Macro Aplia

2. Money supply, money demand, and adjustment to monetary equilibrium

The following table shows a money demand schedule, which is the quantity of money demanded at various price levels (P).

Fill in the Value of Money column in the following table.

Price Level (P)	Value of Money (1/P)	Quantity of Money Demanded
		(Billions of dollars)
1.00	1.00	2.0
1.33	0.75	2.5
2.00	0.50	4.0
4.00	0.25	8.0

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Now consider the relationship between the price level and the quantity of money that people demand. The lower the price level, theless   money the typical transaction requires, and theless   money people will wish to hold in the form of currency or demand deposits.

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Explanation:

The price level (P) is a measure of the average level of prices in the economy. The value of money (1/P) is the value of money measured in terms of goods and services. For example, when the price level is 1.33, the value of money is   . The following table shows that the value of money declines as the price level rises. That is, as the prices of goods and services rise, the number of goods and services that can be purchased with one dollar declines.

Price Level (P)	Value of Money (1/P)	Quantity of Money Demanded
		(Billions of dollars)
1.00	1.00	2.0
1.33	0.75	2.5
2.00	0.50	4.0
4.00	0.25	8.0

The table also shows the positive relationship between the price level and the quantity of money demanded. As the price level rises (and the value of money falls), the typical transaction requires more money, and people will need to hold a larger quantity of money in the form of currency and demand deposits in order to conduct day-to-day transactions. Conversely, as the price level falls (and the value of money rises), the typical transaction requires less money, and people will need to hold a smaller quantity of money to conduct day-to-day transactions.

Assume that the Fed initially fixes the quantity of money supplied at $2.5 billion.

Use the orange line (square symbol) to plot the initial money supply (  ) set by the Fed. Then, referring to the previous table, use the blue connected points (circle symbol) to graph the money demand curve.

Your AnswerMS1Money DemandMS20123456781.251.000.750.500.250VALUE OF MONEYQUANTITY OF MONEY (Billions of dollars)4, 1.25

Correct Answer

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According to your graph, the equilibrium value of money is0.75   , therefore the equilibrium price level is1.33   .

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Explanation:

When the Fed fixes the quantity of money, the money supply curve is a vertical line at the quantity it selects—in this case, $2.5 billion. The money demand curve slopes downward, passing through each combination from the table of the value of money and the quantity of money demanded. For example, when the value of money is 1.00, the quantity of money demanded is $2 billion. You should have plotted the first point on the money demand curve at the coordinate (2, 1.00), the second at (2.5, 0.75), the third at (4, 0.50), and the fourth at (8, 0.25).

At the intersection of the money supply and money demand curves, the equilibrium quantity of money is $2.5 billion, the equilibrium value of money (1/P) is 0.75, and the equilibrium price level is 1.33.

Now, suppose that the Fed increases the money supply from the initial level of $2.5 billion to $4 billion.

In order to increase the money supply, the Fed can use open-market operations tobuy bonds from   the public.

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Use the purple line (diamond symbol) to plot the new money supply (  ).

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Explanation:

In order to increase the money supply, the Fed uses open-market operations to buy bonds from the public. By buying bonds, the Fed takes bonds from the public and replaces them with money, thereby increasing the amount of money in circulation. The new money supply curve is a vertical line at $4 billion.

At the initial equilibrium value of money and price level, the quantity of money supplied is nowgreater   than the quantity of money demanded. This expansion in the money supply willincrease   people's demand for goods and services. In the long run, since the economy's ability to produce goods and services has not changed, the prices of goods and services willrise   and the value of money willfall   .

Points:

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Explanation:

At the initial value of money (0.75) and the initial price level (1.33), the quantity of money supplied is now greater than the quantity of money demanded. The increase in the supply of money causes the demand for goods and services to rise but does not impact the economy's long-run productive capacity. In the long run, the increase in demand leads to higher prices for products, with no change in the number of products produced. As a result, one dollar will buy fewer goods and services than before the monetary expansion—in other words, the value of money falls.

