Concept 5. Inflation What Is Inflation Rate?

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What is inflation rate? The inflation rate is the percentage increase in pricesover a period of time ExamplesConcept 5. Inflation What is inflation? Inflation means prices are rising and the purchasingpower of the dollar is declining. The inflation rate for a group of products or services Medical care 2012-2013: 2.5% 1990 – 2013: 154.9%Food and beverages 2012-2013: 1.4 % 1990 - 2013: 76.9 %The inflation rate for all products and services 2012 - 2013: 1.5% (annual inflation rate)1990 - 2013: 75.6 %12 How to compute the numbers in the previous table? Notations: What is the relationship between inflation rate and the value ofyour dollars? The higher the inflation rate, the less the value of your dollars over The table below shows how much 1 dollar will be worth after certain time.years given certain inflation rates. For example, the number 50 cents means: At an annual inflation Formula:rate of 15%, one dollar will only worth 50 cents after 5 years.YearsAnnual inflationrate at 2%Annual inflationrate at 6%Annual inflationrate at 15%591 cents75 cents50 cents1082 cents56 cents25 cents4045 cents10 cents0.3 centYn the purchasing power of one dollar after n yearsia annual inflation raten number of years1 nYn ()1 ia3Examples At 2% annual inflationrate, how much will 1worth in 5 years? At 6% annual inflationrate, how much will 1worth in 10 years?4One More Example1 5Y5 () 0.911 2% If the inflation rate is 4% per year, what is thepurchasing power of 1000 dollars after 20 years?Y20 1,000 * (Y10 (1 10) 0.561 6%51) 20 1,000 * 0.456 4561 4%6

What is escalating inflation? Prices rise at an increasing rate. Example: 3%, 4%, 5%, 6% for four consecutive years What is disinflation? Prices rise at a decreasing rate. Example: 6%, 5%, 4%, 3% for four consecutive years. What is deflation? Prices decline. Example: -2% inflation rate in 2009.7How do we know what theinflation rate is?8Consumer Price Index (CPI) Visit the CPI website at Inflation rates are computed using Consumer PriceIndex (CPI) http://www.bls.gov/cpi/home.htm CPI is available for different commodity groups and different In the U.S., the Bureau of Labor Statistics (BLS) collectsregions/areasmonthly price data on over 100,000 items at 85 differentlocations across the country from 19,000 retailestablishments. The prices collected are used to form one price index,called the Consumer Price Index (CPI). The CPI is weighted by commodities’ relativeimportance in the average consumer's budget. Weights are obtained from the Consumer ExpenditureSurvey, also conducted quarterly by the BLS. 1982-1984 CPI 100, set as the base. Selected Annual Average CPI numbers for urban CPI9.929.682.4130.7172.2218.1229.5232.9236.4 Here is a link to more detailed CPI data. http://www.bls.gov/cpi/cpid1406.pdf9How to compute inflation ratefrom year A to year B?10Examples The overall CPI in 1992 was 140.3. The overallCPI was 144.5 in 1993. What was the annualinflation rate from 1992 to 1993? Notations: iAB inflation rate from year A to year B CPIA CPI for year A CPIB CPI for year Bi1992 1993 Formula:i AB CPI1993144.5 1 1 0.03 3%CPI1992140.3CPI B 1CPI A1112

Applications of CPI What is the inflation rate from 2001 to 2002, CPI can be used to compare standard of living overgiven that 2001 CPI 177.1, 2002 CPI 179.9?time. Suppose that your income was 20,000 in 1992 (year A),i 2001 2002and 25,000 in 1997 (year B), were you really better off in1997 compared to 1992? Note that CPI for 1992 was 140.3,CPI for 1997 was 160.5. There are three methods one can use to do thiscomparison. All three will lead to the same conclusion.CPI 2002179.9 1 1 0.016 1.6%CPI 2001177.113Method 1- Converting today’s dollar intoyesterday's dollar14 Method 2. Converting yesterday’s dollar into today’sdollar In this example we convert 1992 (Year A) income into1997 (Year B) dollar value In this example we convert 1997 (Year B) income into 1992(Year A) dollar valueY1997 1992 Y1997 Y1992 1997 Y1992 CPI1992140.3 25,000 21,854CPI1997160.5 Because 21,854 (1997) 20,000 (1992), better off in1997 General formula for converting today’s dollar intoyesterday’s dollar:CPI AYB A YB CPI BCPI1997160.5 20,000 22,880CPI1992140.3Because 22,880 (1992) 25,000 (1997), better off in1997General formula for converting yesterday’s dollar intotoday’s dollar:YA B YA CPI BCPI A15 Method 3. Compare percentage changes of incomeAnother Exampleand price % change in price from 1992 to 1997 inflation Consider the previous salary increase case (salaryrate 1992-1997i1992 1997 16increase from 20,000 to 25,000) using two differentyears, say, 1977 -1982? 1977 CPI: 60.6; 1982 CPI: 96.5. Inwhich year was the consumer better off?CPI1997160.5 1 1 0.144 14.4%CPI1992140.3% change in income 25000/20000 -1 25%Because income increase at 25% is higher than priceincrease at 14.4%, better off in 19971718

