 600.
Nominal money demand is
Md = (Md/P) ´ P = 600 ´ 100 = 60,000.
Velocity is
V = PY/Md = 100 ´ 1000/60,000 = 1 2/3.
(b) Real money demand is unchanged, because neither Y nor i has changed.
Nominal money demand is
Md = (Md/P) ´ P = 600 ´ 200 = 120,000.
Velocity is unchanged, because neither Y nor Md/P has changed, and we can write the equation for velocity as
V = PY/Md = Y/(Md/P).
(c) It is useful to use the last expression for velocity,
V = Y/(Md/P) = Y/(500 + 0.2Y – 1000i).
(1) Effect of increase in real income:
When i = 0.10,
V = Y/[500 + 0.2Y – (1000 ´ 0.10)]
= Y/(400 + 0.2Y)
= 1/[(400/Y) + 0.2].
When Y increases, 400/Y decreases, so V increases. For example, if Y = 2000, then V = 2.5, which is an increase over V = 1 2/3 that we got when Y = 1000.
(2) Effect of increase in the nominal interest rate:
When Y = 1000, V = 1000/[500 + (0.2 ´ 1000) – 1000i]
= 1000/(700 – 1000i)
= 1/(0.7 – i).
When i increases, 0.7 – i decreases, so V increases. For example, if i = 0.20, then V = 2, which is an increase over V = 1 2/3 that we got when i = 0.10.
(3) Effect of increase in the price level:
There is no effect on velocity, since we can write velocity as a function just of Y and i. Nominal money demand changes proportionally with the price level, so that real money demand, and hence velocity, is unchanged.
3. (a) Md = $100,000 – $50,000 – [$5000 ´ (i – im) ´ 100]. (Multiplying by 100 is necessary since i and im are in decimals, not percent.) Simplifying this expression, we get
Md = $50,000 – $500,000(i – im).
(b) Bd = $50,000 + $500,000(i – im).
Adding these together we get Md + Bd = $100,000, which is Mr. Midas’s initial wealth.
(c) This can be solved either by setting money supply equal to money demand, or by setting bond supply equal to bond demand.
Md = Ms

$50,000 – $500,000(i – im) = $20,000
$30,0

Money Supply Divided By Velocity Equals Real Gdp