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3. The classical dichotomy and the neutrality of money The classical dichotomy is the separation of real and nominal variables. The following questions test your understanding of this distinction. Valerie spends all of her money on comic books and donuts. In 2009, she earned $14.00 per hour, the price of a comic book was $7.00, and the price of a donut was $2.00. Which of the following give the nominal value of a variable? Check all that apply. The price of a donut is $2.00 in 2009. The price of a donut is 0.29 comic books in 2009. Valerie's wage is 2 comic books per hour in 2009. Points: 1 / 1 Which of the following give the real value of a variable? Check all that apply. The price of a comic book is 3.5 donuts in 2009. The price of a comic book is $7.00 in 2009. Valerie's wage is $14.00 per hour in 2009. Points: 0 / 1 Close Explanation Explanation: Nominal variables are measured in monetary units. Any price or wage denominated in money, such as Valerie's $14.00 per hour wage, is an example of a nominal variable. Real variables are measured in physical units. Any price or wage stated in terms of goods is a real variable. For example, in 2009, the relative price of a donut is 0.29 comic books. Suppose that the Fed sharply increases the money supply between 2009 and 2014. In 2014, Valerie's wage has risen to $28.00 per hour. The price of a comic book is $14.00 and the price of a donut is $4.00. In 2014, the relative price of a comic book is3.5 donuts   . Points: 1 / 1 Between 2009 and 2014, the nominal value of Valerie's wageincreases   , and the real value of her wageremains the same   . Points: 1 / 1 Monetary neutrality is the proposition that a change in the money supplyaffects   nominal variables anddoes not affect   real variables. Points: 1 / 1 Close Explanation Explanation: Valerie's wage and the prices of comic books and donuts double as the Fed increases the money supply between 2009 and 2014. Since all prices have doubled, the relative price of a comic book remains   . The money-denominated, or nominal, value of Valerie's wage increases over this period. Valerie's real wage, however, does not change. Her relative wage is still    or    after the increase in the money supply. Valerie's experience is consistent with monetary neutrality, which is the proposition that a change in the money supply affects nominal variables but does not affect real variables.

4. Velocity and the quantity equation

Consider a simple economy that produces only cell phones. The following table contains information on the economy's money supply, velocity of money, price level, and output. For example, in 2016, the money supply was $400, the price of a cell phone was $5.00, and the economy produced 800 cell phones.

Fill in the missing values in the following table, selecting the answers closest to the values you calculate.

Year	Quantity of Money	Velocity of Money	Price Level	Quantity of Output	Nominal GDP
	(Dollars)		(Dollars)	(Cell phones)	(Dollars)
2016	400	10	5.00	800	4,000.00
2017	404	10	5.05	800	4,040.00

Points:

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Explanation:

Recall that the value of nominal GDP equals the price of output (  ) times the quantity of output (  ). In this case, nominal GDP in 2016 equals   .

The velocity of money measures the number of times the typical unit of currency is used to pay for newly produced goods or services. To calculate the velocity of money, divide the value of output (nominal GDP) by the quantity of money. Let    be the velocity of money,    be the price level,    be the quantity of output (real GDP), and    be the quantity of money. Recall that nominal output is the value of current output measured with current prices, or   .

Therefore, you should have entered 10 for the velocity of money in 2016.

Notice that the value of nominal GDP is $4,000 in 2016. In order for people to buy $4,000 worth of cell phones with a quantity of money equal to only $400, each unit of currency must have turned over, on average, 10 times per year.

Rearrange the quantity equation to solve for the price level (  ) in 2017:

Therefore, you should have entered $5.05 for the price level in 2017.

In 2017, nominal GDP equals   .

The money supply grew at a rate of1%   from 2016 to 2017. Since cell phone output did not change from 2016 to 2017 and the velocity of moneyremained the same   , the change in the money supply was reflectedentirely   in changes in the price level. The inflation rate from 2016 to 2017 was1%   .

