How To Calculate Percentage Change In Real Gdp

Learning Objectives

• Calculate existent GDP based on nominal GDP values
• Calculate the real growth rate in Gross domestic product

Now we're in a position to answer the question that we posed previously: given nominal Gross domestic product for the U.S. economic system from 1960-2010, how much did real GDP really increase?

In order to encounter how much production has actually increased, nosotros need to extract the furnishings of college prices on nominal GDP, then that what nosotros're left with is real GDP, the increase in the quantity of goods and services produced. This tin exist easily done using a concept known equally the GDP deflator. The GDP deflator is a price index measuring the average cost of all goods and services included in the economic system. We will explore price indices in particular and how they are computed when nosotros learn more well-nigh inflation, but this definition will do for now. The data for the Gdp deflator are given in Tabular array 1 and shown graphically in Figure 1.

Tabular array 1. U.Southward. GDP Deflator, 1960-2010
1960	19.0	Figure 1. U.Southward. Gdp Deflator, 1960–2010. Much like nominal GDP, the Gross domestic product deflator has risen exponentially from 1960 through 2010. (Source: BEA).
1965	20.iii
1970	24.8
1975	34.1
1980	48.3
1985	62.3
1990	72.7
1995	81.7
2000	89.0
2005	100.0
2010	110.0
Source: www.bea.gov, National Accounts

Figure 1 shows that the price level, equally measured by the Gross domestic product deflator, has risen dramatically since 1960. Using the simple growth charge per unit formula that we explained on the terminal page, we see that the price level in 2010 was almost six times higher than in 1960 (the deflator for 2010 was 110 versus a level of 19 in 1960). Clearly, much of the apparent growth in nominal GDP was due to aggrandizement, not an actual modify in the quantity of appurtenances and services produced, in other words, non in real GDP. Recall that nominal GDP can rise for two reasons: an increase in output, and/or an increase in prices. What is needed is to extract the increase in prices from nominal GDP so as to measurejustchanges in output. After all, the dollars used to measure nominal GDP in 1960 are worth more than the inflated dollars of 1990—and the price index tells exactly how much more than. This adjustment is easy to do if you lot employ the Nominal-to-Real formula that nosotros explained previously:

[latex]\text{Nominal Value of Output}=\text{Price}\times\text{Quantity of Output}[/latex]

Taking the Gdp form of this equation:

[latex]\text{Nominal Gdp}=\text{GDP Deflator}\times\text{Existent GDP}[/latex]

Carve up both sides by the Gross domestic product Deflator:

[latex]\displaystyle\text{Real Gross domestic product}=\frac{\text{Nominal GDP}}{\text{GDP Deflator}}[/latex]

For reasons that will be explained in more detail below, mathematically, a price index (like the Gross domestic product Deflator) is a two-digit decimal number like 1.00 or 0.85 or 1.25. Because some people take problem working with decimals, when the price alphabetize is published, it has traditionally been multiplied past 100 to go integer numbers like 100, 85, or 125. What this ways is that when we "deflate" nominal figures to get existent figures (by dividing the nominal past the price index), we as well need to call up to divide the published price index by 100 to make the math piece of work. So the formula becomes:

[latex]\displaystyle\text{Existent Gross domestic product}=\frac{\text{Nominal Gross domestic product}}{\frac{\text{GDP Deflator}}{100}}[/latex]

Computing Real Gdp

Let'south practice finding real GDP by looking at the actual data on nominal Gross domestic product and the Gross domestic product deflator.

Table 2.U.Due south. Nominal GDP and the Gdp Deflator
Year	Nominal Gross domestic product (billions of dollars)	Gross domestic product Deflator (2005 = 100)
1960	543.three	19.0
1965	743.7	20.three
1970	1,075.9	24.8
1975	1,688.9	34.one
1980	two,862.5	48.iii
1985	iv,346.7	62.3
1990	v,979.half-dozen	72.vii
1995	7,664.0	81.7
2000	10,289.seven	89.0
2005	13,095.4	100.0
2010	14,958.three	110.0
Source: www.bea.gov

Step 1. Look at Table two to see that, in 1960, nominal GDP was $543.3 billion and the price index (Gross domestic product deflator) was 19.0.

