Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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.