Points:

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Explanation:

To compute the percentage change in the quantity of money (  ), use the following equation:

Recall the quantity equation:

If the quantity of money (  ) increases and the velocity of money (  ) and the quantity of output (  ) remain the same, the increase in the quantity of money will be reflected entirely in a rising price level.

To compute the percentage change in the price level from 2016 to 2017, use the following equation:

This illustrates the quantity theory of money. Specifically, if the velocity of money and real output are constant, changes in the money supply cause proportionate changes in the price level.

5. Using money creation to pay for government spending

Consider Tralfamadore, a hypothetical country that produces only burgers. In 2015, a burger is priced at $4.00.

Complete the first row of the table with the quantity of burgers that can be bought with $700.

Note: In this problem, assume it is not possible to buy a fraction of a burger, and always round down to the nearest whole burger.

Year	Price of a Burger	Burgers Bought with $700
	(Dollars)	(Quantity)
2015	4.00	175
2016	4.80	145

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Suppose the government of Tralfamadore cannot raise sufficient tax revenue to pay its debts. In order to meet its debt obligations, the government prints money. As a result, the money supply rises by 20% by 2016.

Assuming monetary neutrality holds, complete the second row of the table with the new price of a burger and the new quantity of burgers that can be bought with $700 in 2016.

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Explanation:

With $700, 175 burgers can be purchased at the initial price of $4.00 per burger. Monetary neutrality is the proposition that changes in the money supply do not affect real variables, such as the number of burgers produced. If monetary neutrality holds, a 20% increase in the money supply will be fully reflected in the dollar price of a burger. Thus, the price of a burger will rise by 20% as well, from $4.00 to $4.80. The price increase causes the purchasing power of money to decline, so that $700 can now buy only    (when rounded down to the nearest whole burger).

It is important to note that the increase in the money supply impacts only the purchasing power of money (including money in non-inflation-adjusted accounts and assets) held while the government is printing money. Since wages tend to rise with the overall price level, nominal wages will rise to reflect changes in the quantity of money, and the purchasing power of earnings will not be affected in the long run.

The impact of the government's decision to raise revenue by printing money on the value of money is known as theinflation tax   .

Points:

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Explanation:

When the government pays its debts by printing money, the value of money will decline, a phenomenon known as an inflation tax. Specifically, $700 will purchase fewer burgers—approximately 145 compared with 175 before the government's decision to print money. By printing money in order to pay its debts, the government effectively taxes anyone who holds money. Revenue raised through an inflation tax is known as seigniorage.

6. The Fisher effect and the cost of unexpected inflation

Suppose the nominal interest rate on car loans is 11% per year, and both actual and expected inflation are equal to 4%.

Complete the first row of the table by filling in the expected real interest rate and the actual real interest rate before any change in the money supply.

Time Period	Nominal Interest Rate	Expected Inflation	Actual Inflation	Expected Real Interest Rate	Actual Real Interest Rate
	(Percent)	(Percent)	(Percent)	(Percent)	(Percent)
Before increase in MS	11	4	4	4	7
Immediately after increase in MS	11	4	6	4	5

Points:

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Now suppose the Fed unexpectedly increases the growth rate of the money supply, causing the inflation rate to rise unexpectedly from 4% to 6% per year.

Complete the second row of the table by filling in the expected and actual real interest rates on car loans immediately after the increase in the money supply (MS).

The unanticipated change in inflation arbitrarily benefitsborrowers   .

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Explanation:

The real interest rate adjusts the nominal interest rate (11%) to the rate of inflation and equals the nominal rate minus the inflation rate. The real interest rate indicates the change in purchasing power experienced by a lenders. In this case, borrowers and lenders anticipate an inflation rate of 4%, so the expected real interest rate is calculated as follows:

If inflation rises unexpectedly, in the short run borrowers and lenders will not set the nominal interest rate to reflect the increase in the inflation rate. The actual real interest rate will, therefore, turn out to be different from the expected real interest rate. In this case, inflation rises unexpectedly from 4% to 6%.

