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Money and Inflation He realised well that the abundance of money makes everything dear, but he did not analyse how that takes place. The great difficulty of this analysis consists in discovering by what path and in what proportion the increase of money raises the price of things. RICHARD CANTILLON (died 1734), Essai sur la nature du commerce en général, II, 6. Money and Inflation Price = amount of money required to buy a good. Inflation rate = ΔP/P = the percentage increase in the average level of prices (e.g. π = 5 % p.a.). Deflation = decrease in the average level of prices. (e.g. π = - 1 % p.a.) Disinflation = decrease in the inflation rate (e.g. π1 = 5 % → π2 = 3 %) Price level stability: π = 0 % p.a. Price of beer in the Czech Republic CPI in the Czech Republic 150 140 130 120 110 100 90 80 70 60 50 I.13 I.12 I.11 I.10 I.09 I.08 I.07 I.06 I.05 I.04 I.03 I.02 I.01 I.00 I.99 I.98 I.97 I.96 I.95 I.94 I.93 Price level has more than doubled since 1993 12,0% 10,0% Inflation rate, Czech Republic 8,0% 6,0% 4,0% 2,0% 0,0% 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 Inflation rate in the Czech Republic 8,00% 7,00% 6,00% 5,00% 4,00% 3,00% 2,00% 1,00% I.15 I.14 I.13 I.12 I.11 I.10 I.09 I.08 I.07 I.06 I.05 I.04 I.03 I.02 -1,00% I.01 0,00% I.13 VII.12 I.12 VII.11 I.11 VII.10 I.10 VII.09 I.09 VII.08 I.08 VII.07 I.07 VII.06 I.06 VII.05 I.05 VII.04 110 I.04 120 VII.03 140 I.03 150 VII.02 I.02 VII.01 I.01 VII.00 I.00 Food and rents in the CR Food and nonalcoholic beverages 130 Housing, water, electricity, gas and other fuels 100 90 80 70 Average inflation rate 2000 - 2013 U.S. inflation rate (% per year) 25 20 15 10 5 0 -5 -10 -15 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 The Quantity Theory of Money o Stock How does the quantity of money affect the economy? QTM - the quantity of money in the economy is related to the number of dollars exchanged in transactions. Suppose that the supply of money in the economy is $10. In the first half of the year, 5 bottles of beer are sold each for $2. The owners of money then buy 1 lb. of ham for $10. The total value of transactions over the year: $2×5 + $10×1 = $20 M Velocity = $10, of socirculation each unit of M was transacted twice/year. $10 × 2 = $2×5 + $10×1 M × V = ∑piqi Flow The Quantity Theory of Money Fisher (1911): The Purchasing Power of Money: Let us begin with the money side. If the number of dollars in a country is 5,000,000, and their velocity of circulation is twenty times per year, then the total amount of money changing hands (for goods) per year is 5,000,000 times twenty, or $100,000,000. This is the money side of the equation of exchange… 200,000,000 loaves of bread at $ .10 a loaf, 10,000,000 tons of coal at 5.00 a ton, and 30,000,000 yards of cloth at 1.00 a yard. The value of these transactions is evidently $100,000,000, i.e. $20,000,000 worth of bread plus $50,000,000 worth of coal plus $30,000,000 worth of cloth. The equation of exchange therefore (remember that the money side consisted of $5,000,000 exchanged 20 times) is as follows:— $5,000,000 × 20 times a year = 200,000,000 loaves × $ .10 a loaf +10,000,000 tons × 5.00 a ton +30,000,000 yards × 1.00 a yard. The Quantity Theory of Money If we aggregate over the entire economy (and over all transactions), we may write: M × VT = P × T IDENTITY T … the total number of transactions during some period of time P … price of a typical transaction PT … number of dollars exchanged in a year M … quantity of money VT … transactions velocity of money The rate at which money circulates in the economy The Quantity Theory of Money Number of transactions T is difficult to measure so it is replaced by the total output in the economy Y. Assume that Y is proportional to T: T = aY M × VT = P × T M × VT = P × aY M × VT/a = P × Y M × VY = P × Y VY …Income velocity of money Number of times a dollar bill enters someone’s income in a given period of time. The Quantity Theory of Money