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Business Statistics: Communicating with Numbers By Sanjiv Jaggia and Alison Kelly

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## Business Statistics: Communicating with Numbers By Sanjiv Jaggia and Alison Kelly

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**Business Statistics: Communicating with Numbers**By Sanjiv Jaggia and Alison Kelly**Chapter 19 Learning Objectives (LOs)**LO 19.1:Define and compute investment returns. LO 19.2:Use the Fisher equation to convert nominal returns into real returns and vice versa. LO 19.3:Calculate and interpret a simple price index. LO 19.4:Calculate and interpret the unweighted aggregate price index. LO 19.5:Compare the Laspeyres and the Paasche methods for computing the weighted aggregate price index. LO 19.6:Use price indices to deflate economic time series and derive the inflation rate.**Analyzing Beverage Price Changes**• Jehanne-Marie Roche owns a convenience store in Mt. Angel, Oregon. Though the store sells groceries, its major source of revenue is from liquor sales. • Due to the economic downturn in 2008, she has had to offer many price discounts to keep sales up. • Our goal is to better understand price movements at her store during the 2007-2009 time period.**Investment Return**LO 19.1 Define and compute investment returns.**Example 19.1**LO 19.1**Example 19.2**LO 19.1**Using Adjusted Closing Prices**LO 19.1**Example 19.3**LO 19.1**Nominal versus Real Rates of Return**LO 19.2 Use the Fisher equation to convert nominal returns into real returns and vice versa. • So far we have focused on nominal returns. • However, the nominal return does not represent a true picture because it does not capture the erosion of purchasing power due to inflation. • The real rate of return captures the change in purchasing power; it is a more complete assessment of the benefit of asset ownership.**The Fisher Equation**LO 19.2**Example 19.4**LO 19.2**Example 19.5**LO 19.2**19.2 Index Numbers**LO 19.3 Calculate and interpret a simple price index.**Example 19.6**LO 19.3 • For the introductory case, compute the price indices using 2007 as the base.**A Gasoline Price Index**LO 19.3 Since 2000 is the base year, we interpret the index relative to 2000. So in 2001, gasoline prices had fallen by 3.31 percent, but by 2008, gasoline prices were 116.56 percent higher than they were in 2000. • The table below shows the average price of gasoline and its price index for 2000 to 2008.**Gasoline Prices**LO 19.3**Re-indexing**LO 19.3**Unweighted Aggregate Price Index**LO 19.4 Calculate and interpret the unweighted aggregate price index.**Example 19.9**LO 19.4**Weighted Aggregate Price Index**LO 19.5 Compare the Laspeyres and the Paasche methods for computing the weighted aggregate price index. • The weighted aggregate price index does not treat prices of different items equally. Rather, a higher weight is given to items that are sold in higher quantities. • There is no unique way of determining the weights. One option is to reweight each year as the quantities change, but often data are unavailable for this method. • Two popular methods are based on utilizing the quantities from the base period and the current period.**The Laspeyres Price Index**LO 19.5**Example 19.10**LO 19.5 • By combining the quantity data with the price data presented on the previous slide, we can compute the appropriate weighted sums and the Laspeyres Index, given a base year of 2007. • Notice that compared to the unweighted index, the Laspeyres Index suggests a sharper drop in property values.**The Paasche Price Index**LO 19.5**Example 19.11**LO 19.5**Changing Consumption Patterns**LO 19.5 • The Laspeyres and Paasche methods provide similar results if the time periods being compared are not too far apart. • Over time, consumers tend to adjust their consumption patterns. As a result, the Paasche index will tend to produce a lower estimate than the Laspeyres index if prices are rising, and a higher estimate than the Laspeyres index if they are falling. • However, since the Paasche index requires weights to be updated each year, in practice the Laspeyres index is more widely used.**Example 19.12**LO 19.5**Example 19.12**LO 19.5**Example 19.12**LO 19.5**19.3 Using Price Indices to Deflate a Time Series**LO 19.6 Use price indices to deflate economic time series and derive the inflation rate. • Many economic time series are reported in nominal terms, implying they are measured in dollar amounts. • But since inflation erodes the value of money over time, comparing starting salaries in 2000 to those in 2010 does not tell the whole story. • An important function of price indices is to serve as a price deflator, allowing us to compare differences in purchasing power over time.**Nominal versus Real Values**LO 19.6**The Consumer Price Index**LO 19.6 • Each month the U.S. Bureau of Labor Statistics reports the Consumer Price Index (CPI) based on the prices paid by urban U.S. consumers for a representative basket of goods. • The CPI is perhaps the best-known weighted aggregate price index, and is commonly used to deflate economic time series. • As of 2010, the CPI uses 1982 as the base year.**The Producer Price Index**LO 19.6 • The Producer Price Index (PPI) measures prices paid at the wholesale or producer level. • So while the CPI is based on out-of-pocket expenses of the consumer, the PPI is the portion of those expenses actually received by producers. • One of the major differences is that sales and excise taxes are part of the CPI but not PPI.**The Two Major Indices**LO 19.6 • We plot these two indices from 1960 through 2010. These indices moved in sync until the early 1980s, when the prices paid by consumers outstripped those received by producers.**Example 19.13**LO 19.6**Example 19.13**LO 19.6**Inflation Rate**LO 19.6**Example 19.14**LO 19.5 • The CPI for 2006, 2007, and 2008 are reported as 201.59, 207.34, and 215.30, respectively, by the Bureau of Labor Statistics. • Let’s use these values to compute the inflation rates for 2007 and 2008: