Download Homework Answers Chapters 23, 3, and 27 Chapter 23 Questions 1

Homework Answers Chapters 23, 3, and 27
Chapter 23
Questions 1, 3, and 6
1. Money refers to any asset that can be used in making purchases (examples are cash
and checking account balances). People hold money despite its lower return
precisely because of its usefulness in transactions; a person who held no money and
wanted to make a purchase would either have to resort to time-consuming barter or
else incur the costs of selling other assets to obtain money.
3. The Fed’s three tools to reduce the money supply are to conduct an open-market sale
of bonds, to reduce lending to banks at the discount window, or to increase legal
reserve requirements.
If the Fed sells $1 million in government bonds to the public, it will receive $1
million in checks drawn against banks in return. By presenting these checks to
banks, the Fed can take $1 million in bank reserves out of the system, which results
in a decline in deposits (by $1 million divided by the reserve/deposit ratio) and
hence a decline in the money supply.
Similarly, if the Fed reduces its lending to banks at the discount window by $1
million, bank reserves again fall by $1 million, and deposits fall by $1 million
divided by the reserve-deposit ratio.
Raising legal reserve requirements does not reduce bank reserves; however, by
raising the reserve/deposit ratio this action reduces the amount of deposits that
banks can hold, given the amount of reserves they have. So again deposits and the
money supply decline.
6. The quantity equation is written as M × V = P × Y. If we assume that velocity and
output are constant during the period of time we are considering, then changes in M,
the money stock, are directly proportional to changes in P, the price level. For
example, a 10% increase in the money stock will lead to a 10% increase in the price
level; i.e. a 10% inflation rate. Larger percentage increases in the money stock will
lead to higher inflation rates while lower percentage increases in the money stock
will lead to lower inflation rates, according to the quantity equation (again,
assuming that velocity and output are constant). This conceptual relationship is
generally supported by empirical evidence over long periods of time, as illustrated
in Figure 23.1.
Exercises 1, 4, 5, 8
1
a.
p. 614-615
Cigarettes were passed hand to hand in exchange for goods and services, hence
they were a medium of exchange. Prices were quoted in terms of cigarettes so
they were a unit of account. Finally, as prisoners held hoards of cigarettes for
future use they functioned as a store of value.
b. Cigarettes are relatively durable (chocolate, for example, can melt) and low
enough in value to be useful in small transactions (with highly valuable boots
there is no way to purchase a small item or “make change”). Other advantages
of cigarettes include their portability and their relative uniformity in value (one
pair of boots might be worth much more than another pair).
c. Yes, because he could trade them for something else that he wanted. In the same
way, we have no direct use for dollar bills (they are not very good wallpaper, for
example), but we accept them because we can trade them for things that we do
want.
4
a. Deposits equal bank reserves/(desired reserve-deposit ratio) = 100/0.25 = 400.
The money supply equals currency held by the public + deposits = 200 + 400 =
600.
b. Let X = currency held by the public = bank reserves. Then the money supply
equals X + X/(reserve/deposit ratio), or
500 = X + X/0.25 = 5X
and
X = 100
So currency and bank reserves both equal 100.
c. As the money supply is 1250 and the public holds 250 in currency, bank deposits
must equal 1000. If bank reserves are 100, the desired reserve/deposit ratio
equals 100/1000 = 0.10.
1250 = 250 + 100/r
1000 = 100/r so r = 0.10
5
a
In a fractional-reserve banking system (where the reserve/deposit ratio is less
than one), banks loan out part of their deposits. The process of banks making
loans and the public redepositing their funds in banks increases deposits and the
money supply, until the point that the banking system has reached its desired
ratio of reserves to deposits. Because each dollar of reserves ultimately
“supports” several dollars of deposits, one extra dollar of bank reserves results in
an increase in the money supply of several dollars (the money multiplier is
greater than one). The money multiplier equals one only in the case of 100%
reserve banking. In that case reserves are equal to deposits, so that an extra dollar
of bank reserves increases deposits and the money supply by only one dollar.
b.
Initially the money supply is $1000 and currency held by the public is $500,
hence deposits are $500. As the desired ratio of reserves to deposits is 0.2, initial
bank reserves must be $100.
An increase of $1 in bank reserves expands deposits from $500 to $101/0.2 =
$505, increasing deposits and the money supply by $5. Similarly, an increase of
$5 in reserves increases deposits and the money supply by $5/0.2 = $25, and an
increase of $10 raises deposits and the money supply by $10/0.2 = $50. As the
money supply rises by 5 times the increase in bank reserves, the money
multiplier in this economy is 5.
8.
c.
As the example in part b illustrates, in general the increase in deposits and the
money supply equals the change in bank reserves times 1/(desired
reserve/deposit ratio). Hence the money multiplier equals 1/(desired
reserve/deposit ratio). In the example of this problem the money multiplier
equals 1/0.2 = 5.
d.
The Fed could raise legal reserve requirements. If this action forced banks to
raise their ratio of reserves to deposits, the result would be a smaller money
multiplier (since the money multiplier is the inverse of the reserve/deposit ratio).
a. The price level for 2004 and 2005, along with the inflation rate between the two
years is given below.
M
V
Y
2004
1000.0
8.0
12000.0
0.667
P = MV/Y
Inflation Rate =
2005
1050.0
8.0
12000.0
0.700
4.94%
b. As the following table illustrates, when the money supply increases the inflation
rate also rises, holding output at its previous level.
M
V
Y
2004
1000.0
8.0
12000.0
0.667
P = MV/Y
Inflation Rate =
2005
1100.0
8.0
12000.0
0.733
10%
c. As the following table illustrates, if the money supply rises at nearly the same rate
that real output rises, the inflation rate remains at a similar level.
M
V
Y
2004
1000.0
8.0
12000.0
0.667
P = MV/Y
Inflation Rate =
2005
1100.0
8.0
12600.0
0.698
4.76%
The German Hyperinflation
Taken from http://www.usagold.com/GermanNightmare.html
Introduction
Especially in an economic crisis or a war, the pressure to inflate becomes
overwhelming. Any alternative may seem politically disastrous. Whether it be the
Roman emperors repeatedly debasing their coinage, the French revolutionary
government printing a flood of assignats, John Law flooding France with debased
money, or the Continental Congress issuing money until it was literally "not worth a
Continental," the story is similar. A government in financial straits finds its easiest
recourse is to issue more and more money until the money loses its value. The entire
process is accompanied by a barrage of explanations, propaganda and new
regulations which hide the true situation from the eyes of most people until they
have lost all their savings. In World War I, Germany--like other governments-borrowed heavily to pay its war costs. This led to inflation, but not much more than
in the U.S. during the same period. After the war there was a period of stability, but
then the inflation resumed. By 1923, the wildest inflation in history was raging. Often
prices doubled in a few hours. A wild stampede developed to buy goods and get rid
of money. By late 1923 it took 200 billion marks to buy a loaf of bread.
Millions of the hard-working, thrifty German people found that their life's savings
would not buy a postage stamp. They were penniless. How could this happen in a
highly civilized nation run at the time by intelligent, democratically chosen leaders?
What happened to business, to wages and employment? How did some people
manage to save their capital while a few speculators made fortunes?
The Years 1914-1921
When the war broke out on July 31, 1914, the Reichsbank (German Central Bank)
suspended redeemability of its notes in gold. After that there was no legal limit as to
how many notes it could print. The
government did not want to upset
people with heavy taxes. Instead it
borrowed huge amounts of money
which were to be paid by the enemy
after Germany had won the war, Much
of the borrowing was discounted and
monetized by the Reichsbank. As
explained later, this amounted to
issuing straight printing press money.
By the end of the war, the amount of
money in circulation had increased
four-fold. In view of this, the extent of
inflation was less than one might have
expected. The consumer price index
had risen 140% by December 1918.
This was equal to the inflation during the same time in England, a little more than in
the United States, but less than in France. Yet the floating debt of the Reichsbank
had increased from 3 billion to 55 billion marks!
Why was inflation kept within bounds? For the same reason that it got off to a slow
start in the Unites States during World War II. Necessities were rationed and luxury
goods were not easily available. Millions of men were at the front and not in the
market for goods. Civilians worked hard and had little leisure for spending. People
saved money against peace time, and in some cases to evade taxes. But the fuel for
inflation was accumulating in the form of vast hoards of money.
The harsh reparation payments imposed on Germany led the mark to depreciate
against foreign currencies. Also, the new democratic socialist leaders had promised
the people all types of bounties--increased wages, reduced hours, an expanded
educational system, and new social benefits. But all this meant a vastly increased
demand on a limited production capacity.
For these reasons inflation resumed after the peace until by February 1920 the price
level was five times as high as it had been at the armistice. Yet during this same
time the amount of currency in circulation had only doubled. Prices were in fact
rising much faster than the rate at which money was being printed. Therefore,
reasoned the officials, the price inflation could hardly be blamed on the government.
Actually, as we shall see, the ebb and flow of confidence can play a big role in the
short-term trend of prices. Confidence in the mark had weakened. At the same time,
and as a consequence, billions of hoarded marks came out of hiding and entered the
marketplace. The accumulated fuel was burning.
By February 1920 this inflationary episode had run its course. For the next fifteen
months the price index held stable. The mark actually gained in value against foreign
currencies, so that prices of imported goods fell by some 50%. Here was a golden
opportunity to establish a stable currency. However, during these fifteen months the
government kept issuing new money. The currency in circulation increased by 50%
and the floating debt of the Reichsbank by 100%, providing fuel for a new outbreak.
In May 1921, price inflation started again and by July 1922 prices had risen 700%.
The Reichsbank continued printing new currency, although more slowly than the rate
at which prices were rising. In fact, all through this period the issue of currency
proceeded at a fairly smooth steady rate, while the price index moved up in great
surges, interspersed by periods of stability.
After July 1922 the phase of hyperinflation began. All confidence in money vanished
and the price index rose faster and faster for fifteen months, outpacing the printing
presses which could not run out money as fast as it was depreciating.
Wholesale Price Index
July 1914
1.0
Jan 1919
2.6
July 1919
3.4
Jan 1920
12.6
Jan 1921
14.4
July 1921
14.3
Jan 1922
36.7
July 1922
100.6
Jan 1923
2,785.0
July 1923
194,000.0
Nov 1923 726,000,000,000.0
The Years 1922-1923 -- Hyperinflation!
From Mid-1922 to November 1923 hyperinflation raged. The table above tells the
story. Seemingly Reichsbank officials believed that the basic trouble was the
depreciation of the mark in terms of foreign currencies. In late 1922 they tried to
support the mark by purchasing it in the foreign exchange markets. However, since
they continued printing new currency at a feverish rate, the attempt failed. They
merely succeeded in buying worthless marks in return for valuable gold and foreign
exchange.
All hope of checking the collapse of the mark vanished in January 1923 when the
French--alleging treaty violations--occupied Germany's key industrial district, the
Ruhr. Germany subsidized the occupied companies and financed an expensive
program of "passive resistance." New billions of marks were printing to finance these
heavy new costs. By late 1923, 300 paper mills were working top speed and 150
printing companies had 2000 presses going day and night turning out currency.
Under the forced draft of inflation, business was now operating at feverish speed and
unemployment had disappeared. However, the real wages of workers dropped badly.
Unions obtained frequent increases, but these could not keep pace. Workers -domestics, farm workers and various white collar groups-- fared especially badly.
They had no unions to fight for pay boosts for them, and often they were reduced to
hunger. Many people showed visible signs of malnutrition. Skilled workers, writers,
artisans and professionals found their wages lagging until they reached the unskilled
worker level, which often meant the bare minimum needed to support life.
Businessmen began to abandon their legitimate occupations to speculate in stocks
and in goods. Thousands of small businessmen tried to eke out a living by
speculating in fabrics, shoes, meat, soap, clothing--in any produce they could obtain.
Each fall in the mark brought a rush to the shops. People bought dozens of hats or
sweaters.
By mid-1923 workers were being paid as often as three times a day. Their wives
would meet them, take the money and rush to the shops to exchange it for goods.
However, by this time, more and more often, shops were empty. Storekeepers could
not obtain goods or could not do business fast enough to protect their cash receipts.
Farmers refused to bring produce into the city in return for worthless paper. Food
riots broke out. Parties of workers marched into the countryside to dig up vegetables
and to loot the farms. Businesses started to close down and unemployment suddenly
soared. The economy was collapsing.
Meanwhile, middle-class people who depended on any sort of fixed income found
themselves destitute. They sold furniture, clothing, jewelry and works of art to buy
food. Little shops became crowded with such merchandise. Hospitals, literary and art
societies, charitable and religious institutions closed down as their funds
disappeared.
Then by a mere effort of will, the government stepped in and stabilized the currency
overnight.
Throughout the "miracle of the Rentenmark" the depreciation halted in its tracks,
business revived, the inflationary spree was ended although, as we shall see, there
was a nasty hangover yet to come.
Millions of middle-class Germans--normally the mainstay of a republic--were ruined
by the inflation. They became receptive to rabid right wing propaganda and formed a
fertile soil for Hitler. Workers who had suffered through the inflation turned, in many
cases, to the Communists. The biggest beneficiaries of this enormous redistribution
of wealth were feudalistic industrial leaders who distrusted the democracy and who
proved willing to deal with Hitler, thinking that they could control him. The
democratic parties and the labor unions lost their capital and were weakened. The
liberal democratic regime was discredited.
Chapter 3
Question 2
A change in demand means a shift of the entire demand curve. If the demand
curve shifts out, buyers are willing to pay higher prices for the same quantities.
Equivalently, they are willing to buy greater quantities at the same prices.
Price
Quantity
A change in the quantity demanded means a movement along the demand curve
in response to a change in price. This follows the Law of Demand: higher prices
lead to lower quantity demanded; lower prices lead to higher quantity
demanded.
Price
Quantity
To distinguish among these two kinds of shifts, it’s important to notice what is
causing the change in quantity demanded.
• If the cause of the change in QD is a change in price, i.e., a change in the
variable on the axis, then you have a movement along the curve.
• If the cause of the change in QD is a change in anything besides prices, that is, a
change in something that is not on the axes, then you have a shift of the curve.
So for example, the money demand curve has the interest rate on the vertical axis.
• A change in quantity of money demanded caused by a change in interest
rates represents a movement along the curve.
• A change in quantity of money demanded caused by a change in income or
prices or transactions technology (which are not on the axes of the money
demand graph) represents a shift of the curve.
Supply and Demand Exercises (the four pages following this one)
Exercises
P
Consider this system of equations:
S
90
S
80
D
Q = 2 P + 5;
100
Q = 200 – 2 P
70
60
Its solution is P* = 48.75; Q* = 102.5,
(Q*, P*)
50
and its graph is
40
30
D
20
You may find this information useful as a comparison.
10
0
0
1.
20
40
60
80
100
120
140
160
180
200
220
Graph this new system of equations.
QS = 2 P + 20;
QD = 200 – 2 P
a. Using algebra, find EXACT answers for equilibrium price and quantity.
b. Compared with the example above, which curve moved to the right? What
happened to P* and Q*?
P
100
2P + 20 = 200 – 2P
4P=180
P = 45
90
80
70
QS=2*45 + 20 = 110
QD=200 – 2*45 = 110
60
50
40
The supply curve shifted
right. Equilibrium price fell
and quantity increased.
30
20
10
0
0
2.
20
40
60
80
100
120 140
160
180 200 220
Q
Graph this new system of equations.
QS = 2 P + 5;
QD = 150 – 2 P
a. Using algebra, find EXACT answers for equilibrium price and quantity.
b. Compared with the example at the top of the page, which curve moved to the
left? What happened to P* and Q*?