V can be viewed as a ratio of nominal GDP (PY), to the quantity of money (M): V = PY/M Assume that V is constant and exogenousV V M×V=P×Y If V is constant, a change in the quantity of money (M) must cause a proportionate change in nominal GDP (PY). U.S. Nominal GDP, M2, and Velocity 1960–2011 3,000 1960=100 2,500 Velocity is fairly stable over the long run. Nominal GDP 2,000 M2 1,500 1,000 500 Velocity 0 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 The Quantity Theory of Money Recall that in the classical model: Y*=F(Kfixed,Lfixed) M×V=P×Y Classical Dichotomy Fixed M P The quantity theory implies that the price level is proportional to the money supply. MONEY IS NEUTRAL -Does not affect Y -Does not affect relative prices ACTIVE LEARNING 1 Exercise One good: corn. The economy has enough labor, capital, and land to produce Y = 800 bushels of corn. V is constant. In 2008, MS = $2000, P = $5/bushel. Compute nominal GDP and velocity in 2008. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. ACTIVE LEARNING 1 Answers Given: Y = 800, V is constant, MS = $2000 and P = $5 in 2005. Compute nominal GDP and velocity in 2008. Nominal GDP = P x Y = $5 x 800 = $4000 $4000 PxY = 2 = V = $2000 M © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. The Quantity Theory of Money M×V=P×Y See the BB: %ΔM + %ΔV = %ΔP + %ΔY %ΔV = 0 by assumption %ΔY depends on the growth of K,L and A. All constant by assumption => %ΔY = 0 Hence, the growth in the money supply (%ΔM) determines the rate of inflation (%ΔP = π). ACTIVE LEARNING 2 Exercise One good: corn. The economy has enough labor, capital, and land to produce Y = 800 bushels of corn. V is constant. In 2008, MS = $2000, P = $5/bushel. For 2009, the Fed increases MS by 5%, to $2100. a. Compute the 2009 values of nominal GDP and P. Compute the inflation rate for 2008–2009. b. Suppose tech. progress causes Y to increase to 824 in 2009. Compute 2008–2009 inflation rate. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. ACTIVE LEARNING 2 Answers Given: Y = 800, V is constant, MS = $2000 and P = $5 in 2008. For 2009, the Fed increases MS by 5%, to $2100. a. Compute the 2009 values of nominal GDP and P. Compute the inflation rate for 2008–2009. Nominal GDP = P x Y = M x V (Quantity Eq’n) = $2100 x 2 = $4200 P = P x Y = $4200 = $5.25 800 Y $5.25 – 5.00 Inflation rate = = 5% (same as MS!) 5.00 © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. ACTIVE LEARNING 2 Answers Given: Y = 800, V is constant, MS = $2000 and P = $5 in 2005. For 2009, the Fed increases MS by 5%, to $2100. b. Suppose tech. progress causes Y to increase 3% in 2009, to 824. Compute 2008–2009 inflation rate. First, use Quantity Eq’n to compute P in 2009: $4200 MxV P = = $5.10 = 824 Y $5.10 – 5.00 Inflation rate = = 2% 5.00 © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. U.S. inflation and money growth, 1960-2006 15% 12% Over the long run, the inflation and money growth rates move together, M2 growth as the quantity theory rate predicts. 9% 6% 3% 0% 1960 1965 inflation rate 1970 1975 1980 1985 1990 1995 2000 2005 slide 23 I.13 I.12 I.11 I.10 I.09 I.08 I.07 I.06 I.05 I.04 M2 I.03 160 I.02 CPI I.01 180 I.00 I.99 I.98 I.97 I.96 I.95 I.94 I.93 Money and prices in the CR 240 220 200 140 120 100 80 60 40 I.13 I.12 I.11 I.10 I.09 I.08 I.07 I.06 I.05 I.04 I.03 20,0% I.02 I.01 I.00 I.99 I.98 I.97 I.96 I.95 I.94 Money and prices in the CR 25,0% Inflation Money growth 15,0% 10,0% 5,0% 0,0% I.13 I.12 I.11 I.10 I.09 I.08 I.07 I.06 I.05 I.04 Inflation I.03 I.02 I.01 I.00 I.99 I.98 I.97 I.96 I.95 I.94 Money and prices (MA-12) 25,0% 20,0% 15,0% Money growth 10,0% 5,0% 0,0% International data on inflation and HW (p.88) Seigniorage: money growthThe Revenue From Printing Money Turkey 100 Ecuador Inflation rate Indonesia Belarus (percent, logarithmic scale) 10 1 Argentina U.S. Singapore Switzerland 0.1 Milton Friedman: “Inflation 10 1 is always and everywhere a monetary phenomenon.’’ 