OVERTIME: Unit 5 Price Index Problems

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1 OVERTIME: Unit 5 Price Index Problems Name: Base year = 2000 Market basket value = $15,000; Round all numbers to 2 decimals. Answers must be in the proper format ($, % or #). Year Market Basket Value Nominal GDP Population 2007 $17,500 $3,200, $17,750 $3,750, $18,500 $5,000, $20,000 $5,800, $21,000 $6,500, The Consumer Price Index is a measure of how much prices have changed over time. Prices in the year being examined are compared to prices in a predetermined year from the past, called the base year. In this example, 2000 is our base year. CPI = (value of market basket in current year / value of market basket in base year) x 100 The base year has an index value of 100. This serves as our baseline value. How do we know this? Calculate the CPI for 2000: ($15,000 / $15,000) x 100 = 100 If inflation occurs, your CPI will be greater than 100. If the CPI for a year is 107, this means that there has been 7% inflation since the base year. CPI: Year:

2 Most people don t care about comparing this year s prices to a base year, especially if the base year is over a decade ago. Only economists care about how today s prices compare to 10 years ago. The average consumer is more concerned with how things have changed recently. This is where calculating the inflation rate comes in handy. The inflation rate is the percentage change in the CPI between any two years. To calculate this value, you will need to use the percentage change formula. % change = (change in value / original value) x 100 When calculating the change in value, you always subtract the earlier year s data from the later year s data. % change = [(year 2 data-year 1 data) / year 1 data] x 100 Inflation Rate: Range: Nominal GDP is the dollar value of all final goods and service produced in a country in a year. It is distorted by inflation. As prices increase over time, the dollar value of goods and services increases. Real economic growth occurs when we produce a greater quantity of goods and services. Real GDP (RGDP) is GDP expressed in constant dollars (base year prices). Real GDP = (nominal GDP / CPI) x 100 By dividing nominal GDP by the CPI for the year in question, we deflate the nominal value. If you are calculating 2007 RGDP, you are basically multiplying 2007 quantities of goods and services by their 2000 prices. By using a constant base year, you can accurately compare a series of years to see if there has been real economic growth. Real GDP: Year:

3 Looking at the change in RGDP from year to year is important, but it does not provide the whole picture. Calculating the percentage change in RGDP shows the rate of economic growth. A $500 million increase in GDP may sound like a lot, but if your GDP was $500 billion the year before, that only represents a 0.1% increase barely a drop in the bucket. If your GDP was $10 billion, an increase of $500 million would represent a 5% increase a very respectable rate of growth. For this calculation, you will use the percentage change formula. % change in Real GDP: Year: Real GDP per capita (per person) is an even more accurate way to examine your economy. An increase in RGDP is good, but if your population growth is substantial, you will have to share that increase in goods and services with more people. RGDP per capita = RGDP / population Real GDP per capita: Year:

4 As mentioned before, looking at the percentage change in your data is a more accurate way to see if your economy has progressed. % change in Real GDP per capita: Year:

5 Helpful Hints for Calculating Price Index Problems Consumer Price Index = (current year market basket / base year market basket) x 100 The CPI measures inflation by comparing the current year prices of a sampling of consumer items (known as a market basket ) to the prices of those same goods in some previous year (known as the base year ). Since the CPI is an index, the result of the formula is simply a number, not a percentage or dollar amount. For this index number to make sense, you need to know the baseline number the value of the index when there is no inflation. If there is no inflation, the value of the market basket in the current year will be equal to the value in the base year. For example: ($1,000,000 / $1,000,000) x 100 = 100 Therefore, an index value of 100 means zero inflation over that time period. If inflation has occurred, the result will be an index value of greater than 100. For example: ($1,050,000 / $1,000,000) x 100 = 105 The number 105 is not very user-friendly. Most people don t want to know the CPI value for the current year, since it compared this year s prices to a base year so far in the past that it is no longer relevant to our day-to-day lives. For example, the CPI as of February 2013 is 232. The base year for these calculations is This means that prices have increased 132% since While it is interesting to know that prices have increased that much over a 30-year time span, this does not help us understand more recent changes in the economy. This is where calculating the inflation rate comes in handy Inflation rate = [(current year CPI previous year CPI) / previous year CPI] x 100 Notice that this formula is a percentage change formula. It calculates the percentage change in the CPI between 2 years. As long as you have the CPI data for a range of years, you can use this formula to find out how much prices have changed between any 2 years. For example: 2011 CPI = CPI = Inflation rate between = [( ) / ] x 100 = 2.07% Economists calculate the CPI so that they can deflate nominal GDP and discover Real GDP.

6 RGDP = (nominal GDP for year Y / CPI for year Y) x nominal GDP = 15,653,366,000, CPI = RGDP = (15,653,366,000,000 / ) x 100 = $6,817,846,285, While this is a huge drop ($15.6 trillion down to $6.8 trillion), remember we are converting everything to 1982 dollars (our base year). If we use this formula to covert the nominal GDP of every year between 1983 and 2012, we can see how much REAL growth we have experienced. To understand how much the economy has grown, we need to look at the percentage change in Real GDP each year. (Remember, saying our RGDP grew by $1 million does not tell the whole story. If our initial RGDP was $1 million and we grew by $1 million our economy doubled in size! If our initial RGDP was $100 million and we grew by $1 million, our economy only grew by 1%. Percentage change in RGDP = [(current year RGDP previous year RGDP) / previous year RGDP] x 100 Notice that this is the same percentage change formula that we used to calculate the inflation rate we just plugged in RGDP data instead of CPI data. If we really want to understand how our economy has grown, we also need to take population into account. RGDP per capita (per person) = RGDP / population