P
100
2P + 5 = 150 – 2P
4P=145
P = 36.25
90
80
70
QS=2*36.25 + 5 = 77.5
QD=150 – 2*36.25 = 77.5
60
50
40
The demand curve shifted
left. Equilibrium price fell
and quantity fell.
30
20
10
0
0
20
40
60
80
100
120 140
160
180 200 220
Q
Q
Shifting the Demand and Supply Curves
Answer the following questions.
1.
P
Supply
D’ Demand
Q
2.
S
D
Q
3.
P
D’
fell / rose
fell / rose
Equilibrium price
Equilibrium quantity
fell / rose
fell / rose
This graph illustrates:
a. An increase in willingness to buy
b. A decrease in willingness to buy
c. An increase in ability to sell
d. A decrease in ability to sell
S
D
Equilibrium price
Equilibrium quantity
This graph illustrates:
a. An increase in willingness to buy
b. A decrease in willingness to buy
c. An increase in ability to sell
d. A decrease in ability to sell
P
S’
This graph illustrates:
a. An increase in willingness to buy
b. A decrease in willingness to buy
c. An increase in ability to sell
d. A decrease in ability to sell
Q
Equilibrium price
Equilibrium quantity
fell / rose
fell / rose
Now, answer these questions. Assume only one of the curves moves. (Hint: use the graphs
above)
1. P* rises, Q* falls. This means
a. Demand increased.
b. Supply decreased.
c. Supply increased.
3. P* falls, Q* rises. This means
a. Demand decreased
b. Supply decreased.
c. Supply increased.
2. P* falls, Q* falls. This means
a. Demand increased.
b. Demand decreased
c. Supply increased.
4. P* rises, Q* rises. This means
a. Demand increased.
b. Demand decreased
c. Supply increased.
Shifting two curves.
This is a little bit more complicated, but more realistic.
1.
P
S’
S
D’ D
2.
P
Q
S’ S
D’ D
Q
3.
P
D’
S’
S
D
Q
4.
P
D’
S’
S
D
Q
What happened to supply and
demand in this graph?
Both decreased, but supply
contracted by more.
What happened to equilibrium price
and equilibrium quantity?
P* ↑
Q* ↓
What happened to supply and
demand in this graph?
Both decreased, but demand
shifted in more than supply.
What happened to equilibrium price
and equilibrium quantity?
P* ↓
Q* ↓
In this graph, supply decreased
because sellers have made it harder
(more expensive) to buy a given
quantity (look at the intercept).
What happened to demand?
Demand increased by less than S.
What happened to equilibrium price
and equilibrium quantity?
P* ↑
Q* ↓
Here, supply also decreased.
What happened to demand?
Demand increased by more than
S.
What happened to equilibrium price
and equilibrium quantity?
P* ↑
Q* ↑
Finally, answer these questions. (Hint: look at the graphs on the previous page).
1. P* rises, Q* falls. This means
a. Demand decreased more than supply
b. Demand and supply both decreased by the same proportion.
c. Supply decreased more than demand.
2. P* falls, Q* falls. This means
a. Demand decreased more than supply
b. Demand and supply both decreased by the same proportion.
c. Supply decreased more than demand.
3. P* rises, Q* rises. This means
a. Buyer’s willingness to pay rose by more than seller’s costs.
b. Buyer’s willingness to pay and seller’s costs rose by the same proportion.
c. Seller’s costs rose by more than buyer’s willingness to pay.
4. P* rises, Q* falls. This means
a. Buyer’s willingness to pay rose by more than seller’s costs.
b. Buyer’s willingness to pay and seller’s costs rose by the same proportion.
c. Seller’s costs rose by more than buyer’s willingness to pay.
Chapter 27
Questions 1, 2, 3
Exercises 3, 4
1.
The demand for money is the amount of money that an individual or other wealth-holder
chooses to hold; the economy-wide demand for money is the amount of money held by all
wealth-holders taken together. Because a higher nominal interest rate increases the
opportunity cost of holding money (funds not held in the form of money could be earning
interest), the demand for money falls when the nominal interest rate rises. Increases in the
price level or income tend to increase the dollar volume of transactions, increasing the
benefit of holding money and thus the demand for money.
2.
Equilibrium in the market for money is shown in the figure below. The nominal interest
rate is determined at the intersection of the downward-sloping demand for money curve
and the vertical supply curve for money (as established by the Fed). The Fed can affect the
nominal interest rate by changing the supply of money and thus shifting the supply curve
of money (see below). An increase in the supply of money shifts the vertical supply curve
for money to the right, lowering the nominal interest rate, while a reduction in the money
supply shifts the supply curve to the left and raises the nominal interest rate.
The real interest rate is the nominal interest rate minus the rate of inflation; because the rate
of inflation adjusts relatively slowly, the Fed can control the real interest rate in the short
run. In the long run, the real interest rate is determined by the equality of saving and
investment.
Nominal
Interest
Rate, i
MS MS’
MD
Quantity of
Money, M
3.
In an open-market purchase of bonds, the Fed uses newly created money to buy
government bonds from the public. This action lowers the nominal interest rate, as can be seen in
two ways: a) First, the purchase of bonds raises the demand for and hence the price of bonds.