100 Money Supply Growth (percent, logarithmic scale) The Consumer Price Index (CPI) measures the typical consumer’s cost of living the basis of cost of living adjustments (COLAs) in many contracts How the CPI Is Calculated 1. 2. 3. Fix the “basket.” The Bureau of Labor Statistics (BLS) surveys consumers to determine what’s in the typical consumer’s “shopping basket.” Find the prices. The BLS collects data on the prices of all the goods in the basket. Compute the basket’s cost. Use the prices to compute the total cost of the basket. How the CPI Is Calculated 4. Choose a base year and compute the index. The CPI in any year equals 100 x cost of basket in current year cost of basket in base year 5. Compute the inflation rate. The percentage change in the CPI from the preceding period. Inflation = rate CPI this year – CPI last year CPI last year x 100% 2010 Price of Apples = $0.50 2010 Quantity of Apples = 4 As if quantity (basket) was 2010 Price of Oranges = $1.00fixed 2010 Quantity of Oranges = 3 2015 Price of Apples = $1.00 (i.e. increase by 100%) 2015 Price of Oranges = $3.00 (i.e. increase by 200%) 1 4 3 3 13 CPI 2015 100 100 0.5 4 1 3 5 2.6 100 260 2010 Price of Apples = $0.50 2010 Quantity of Apples = 4 2010 Price of Oranges = $1.00 2010 Quantity of Oranges = 3 … weight_apples in the base year = 2/6 = 40% … weight_oranges in the base year = 3/6 = 60% EXAMPLE basket: {4 pizzas, 10 lattes} year price of pizza price of latte 2013 $10 $2.00 $10 x 4 + $2 x 10 2014 $11 $2.50 $11 x 4 + $2.5 x 10 = $69 2015 $12 $3.00 $12 x 4 + $3 x 10 cost of basket = $60 = $78 Compute CPI in each year Inflation rate: 2013: 100 x ($60/$60) = 100 115 – 100 x 100% 15% = 100 130 – 115 x 100% 13% = 115 2014: 100 x ($69/$60) = 115 2015: 100 x ($78/$60) = 130 What’s in the CPI’s Basket in the U.S.? 4% 3% Housing 6% Transportation 6% Food & Beverages 43% 6% Medical care Recreation Education and communication Apparel 15% 17% Other 7% 6% FOOD AND NON-ALCOHOLIC BEVERAGES 17% CPI CR 1% ALCOHOLIC BEVERAGES AND TOBACCO CLOTHING AND FOOTWEAR 9% HOUSING, WATER, ELECTRICITY, GAS AND OTHER FUELS 9% 3% FURNISHINGS, HOUSEHOLD EQUIPMENT AND ROUTINE MAINTENANCE OF THE HOUSE HEALTH TRANSPORT 3% COMMUNICATION 10% RECREATION AND CULTURE EDUCATION 2% RESTAURANTS AND HOTELS 6% 27% MISCELLANEOUS GOODS AND SERVICES CPI CPI 2015 papple, 2015 qapple, 2010 porange, 2015 qorange, 2010 papple, 2010 qapple, 2010 porange, 2010 qorange, 2010 papple, 2015 papple, 2010 papple, 2010 qapple, 2010 porange, 2015 porange, 2010 porange, 2010 qorange, 2010 papple, 2010 qapple, 2010 porange, 2010 qorange, 2010 papple, 2015 papple, 2010 weight apple porange, 2015 porange, 2010 weight orange Problems with the CPI: Substitution Bias Over time, some prices rise faster than others. Consumers substitute toward goods that become relatively cheaper, mitigating the effects of price increases. The CPI misses this substitution because it uses a fixed basket of goods. Thus, the CPI overstates increases in the cost of living. Prices of food and rents in the CR 150 Food and nonalcoholic beverages 140 130 Housing, water, electricity, gas and other fuels 120 110 100 90 80 I.13 VII.12 I.12 VII.11 I.11 VII.10 I.10 VII.09 I.09 VII.08 I.08 VII.07 I.07 VII.06 I.06 VII.05 I.05 VII.04 I.04 VII.03 I.03 VII.02 I.02 VII.01 I.01 VII.00 I.00 70 Problems with the CPI: Introduction of New Goods The introduction of new goods increases variety, allows consumers to find products that more closely meet their needs. In effect, dollars become more valuable. The CPI misses this effect because it uses a fixed basket of goods. Thus, the CPI overstates increases in the cost of living. Problems with the CPI: Unmeasured Quality Change Improvements in the quality of goods in the basket increase the value of each dollar. The BLS tries to account for quality changes but probably misses some, as quality is hard to measure. Thus, the CPI overstates increases in the cost of living. Problems with the CPI Each of these problems causes the CPI to overstate cost of living increases. The BLS has made