Concept 6: Interest Rate Converting 1982 dollars to 1977 dollars 25,000*(60.6/96.5) 15,699 They were worse off in 1982 because 15,699 20,000 Why do interest rates exist? There are three legitimatereasons why interest rates exist Converting 1977 dollars to 1982 dollars 20,000*(96.5/60.6) 31,848 They were worse off in 1982 because 25,000 31,848 1. Risk: Borrower may not repay, or not repay on time;Your circumstances may change and the money mayworth less to you one year later than now. (mortalityrisk) 2. Opportunity cost: You could use the money onsomething that derives pleasure 3. Inflation: Money repaid to you in the future is notworth as much as money loaned today in purchasingpower. Comparing changes in prices and income Total inflation: 96.5/60.6-1 59.2% % income increase 25000/20000 -1 25% Same conclusion because price increase incomeincrease2019Rate of Time Preference What is rate of time preference? If you loan money to others, what rate would you Some people may have difficulty postponing pleasure, whilecharge?some others find it easier. Different people will want to charge different rates This difference is measured by the rate of time preference.because Individuals with high rates of time preference have a hardThe risk is different – you want to charge more if the borrowerhas a bad credit history because you are taking a higherdefault risk.Your opportunity cost may be different.Your estimation of future inflation rate can be different.time postponing pleasure More borrowing/spending Less saving/lending Individuals with low rates of time preference have an easiertime postponing pleasure Less borrowing/spending More saving/lending21The Relationship between Real andNominal Interest RatesReal and Nominal Interest Rates What is nominal interest rate? Notations: nr nominal interest rate (annual) rr real interest rate (annual) i inflation rate for the loan period (annual) Formula (note one formula can be converted to the Nominal interest rate is the interest rate we observe in themarket. It compensates lenders for three things: the risk they take,the opportunity cost they incur, andfuture inflation.other): What is real interest rate? Because being compensated for inflation is not a real gain fornr rr i ( rr i ) orthe lenders, real interest rate only takes into considerationtwo of these three factors: 22rr the risk they take, andthe opportunity cost they incur.23nr i1 i24

ExamplesExamples If you want to charge a 8% real interest rate, and the Your savings account pays you an interest rate ofinflation rate is expected to be 10%, what is thenominal interest rate you should charge?5%. The inflation rate is 3%. What is your realinterest rate? Note: For all interest rate problems, please keepthe decimal point to 6 digits (18.8000% or0.188000).rr nr rr i (rr i ) 8% 10% (8% 10%) 18.8000%nr i 5% 3% 1.9418%1 i1 3%25Examples26Examples Your savings account pays you an interest rate of If you want to charge a 8% real interest rate, and7%. The inflation rate is 5%. What is your realinterest rate?the inflation rate is expected to be 2%, what is thenominal interest rate you should charge?rr nr rr i (rr i) 8% 2% (8% 2%) 10.1600%nr i 7% 5% 1.9048%1 i1 5%27Concept 7. Uncertainty andExpectation28Example 1 Expected salary next year What are the uncertainty we face that are important toconsumer decision making? Many, such as future inflation rate, future income, etc. What do we do when we have to use futureinformation?OutcomeProbabilityStay the al 100% We have to make educated guesses about the future.Expected salary next year 25,000*50% 30,000*40% 20,000*10% 12500 12000 2000 26,500 The key word to scientific guesses is expected value. Expected value Sum of (outcome i * probability ofoutcome i )2930

Example 2. Suppose you are taking three classes. The semester hasnot ended but you need to report your GPA for thatsemester on your application form for graduate school.What is your expected GPA given the informationbelow?G ra d e s fo r 3 C la s s e sO u tc o m eP r o b a b i lit yA A A450 %A A B3 .6 735 %A B B3 .3 310 %A B C35%T o ta l 1 0 0 %Expected GPA this semester 4*50% 3.67*35% 3.33*10% 3*5% 3.7675031

Food and beverages 2012-2013: 1.4 % 1990 -2013: 76.9 % The inflation rate for all products and services 2012 -2013: 1.5% (annual inflation rate) 1990 -2013: 75.6 % 2 What is the relationship between inflation rate and the value of your dollars? The higher the infl

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