Since bond prices are inversely related to nominal interest rates, an increase in bond prices is
equivalent to a decline in interest rates. b) Second, an increase in the money supply shifts the
money supply curve to the right (see Review Question 2), lowering the nominal interest rate that
clears the market for money. In economic terms, people are willing to hold more money only if
the opportunity cost of doing so – which is the nominal interest rate – declines.
Exercises 3, 4
3
a.
Lower commission charges reduce the cost of converting non-money assets into money.
People will tend to hold less money, knowing that it is relatively cheap to sell other assets
to obtain money as needed to make transactions. So the economy-wide demand for
money declines.
b. Now people can charge their groceries instead of using money (cash or check). A
checking balance is still necessary in order to pay the credit card bill at the end of the
c.
d.
e.
f.
month. But the overall effect is likely to be to reduce the amount of money people need
to hold on average over the month. The demand for money declines.
If stocks become more risky, people will demand relatively more safe assets, money
among them. The demand for money rises.
Mutual fund investments are not part of the money stock. As in part a, if people can
conveniently and cheaply convert non-money assets into money as needed for
transactions, they can get by holding less money on average. The demand for money
declines.
Higher income raises the volume of transactions. The demand for money increases.
Worried about inflation or even confiscation of their domestic assets, citizens of
developing nations may choose to hoard dollars. The total demand for U.S. money
(including the overseas demand) rises.
4. Under the assumptions P = 3.0 and Y = 10,000 , the demand for money is given by
3.0(0.2x10,000-25,000i) = 6,000-75,000i. We know that equilibrium is found when the quantity
supplied is equal to the quantity demanded: in this case, when quantity of money demanded
equals quantity of money supplied.
If quantity of money demanded is given by
MD = P(0.2Y – 25,000)
Then the equilibrium is found when MD=M, so
M = P(0.2Y – 25,000)
For this particular example, the equilibrium interest rate i sets money demand equal to the
money supply set by the Fed:
6,000 − 75,000i = M
a.
The Fed wants i to equal 4%, or 0.04. To find the money supply needed to obtain this
result, set i = 0.04 in the equation above to get
6,000 − 75,000(0.04) = M
M = 3,000
b.
To obtain an interest rate of 6%, set
i = 0.06 :
6,000 − 75,000(0.06) = M
M = 1,500
Notice that to set the interest rate at a higher level the Fed must reduce the money
supply.
Chapter 27
Questions 5, 6, 7, 8
Exercises 5, 6, 7
Skip part (c) of Problem 6.
5. A higher real interest rate increases the reward for saving; if people save more in response to
a higher real interest rate, than they are necessarily consuming less. A higher real interest rate
also makes it more costly to finance consumer durables and housing, reducing spending on those
items. Firms will be more reluctant to invest in new capital goods when the real interest rate is
high, because the cost of borrowing is high. Thus a higher real interest rate is likely to reduce
both consumption and investment spending, both of which are components of planned aggregate
expenditures.
6. The Fed is likely to respond to a recessionary gap with an expansionary monetary policy
intended to stimulate planned aggregate expenditure. The first step is an open-market purchase
of government bonds, which puts additional money into circulation and lowers the nominal
interest rate. The lower interest rate stimulates planned aggregate expenditure (consumption
and investment spending). An increase in planned aggregate expenditure in turn raises shortrun equilibrium output, as firms produce enough to meet the extra demand.
7. If the Federal Reserve takes a contractionary policy action (such as an open-market sale of
government bonds), we would expect the Federal Reserve to raise nominal and real interest rates
by reducing the money supply. An increase in interest rates will reduce overall autonomous
expenditures in the economy, leading to a reduction in equilibrium output in the economy. The
Federal Reserve would most likely undertake such a policy when the economy was experiencing
an expansionary gap to bring the economy back to full employment.
8. A policy reaction function relates the action taken by a policymaker to the state of the
economy. For example, a policy reaction function for the Fed relates the real interest rate that the
Fed chooses to the level of the output gap or the inflation rate. A graph of the Fed’s policy
reaction function, in a diagram with the real interest rate on the vertical axis and the inflation rate
on the horizontal axis, is an upward-sloping line (see Figure 26.9). The upward slope of the Fed’s
policy reaction function tells us that as inflation rises, the Fed raises the real interest rate in order
to reduce planned aggregate expenditure and “cool off” the economy.
Exercises 5, 6
5.
Planned aggregate expenditure (PAE) is given by
PAE = C + I p + G + NX
PAE = [2600 + .8(Y − 3000) − 10,000r ] + (2000 − 10,000r ) + 1800 + 0
PAE = 4000 − 20,000r + .8Y
Now, if r=.10, then
PAE = 2000 + .8Y
Algebraically, short-run equilibrium occurs where output (Y) = PAE, or where
Y = 2000 + .8Y
Y − .8Y = 2000
.2Y = 2000
Y = 10,000
The equilibrium short-run output level is 10,000. In table form,
Output
Y
9,500
9,600
9,700
9,800
9,900
10,000
10,100
10,200
Planned
Aggregate
Expenditure
PAE
9600
9680
9760
9840
9920
10000
10080
10160
Y-PAE
-100
-80
-60
-40
-20
0
20
40
From the table, it is clear that the short-run equilibrium output level occurs at 10,000.
This is the only output level where Y=PAE. The figure below illustrates this equilibrium
graphically (note that in this figure the axes begin with 9500, not 0).