technical adjustments, but the CPI probably still overstates inflation by about 0.5 percent per year. This is important because Social Security payments and many contracts have COLAs tied to the CPI. The GDP Deflator The GDP deflator is a measure of the overall level of prices. nominal GDP Definition: GDP deflator = 100 x real GDP One way to measure the economy’s inflation rate is to compute the percentage increase in the GDP deflator from one year to the next. EXAMPLE: Pizza year 2013 2014 2015 P $10 $11 $12 Latte Q 400 500 600 P $2.00 $2.50 $3.00 Compute nominal GDP in each year: 2013: $10 x 400 + $2 x 1000 Increase: = $6,000 2014: $11 x 500 + $2.50 x 1100 = $8,250 2015: $12 x 600 + = $10,800 $3 x 1200 Q 1000 1100 1200 37.5% 30.9% EXAMPLE: Pizza Latte year P Q P Q 2013 $10 400 $2.00 1000 2014 $11 500 $2.50 1100 2015 $12 600 $3.00 1200 Compute real GDP in each year, using 2013 as the base year: Increase: 2013: $10 x 400 + $2 x 1000 = $6,000 2014: $10 x 500 + $2 x 1100 = $7,200 2015: $10 x 600 + $2 x 1200 = $8,400 20.0% 16.7% EXAMPLE: year 2013 Nominal GDP $6000 Real GDP $6000 2014 $8250 $7200 2015 $10,800 $8400 In each year, nominal GDP is measured using the (then) current prices. real GDP is measured using constant prices from the base year (2013 in this example). EXAMPLE: year 2013 Nominal GDP $6000 2014 $8250 2015 $10,800 37.5% 30.9% Real GDP $6000 $7200 $8400 20.0% 16.7% The change in nominal GDP reflects both prices and quantities. The change in real GDP is the amount that GDP would change if prices were constant (i.e., if zero inflation). Hence, real GDP is corrected for inflation. EXAMPLE: year 2013 2014 2015 Nominal GDP $6000 $8250 $10,800 Real GDP $6000 $7200 $8400 GDP Deflator 100.0 114.6 128.6 14.6% 12.2% Compute the GDP deflator in each year: 2013: 100 x (6000/6000) = 100.0 2014: 100 x (8250/7200) = 114.6 2015: 100 x (10,800/8400) = 128.6 Two Measures of Inflation, 1950–2010 15 Percent per year 10 5 0 -5 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 CPI GDP deflator Contrasting the CPI and GDP Deflator Imported consumer goods: included in CPI excluded from GDP deflator Capital goods: excluded from CPI included in GDP deflator (if produced domestically) The basket: CPI uses fixed basket GDP deflator uses basket of currently produced goods & services This matters if different prices are changing by different amounts. Contrasting the CPI and GDP Deflator n n CPIt p i 1 n p i 1 i ,t qi ,base i ,base i 1 pi ,t p i ,baseqi ,base p i ,base n p qi ,base i 1 i ,base n GDPnom DEFLt GD Pr eal p i 1 i ,t qi ,t i ,base In textbook: Index … × 100 qi ,base n p i 1 n Laspeyres index qi ,t p i 1 n i 1 i ,t qi ,t pi ,t qi ,t pi ,t p i ,base Paasche index Contrasting the CPI and GDP Deflator Weights in the current year may not be known (every month). ACTIVE LEARNING 3 CPI vs. GDP deflator In each scenario, determine the effects on the CPI and the GDP deflator. A. Starbucks raises the price of Frappuccinos. B. Caterpillar raises the price of the industrial tractors it manufactures at its Illinois factory. C. Armani raises the price of the Italian jeans it sells in the U.S. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. ACTIVE LEARNING 3 Answers A. Starbucks raises the price of Frappuccinos. The CPI and GDP deflator both rise. B. Caterpillar raises the price of the industrial tractors it manufactures at its Illinois factory. The GDP deflator rises, the CPI does not. C. Armani raises the price of the Italian jeans it sells in the U.S. The CPI rises, the GDP deflator does not. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Correcting Variables for Inflation Wnom 2000 = 13,219 CZK Wnom 2013 = 25,078 CZK CPI2000 = 100 (e.g. price of beer = 9 CZK) CPI2013 = 137 (e.g. price of beer = 12 CZK) In 2000, one can buy 13,219 / 9 = 1,497 bottles In 2013, one can buy 25,078 / 12 = 2,090 bottles 2,090 / 1,497 = 1.4 One can buy 40% more bottles Real wage in theory Wreal = Wnominal / P P … price level measured by e.g. CPI 10,00% growth in Wnom growth in Wreal 8,77% 8,00% 7,97% 7,80% 7,22% 6,10% 6,00% 5,84% 5,70% 4,00% 6,55% 6,31% 5,03% 4,00% 3,90% 4,30% 3,40% 3,33% 3,00% 2,30% 2,00% 1,40% 2,23% 2,48% 2,50% 0,70% 0,60% 0,04% 0,00% 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 -0,80% -1,40% -2,00% Correcting Variables for Inflation: Very important! Real vs. Nominal Interest Rates The nominal interest rate: the interest rate not corrected for inflation The real interest rate: corrected for inflation Real interest rate = (nominal interest rate) – (inflation rate) Inflation and interest rates o Suppose you deposit $100 in a bank account that pays i=8 % interest annually. Assume that the price of beer this year is P1=$2. Next year, you withdraw your savings and the accumulated interest: $100×(1+i)= $108 Assume that the price of beer next year is P2=$2.04 Are you 8 percent richer than you were when you made the deposit a year earlier? In the first year, you could buy: $100/$2 = 50 bottles In the second year, you can buy: $108/$2.04 = 53 bottles. => You can buy 53/50-1 = 0.06 = 6% more What is the inflation rate in this economy? Inflation and interest rates 100 (1 i ) P2 1 0.06 100 P1 r … real interest rate (1 i ) 1 0.06 P2 1 P1 1 0.06 (1 i ) P2 P1 1 r (1 i ) 1 P2 1 P1 Inflation and interest rates Nominal interest rate, i … the interest rate that the bank pays: is not adjusted for inflation Real interest rate, r … the interest rate that reflects the true increase in the purchasing power (6% in our example): is adjusted for inflation. Inflation and interest rates 1 r (1 i ) 1 (1 r) (1 ) (1 i ) 1 r r 1 i i r Fisher equation If we neglect π×r = 0.02 × 0.06 = 0.0012 r i Correcting Variables for Inflation: Real vs. Nominal Interest Rates Example 1: Deposit $1,000 for one year in 2015. Nominal interest rate is 20%. P2015 = 2; P2016 = 2.1 What is the real interest rate? Correcting Variables for Inflation: Real vs. Nominal Interest Rates Can the real interest rate be zero or even negative? Can the nominal interest rate be zero or even negative? Can the real interest rate exceed the nominal interest rate? Real and Nominal Interest Rates in the U.S., 1950–2010 Fisher equation and the Fisher effect i = r+π r is determined by S = I (Classical model) π is determined by the money growth (QTM) The one-for-one relation between the inflation rate and the nominal interest rate is called the Fisher effect. Inflation and nominal interest rates in the U.S., 1955-2006 percent per year 15 nominal interest rate 10 5 0 inflation rate -5 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 Inflation and nominal interest rates across countries Nominal 100 Interest Rate Romania (percent, logarithmic scale) Zimbabwe Brazil 10 Bulgaria Israel U.S. Germany Switzerland 1 0.1 1 10 100 1000 Inflation Rate (percent, logarithmic scale) Two Real Interest Rates: Ex Ante and Ex Post o o o When a borrower and lender agree on a nominal interest rate, they do not know what the inflation rate over the term of the loan will be. Suppose that they expect πe= 3 %. If the agreed r is 4 %, then: i = r + πe = 7 % If the realised inflation differs, e.g. π = 5 %, then the ex post real interest rate will be: Who lost and who rex post = 7 % - 5 % = 2 % gained when π > πe ? Hence, we must distinguish between two concepts of the real interest rate: The real interest rate the borrower and lender expect when the loan is made: … ex ante real interest rate = i – πe = 4 % and the real interest rate actually realized: … ex post real interest rate = i – π = 2 % Two Real Interest Rates: Ex Ante and Ex Post Because the nominal interest rate agreed by lender and borrower can adjust only to expected inflation (not to the realized inflation), the Fisher effect is more precisely written as: i = r + πe The ex ante real interest rate r is determined by equilibrium in the market for goods and services (or I=S). The nominal interest rate i moves one-for-one with changes in expected inflation πe. The Costs of Inflation Shoeleather costs: the resources wasted when inflation encourages people to reduce their money holdings Includes the time and transactions costs of more frequent bank withdrawals Menu costs: the costs of changing prices Printing new menus, mailing new catalogs, etc. The Costs of Inflation Misallocation of resources from relativeprice variability: Firms don’t all raise prices at the same time, so relative prices can vary… which distorts the allocation of resources. Confusion & inconvenience: Inflation changes the yardstick we use to measure transactions. Complicates long-range planning and the comparison of dollar amounts over time. The Costs of Inflation Tax distortions: Inflation makes nominal income grow faster than real income. Taxes are based on nominal income, and some are not adjusted for inflation. So, inflation causes people to pay more taxes even when their real incomes don’t increase. ACTIVE LEARNING 3 Tax distortions You deposit $1000 in the bank for one year. CASE 1: inflation = 0%, nom. interest rate = 10% CASE 2: inflation = 10%, nom. interest rate = 20% a. In which case does the real value of your deposit grow the most? Assume the tax rate is 25%. b. In which case do you pay the most taxes? c. Compute the after-tax nominal interest rate, then subtract inflation to get the after-tax real interest rate for both cases. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. ACTIVE LEARNING 3 Answers Deposit = $1000. CASE 1: inflation = 0%, nom. interest rate = 10% CASE 2: inflation = 10%, nom. interest rate = 20% a. In which case does the real value of your deposit grow the most? In both cases, the real interest rate is 10%, so the real value of the deposit grows 10% (before taxes). © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. ACTIVE LEARNING 3 Answers Deposit = $1000. Tax rate = 25%. CASE 1: inflation = 0%, nom. interest rate = 10% CASE 2: inflation = 10%, nom. interest rate = 20% b. In which case do you pay the most taxes? CASE 1: interest income = $100, so you pay $25 in taxes. CASE 2: interest income = $200, so you pay $50 in taxes. © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. ACTIVE LEARNING 3 Answers Deposit = $1000. Tax rate = 25%. CASE 1: inflation = 0%, nom. interest rate = 10% CASE 2: inflation = 10%, nom. interest rate = 20% c. Compute the after-tax nominal interest rate, then subtract inflation to get the after-tax real interest rate for both cases. CASE 1: nominal = 0.75 x 10% = 7.5% real = 7.5% – 0% = 7.5% CASE 2: nominal = 0.75 x 20% = 15% real = 15% – 10% = 5% © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. ACTIVE LEARNING 3 Summary and lessons Deposit = $1000. Tax rate = 25%. CASE 1: inflation = 0%, nom. interest rate = 10% CASE 2: inflation = 10%, nom. interest rate = 20% Inflation… raises nominal interest rates (Fisher effect) but not real interest rates increases savers’ tax burdens lowers the after-tax real interest rate © 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. A Special Cost of Unexpected Inflation Arbitrary redistributions of wealth Higher-than-expected inflation transfers purchasing power from creditors to debtors: Debtors get to repay their debt with dollars that aren’t worth as much. Lower-than-expected inflation transfers purchasing power from debtors to creditors. High inflation is more variable and less predictable than low inflation. So, these arbitrary redistributions are frequent when inflation is high. The Costs of Inflation All these costs are quite high for economies experiencing hyperinflation. For economies with low inflation (< 10% per year), these costs are probably much smaller, though their exact size is open to debate. Exercise: Suppose V is constant, M is growing 5% per year, Y is growing 2% per year, and r = 4. a. Solve for i. b. If the central bank increases the money growth rate by 2 percentage points per year, find i. c. Suppose the growth rate of Y falls to 1% per year. What will happen to ? What must the central bank do if it wishes to keep constant?