The unexpected increase in inflation causes the actual real interest rate to fall below the expected real interest rate in the short run. While borrowers benefit from paying a lower real interest rate, lenders, who now receive a smaller-than-expected increase in purchasing power in return for the funds they lend to borrowers.

Now consider the long-run impact of the change in money growth and inflation. According to the Fisher effect, as expectations adjust to the new, higher inflation rate, the nominal interest rate willfall   to

10%

per year.

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Explanation:

The Fisher effect describes the long-run behavior of nominal interest rates and inflation based on the principle of monetary neutrality—the notion that monetary changes do not affect real variables in the long run. In the long run, borrowers and lenders will agree to a new nominal interest rate as their expectations of inflation adjust.

In the long run, the nominal interest rate will adjust to the sum of the old nominal interest rate (11%) and the change in the inflation rate (  ):

In other words, in the long run, the 2-percentage-point increase in inflation will be reflected in a 2-percentage-point increase in the nominal interest rate. The long-run real interest rate is thus reestablished. In accordance with the principle of monetary neutrality, the long-run real interest rate is not affected by the increase in the money supply and the inflation that accompanies it.

8. Inflation-induced tax distortions

Sean receives a portion of his income from his holdings of interest-bearing U.S. government bonds. The bonds offer a real interest rate of 2.5% per year. The nominal interest rate on the bonds adjusts automatically to account for the inflation rate.

The government taxes nominal interest income at a rate of 10%. The following table shows two scenarios: a low-inflation scenario and a high-inflation scenario.

Given the real interest rate of 2.5% per year, find the nominal interest rate on Sean's bonds, the after-tax nominal interest rate, and the after-tax real interest rate under each inflation scenario.

Inflation Rate	Real Interest Rate	Nominal Interest Rate	After-Tax Nominal Interest Rate	After-Tax Real Interest Rate
(Percent)	(Percent)	(Percent)	(Percent)	(Percent)
2.0	2.5	4.5	4.05	2.05
7.5	2.5	10	9	1.5

Points:

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Close Explanation

Explanation:

To maintain the level of the real interest rate, the nominal interest rate must adjust according to the Fisher equation:

At the lower inflation rate of 2% per year, the nominal interest rate is 4.5%, the 2.5% real rate plus the 2% inflation rate. At the higher inflation rate of 7.5% per year, the nominal interest rate is 10%, the 2.5% real rate plus the 7.5% inflation rate.

The government taxes 10% of the nominal interest paid on the bonds. When the inflation rate is 2% per year and the nominal interest rate is 4.5% per year, the tax reduces the nominal interest payment from 4.5% to an after-tax nominal interest payment of   . At an inflation rate of 7.5% per year and a nominal interest rate of 10% per year, the tax reduces the nominal interest payment from 10% to an after-tax nominal interest payment of   .

Rearranging the nominal interest rate equation, you can see that the real interest rate is the difference between the nominal interest rate and the inflation rate. The after-tax real interest rate is, therefore, the after-tax nominal interest rate minus the inflation rate. At the lower inflation rate, the after-tax real interest rate is calculated as follows:

At the higher inflation rate, the after-tax real interest rate is   , which is lower than the after-tax real return at the lower inflation rate.

Compared with higher inflation rates, a lower inflation rate willincrease   the after-tax real interest rate when the government taxes nominal interest income. This tends toencourage   saving, therebyincreasing   the quantity of investment in the economy andincreasing   the economy's long-run growth rate.

Points:

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Explanation:

When the government taxes nominal interest income, inflation distorts the real returns to saving. Compared with a higher rate of inflation, a lower rate of inflation leads to a higher after-tax real interest rate, which tends to encourage saving. Because the economy's level of investment depends on the pool of savings available to finance investment projects (such as acquiring new tools or machinery or building new plants or office buildings), the higher volume of saving will increase the quantity of investment, thereby increasing the economy's rate of physical capital accumulation and increasing the long-run economic growth rate. Thus, to the extent that the central bank can reduce inflation in an economy in which the government taxes nominal interest income, inflation will encourage saving, investment, and growth.