10,200
Planned Aggregate
Expenditure PAE
10,100
10,000
9,900
9,800
9,700
9,600
9,500
9,500
9,600
9,700
9,800
9,900
10,000 10,100 10,200
Output Y
PAE
6.
a.
Y=PAE
The economy is currently experiencing a recessionary gap, since Y=10,000 < Y* = 12,000
and Y*-Y = 2000.
The problem is finding the real interest rate that is consistent with full employment, with
Y=Y*. What is the real interest rate the Federal Reserve should set to attain this goal?
Note that in equilibrium, Y = PAE. So to eliminate the output gap, Y*=Y=PAE.
Substituting Y* = 12,000 for Y in this equilibrium condition, we have Y* = PAE or 12,000
= PAE. From Problem 5 we determined that PAE is given by:
PAE = 4000 − 20,000 r + .8Y
so we have (with Y = Y* = 12,000)
12,000 = 4000 − 20,000r + .8(12,000)
12,000 = 13,600 − 20,000r
− 1,600
= r = .08
− 20,000
Thus, the Fed needs to lower the real interest rate from 10% to 8% to bring the economy
to equilibrium at full employment.
Alternately, we can use the multiplier and the PAE expression to solve this problem.
First, note that to bring the economy to equilibrium at full employment, output must rise
by 2,000 from its current level of 10,000 (from Problem 5).
With a multiplier of 5, this means that autonomous planned aggregate expenditures
(PAE) must rise by 400.
To increase autonomous expenditures, the Federal Reserve must reduce the real interest
rate, but how much? The PAE expression indicates that for each 1% drop in interest
rates, PAE will increase by 200.
Thus, to raise PAE by 400, the Fed will need to reduce real interest rates by 2%, from 10%
to 8%.
b. In this case output must fall by 1,000 to bring the economy to equilibrium at full
employment (the economy is currently experiencing an expansionary gap). With a
multiplier of 5, this means that PAE must fall by 200.
To reduce autonomous expenditures, the Federal Reserve must raise the real interest rate.
The PAE expression indicates that for each 1% rise in interest rates, PAE will fall by 200.
Thus, to reduce PAE by 200, the Fed will need to raise real interest rates by 1%, from 10%
to 11%.
Verify by checking that with r =.11, PAE = Y = C + IP + G + NX = Y*.
Y =
c.
1
[4000 − 20,000 (0.11)] = 9000 = Y *
1 − .08
When the real interest rate, r, equals .08 (8%) and Y = Y* = 12,000,
C = 2600 + .8(12,000 − 3000) − 10,000(.08)
= 9000
I = 2000 − 10,000(.08)
= 1200
p
S = Y * −C − G = 12,000 − 9,000 − 1,800 = 1200
National saving equals planned investment when the economy is in equilibrium at
potential output, consistent with equilibrium in the market for saving. This tells you that
the natural real interest rate, the one that sets Y=Y* is also the one that sets S=I.
Homework ch 28
ECO 201: Principles of Macroeconomics
Questions
1. What two variables are related by the aggregate demand (AD) curve? Explain
how real balances (i.e., the purchasing power of people’s holdings of money) are
related to movements along the curve. List and discuss two other factors that
lead the curve to have a negative slope.
2. State how each of the following affects the AD curve and explain
a. An increase in government purchases
b. A cut in taxes
c. A decline in planned investment by firms
d. A monetary expansion, i.e., a decision by the Fed to increase the money
supply.
Chapter 28
Questions 3, 4, 5, 6, 9 and 10
1.
The AD curve shows the relationship between the inflation rate and shortrun equilibrium output in the economy. As the inflation rate rises, given
the rate of growth of the money supply, real balances (M/P) fall. This tends
to raise the interest rate, which reduces autonomous expenditure and in
turn, short-run equilibrium output. Therefore, along the AD curve, as the
inflation rate rises, the output level falls, leading to a downward-sloping
curve (with inflation on the vertical axis and output on the horizontal axis).
There are four other factors listed in this chapter that could lead to this
downward slope: (1) inflationary effects on the behavior of the Fed, (2)
inflationary effects on the redistribution of income and wealth, which in
turn affect consumption, (3) inflationary effects on investment spending,
and (4) inflationary effects on net exports (for a given exchange rate).
2
a. For given levels of inflation and the real interest rate, an increase in
government purchases raises aggregate demand and short-run equilibrium
output. Thus an increase in government purchases shifts the AD curve to
the right.
b. Because it leads consumers to spend more, a cut in taxes stimulates
aggregate demand at each level of inflation, shifting the AD curve to the
right.
c. A decline in autonomous investment spending by firms reduces
aggregate demand at each level of inflation, shifting the AD curve to the
left.
d. For each level of inflation, a lower real interest rate stimulates
consumption and investment spending, raising aggregate demand and
output. Thus, an expansionary monetary policy shifts the AD curve to the
right.
3. Prices of commodities are set continuously in auction markets and therefore
can adjust quickly to changes in supply or demand. However, most prices
are not determined in auction markets but are set only periodically. In setting
prices or wages for a longer period, individuals’ expectations of future
inflation are important; the higher is expected inflation, the higher the future
wage or price must be set in order to maintain the desired level of purchasing
power. But expectations of inflation in turn depend in part on recent
experience with inflation. So we have a vicious (or virtuous circle), as high
inflation leads to high expectations of inflation, which in turn leads to high
actual inflation (and the reverse if inflation is low). Together with long-term
contracts that “lock in” prices and wages for a period of time, expectations of
inflation contribute to inflation inertia, or “stickiness”.
4. Expansionary gaps tend to raise inflation, and recessionary gaps tend to
reduce it. If an expansionary gap exists, for example, firms are producing
above normal capacity. Eventually they will respond by attempting to raise
their relative price (that is, raising their own price faster than the rate of
inflation). As all firms try to do this, inflation will tend to speed up.
Likewise, a recessionary gap implies that firms are producing below normal
capacity. To stimulate demand for their products, firms will try to reduce
their relative prices, leading to an overall slowdown in inflation.
Graphically, the link between output gaps and inflation is captured by
movements of the short-run aggregate supply (SRAS) line. If an
expansionary gap exists at the current intersection of the SRAS line and the
AD curve (which determines short-run equilibrium output), inflation rises
and the SRAS line moves upward. If a recessionary gap exists in short-run
equilibrium, inflation falls and the SRAS line moves downward. Inflation
and the SRAS line adjust until the economy reaches long-run equilibrium at
the intersection of the AD curve and the long-run aggregate supply (LRAS)
line. See Figures 28.6 and 28.7.
5. Short-run equilibrium occurs at the intersection of the AD curve and the SRAS
line. When short-run equilibrium output is greater than potential output
(that is, equilibrium is to the right of the LRAS line), an expansionary gap
exists. The expansionary gap leads inflation to rise over time; the SRAS line,
which shows the current rate of inflation, therefore also rises over time. The
SRAS line continues to rise until it intersects the LRAS line and AD curve at
point B. At point B, called the long-run equilibrium point, output equals
potential output and the inflation rate is stable. (See below, and see figure
28.6 in the text for the example with a recessionary gap).
Inflation
Long-run
aggregate
supply LRAS
B
π*
SRAS’
A
π
SRAS
A
D
Output Y*
Y
6.
The answer is ambiguous, as whether stabilization policy is useful depends
largely on the speed at which self-correction takes place. The more slowly the
economy adjusts, the more likely it is that stabilization policy will be useful.
Thus if the economy has many long-term contracts or other barriers to rapid
adjustment, or if the economy is initially far from full employment, then
stabilization policy is more likely to be useful.
9.
Assume for concreteness that the economy starts at full employment, but
with an inflation rate higher than the Fed would like. To reduce inflation, the
Fed tightens monetary policy, shifting the AD curve leftward. In the short
run inflation is unchanged (the SRAS line has not shifted), output is lower (a
recession), and the real interest rate is higher (tighter money means that the
Fed raises the real interest rate at any given level of inflation). The
recessionary gap implies that over time inflation will fall; graphically, the
SRAS line shifts downward until long-run equilibrium is restored at the
intersection of the AD curve, the LRAS line, and the SRAS line. In the long
run inflation is lower and output returns to full employment. The real
interest rate declines as inflation falls; indeed, in the long run it returns to its
original full-employment value, consistent with equilibrium in the market for
saving and investment.
10. Moderate and high rates of inflation can impose significant costs to the
economy, in particular with respect to long run growth. Low and stable
inflation helps reduce uncertainty for businesses and helps to encourage
greater investment, which in turn leads to higher productivity and faster
growth of potential output (higher standards of living). High and moderate
inflation has been shown empirically to retard economic growth, thus
policymakers attempt to keep inflation low, even though at times following
this policy may lead to short-run costs in terms of higher unemployment and
lower output.
Exercises 3, 4, 5, 6, 7, and 8
3. a.
In the short run, the equilibrium inflation rate and output level are given by the
intersection of the SRAS and AD curves. Algebraically, the short run equilibrium
level of output is found by substituting the current inflation rate into the AD
equation. Thus, in the short run,
Y = 13,000 − 20,000(.04)
= 12,200
and inflation = 4%, the current level of inflation.
b. In the long run, the equilibrium inflation rate and output level are given by the
intersection of the LRAS and AD curves. Algebraically, the long-run equilibrium
inflation rate is found by substituting the level of potential output into the AD
equation. Thus, in the long run,
12,000 = 13,000 − 20,000π
− 1,000 = −20,000π
− 1,000
= π = .05 = 5%
− 20,000
and the long-run level of output equals 12,000, the potential output level.
4.
a. In the short run, the equilibrium inflation rate is simply the current inflation rate,
10%, and output equals Y = 1,000 - 1,000(.10) = 900. Thus, the economy is
experiencing a recessionary gap, since Y < Y*. In the long run, the equilibrium
output level is the level of potential output, 950. The long run equilibrium
inflation rate is found by substituting Y* for Y in the AD curve equation and
solving the inflation rate:
950 = 1000 − 1000π
− 50 = −1000π
− 50
= .05 = 5%
− 1000
b. The initial values for the inflation rate and the output level are listed below in the
row labeled “Quarter 0.” The resulting inflation rate and output level for each
quarter (1 through 5) are listed. Note that in this example, “this quarter’s
inflation rate” is determined from last quarter’s inflation rate and the difference
between actual and potential output from the previous quarter (i.e. inflation occurs
with a lag). Note that over time the inflation rate appears to be converging on
the long run equilibrium inflation rate, 5%. Note also that the recessionary gap
gets smaller each quarter as the economy moves toward potential GDP.
Quarter
0
1
2
3
4
5
Inflation Rate
0.1000
0.0800
0.0680
0.0608
0.0565
0.0539
Y
900.000
920.000
932.000
939.200
943.520
946.112
Y*
950
950
950
950
950
950
Y*-Y
50.000
30.000
18.000
10.800
6.480
3.888
5. In each part below, point A in the diagram corresponds to the initial
situation, and point B shows the short-run effects of the change. From point
B, the SRAS line adjusts up or down as needed to achieve long-run
equilibrium (adjustment not shown). Long-run equilibrium in each figure is
labeled point C.
a. From A, an increase in autonomous consumption shifts the AD curve
right, increasing output in the short run to point B. In the long run,
inflation rises to a higher level and output returns to potential, in point C.
Inflation
Long-run
aggregate
supply LRAS
C
π*
SRAS’
B
π
SRAS
A
A
D
Output Y*
Y
b. A reduction in taxes increases consumer spending and hence aggregate
demand. The graph and the results in the short run and the long run are
the same as in part a.
c. An easing of monetary policy lowers the real interest rate set by the Fed at
each level of inflation. The aggregate demand curve shifts right. The
graph and results are the same as in part a.
Inflation
d. A sharp drop in oil prices is a favorable inflation shock. The SRAS line
shifts downward, reducing inflation and raising output, going to point B.
If potential output is unchanged, an expansionary gap exists and inflation
will begin to rise. In the long run the economy returns to output and
Long-run aggregate
inflation as originally, point A=C.
supply LRAS
A, C
π
SRAS’
B
π
SRAS
AD
Output Y*
Y
e. Increased government purchases raise aggregate demand and shift the
AD curve right. The graph and results are the same as in part a.
Refer to the figure below: Initially the economy is at equilibrium where a
recessionary gap exists. If no action is taken, inflation will slow, the SRAS
curve will fall to SRAS’, and output will return to potential output at the
long-run equilibrium on the LRAS. If the self-adjustment process plays out in
18 months or less, then by the time the tax cut is put in place the economy
will already be back to full employment. The tax cut, which shifts the AD
curve right, will thus cause the economy to “overshoot” full employment,
leading to an expansionary gap.
π
LRAS
A
SRAS
Inflation
B
SRAS’
AD
Y*
Y
7.
AD’
Output
The economy is initially at equilibrium (at point A) when it is hit by both
an inflation shock (shifting SRAS up to SRAS’) and a shock to potential
output (reducing Y* and shifting LRAS leftward to LRAS’). The AD
curve is unchanged. The short-run equilibrium is at the intersection of
AD and SRAS’ at point B. Inflation has risen and output has declined.
LRAS’ LRAS
π’
Inflation
6.
B
C
π
SRAS’
SRAS’’
A
SRAS
AD
Y*
Output
I’ve drawn it so that the new equilibrium is to the left of LRAS’, so that
there is a recessionary gap even relative to the new, lower level of
potential output. (This need not be the case; if the inflation shock is
Y*’
smaller, the short-run equilibrium could be to the right of LRAS’, though
still to the left of LRAS.) The short-run effect of the combination shock is a
fall in output plus higher inflation. In the long run, inflation and the
SRAS curve will adjust as needed to bring the economy to long-run
equilibrium at point C. Note that at the new equilibrium output is
permanently lower than it was at the initial equilibrium, as potential
output has dropped. With no change in aggregate demand, inflation is
also permanently higher.
Output in the long run will equal the new, lower level of potential output,
whether the Fed responds or not (monetary policy cannot affect potential
output and thus cannot affect output in the long run). If the Fed tries to
fight the recession, it will end up achieving nothing but higher inflation.
But, unless the Fed does something, long-run Inflation will be higher than
originally.
If the Fed responds to the oil price increase by tightening policy, the AD
curve will shift left, along with the leftward shift of LRAS and the upward
shift of SRAS. Inflation will not increase as much in the long run, but the
short-run decline in output will be even worse. In the short run, the
economy moves to point D. If the Fed does respond, the accentuated
short-run recession will lead to lower inflation, now at point E.
LRAS’ LRAS
Inflation
π’
D
B
SRAS’
C
A
π
SRAS
E
AD
Y*’
Y*
Output
a. If the Fed eases its monetary policy, this will reduce the real interest rate
at any level of inflation. Thus, for any inflation, there will be an increase in
autonomous expenditure (due to the Federal Reserve’s reducing interest
rates), shifting the AD curve to the right. Shifting the AD curve to the right to
close the recessionary gap reduces the unemployment rate and increases the
output level. However, the cost is that the inflation rate will remain at its
current level, rather than falling in response to the recessionary gap.
LRAS
Inflation
8.
B
π
SRAS
A
AD
Y
Y*
Output
b. If the Fed takes no action, the economy will continue with a recessionary
gap longer, meaning that unemployment rates will be higher and output
lower, for a longer period than if the Fed had reduced interest rates (as in part
a) – this is the cost of taking no action. However, over time, the inflation rate
will fall and the Fed will then respond (along its monetary policy reaction
function) by reducing interest rates, leading to a move down and to the right
along the AD curve. The economy will eventually return to a long run
equilibrium at potential GDP, with a lower inflation rate than in part a (the
benefit). See figure 28.6.