Stride 2. To calculate the real Gross domestic product in 1960, utilise the formula:

[latex]\brainstorm{assortment}{l}\text{Existent Gdp}=\frac{\text{Nominal Gdp}}{\frac{\text{Price Index}}{100}}\\\text{Real GDP}=\frac{543.3\text{ billion}}{\frac{19}{100}}=\$2,859.5\text{ billion}\end{assortment}[/latex]

Nosotros'll do this in 2 parts to get in clear. First accommodate the price alphabetize: nineteen divided by [latex]100=0.19[/latex]. Then carve up into nominal GDP:

[latex]\frac{\$543.three\text{ billion}}{0.19}=\$two,859.v\text{ billion}[/latex].

Step 3. Apply the same formula to calculate the real GDP in 1965.

[latex]\begin{array}{l}\text{Real GDP}=\frac{\text{Nominal Gross domestic product}}{\frac{\text{Price Index}}{100}}\\\text{Real GDP}=\frac{743.7\text{ billion}}{\frac{20.3}{100}}=\$3,663.5\text{ billion}\end{array}[/latex]

Step 4. Continue using this formula to calculate all of the real GDP values from 1960 through 2010. The calculations and the results are shown in Table 3.

Table 3. Converting Nominal to Real Gross domestic product
Year	Nominal Gdp (billions of dollars)	GDP Deflator (2005 = 100)	Calculations	Real GDP (billions of 2005 dollars)
1960	543.3	19.0	[latex]\displaystyle\frac{543.3}{(\frac{19.0}{100})}[/latex]	Show Answer 2859.5
1965	743.7	20.3	743.7 / (20.3/100) [latex]\displaystyle\frac{743.7}{(\frac{xx.iii}{100})}[/latex]	Show Respond 3663.5
1970	1075.nine	24.8	i,075.9 / (24.8/100) [latex]\displaystyle\frac{i,075.9}{(\frac{24.8}{100})}[/latex]	Show Answer 4338.iii
1975	1688.9	34.one	1,688.9 / (34.1/100) [latex]\displaystyle\frac{ane,688.9}{(\frac{34.1}{100})}[/latex]	Show Answer 4952.8
1980	2862.5	48.3	2,862.five / (48.3/100) [latex]\displaystyle\frac{2,862.five}{(\frac{48.3}{100})}[/latex]	Show Reply 5926.5
1985	4346.7	62.3	four,346.7 / (62.iii/100) [latex]\displaystyle\frac{four,346.7}{(\frac{62.3}{100})}[/latex]	Evidence Respond 6977.0
1990	5979.6	72.7	5,979.6 / (72.7/100) [latex]\displaystyle\frac{five,979.6}{(\frac{72.7}{100})}[/latex]	Testify Answer 8225.0
1995	7664.0	82.0	7,664 / (82.0/100) [latex]\displaystyle\frac{7,664.0}{(\frac{82.0}{100})}[/latex]	Show Answer 9346.3
2000	10289.7	89.0	ten,289.7 / (89.0/100) [latex]\displaystyle\frac{x,289.7}{(\frac{89.0}{100})}[/latex]	Show Answer 11561.5
2005	13095.iv	100.0	13,095.four / (100.0/100) [latex]\displaystyle\frac{xiii,095.4}{(\frac{100.0}{100})}[/latex]	Show Respond 13095.four
2010	14958.3	110.0	14,958.3 / (110.0/100) [latex]\displaystyle\frac{xiv,958.3}{(\frac{110.0}{100})}[/latex]	Show Answer 13598.5
Source: Agency of Economic Analysis, www.bea.gov

There are a couple things to notice hither. Whenever you compute a real statistic, ane year (or catamenia) plays a special role. It is called the base of operations twelvemonth (or base catamenia). The base yr is the year whose prices are used to compute the real statistic (every bit we showed on the concluding folio). When we calculate real GDP, for example, we take the quantities of goods and services produced in each year (for example, 1960 or 1973) and multiply them by their prices in the base yr (in this case, 2005), so we go a measure out of Gross domestic product that uses prices that do non change from yr to year. That is why real Gross domestic product is labeled "Constant Dollars" or "2005 Dollars," which means that real Gross domestic product is constructed using prices that existed in 2005. The formula used is:

[latex]\displaystyle\text{GDP deflator}=\frac{\text{Nominal Gross domestic product}}{\text{Real Gdp}}\times{100}[/latex]

Rearranging the formula and using the data from 2005:

[latex]\brainstorm{array}{l}\text{Real GDP}=\frac{\text{Nominal Gdp}}{\frac{\text{Cost Index}}{100}}\\\text{Real GDP}=\frac{xiii,095.iv\text{ billion}}{\frac{100}{100}}=\$13,095.four\text{ billion}\cease{array}[/latex]

Comparing existent Gross domestic product and nominal GDP for 2005, you see they are the same. This is no accident. It is because 2005 has been chosen equally the "base year" in this instance. Since the cost index in the base year always has a value of 100 (by definition), nominal and real GDP are always the same in the base year. Look at the data for 2010.

[latex]\begin{array}{l}\text{Existent GDP}=\frac{\text{Nominal Gdp}}{\frac{\text{Toll Index}}{100}}\\\text{Real Gdp}=\frac{14,958.three\text{ billion}}{\frac{110}{100}}=\$xiii,598.5\text{ billion}\end{array}[/latex]

Use this data to make another observation: As long as inflation is positive, significant prices increase on boilerplate from twelvemonth to year, real Gdp should be less than nominal GDP in whatsoever year subsequently the base year. The reason for this should exist clear: The value of nominal Gdp is "inflated" by inflation. Similarly, as long as aggrandizement is positive, real Gross domestic product should be greater than nominal Gdp in whatsoever year before the base of operations year.

Try It

Figure 2 shows the U.Due south. nominal and real GDP since 1960. Because 2005 is the base of operations year, the nominal and real values are exactly the same in that yr. However, over fourth dimension, the rise in nominal Gross domestic product looks much larger than the ascension in real GDP (that is, the nominal Gross domestic product line rises more steeply than the real GDP line), because the rise in nominal GDP is exaggerated by the presence of aggrandizement, especially in the 1970s.

Figure 2. U.South. Nominal and Existent Gdp, 1960–2012. The red line measures U.South. Gdp in nominal dollars. The black line measures U.S. GDP in existent dollars, where all dollar values have been converted to 2005 dollars. Since real GDP is expressed in 2005 dollars, the two lines cross in 2005. Even so, real Gdp volition appear higher than nominal Gross domestic product in the years before 2005, because dollars were worth less in 2005 than in previous years. Conversely, existent GDP volition appear lower in the years after 2005, because dollars were worth more in 2005 than in later years.

Let's return to the question posed originally: How much did Gross domestic product increase in real terms? What was the rate of growth of real Gross domestic product from 1960 to 2010? To find the real growth rate, nosotros use the formula for percentage change:

[latex]\displaystyle\frac{2010\text{ real Gross domestic product}-1960\text{ existent Gdp}}{1960\text{ real Gdp}}\times{100}=\text{ percent change}[/latex]

[latex]\displaystyle\frac{xiii,598.v-2,859.5}{2,859.five}\times{100}=376\text{ per centum}[/latex]

In other words, the U.S. economy has increased existent production of goods and services by nearly a factor of four (i.e. 376%) since 1960. Of grade, that understates the material improvement since it fails to capture improvements in the quality of products and the invention of new products.

For short periods of time, there is a quicker way to answer this question approximately, using another math trick. Call back that nominal Gross domestic product increases for two reasons, first, considering prices increase and 2d because real GDP increases. In other words the percentage increase in nominal GDP is (approximately) equal to the percentage increment in prices plus the percent increment in existent GDP.

Expressing this equally an equation,

[latex]\%{\text{ change in nominal GDP}}=\%{\text{ change in prices}}+\%{\text{ alter in real GDP}}[/latex]

Subtracting % change in prices from both sides gives:

[latex]\%{\text{ change in nominal Gross domestic product}}-\%{\text{ alter in prices}}=\%{\text{ change in real Gdp}}[/latex]

Therefore, the growth rate (pct change) of real GDP equals the growth charge per unit in nominal GDP (% alter in value) minus the growth charge per unit in prices (% change in GDP Deflator).

Two Ways to Calculate Growth Rates

Permit's await at the bottom numbers from the following table:

Year	Nominal Gross domestic product	GDP Deflator	Real Gross domestic product
2005	$13095.4	100	$13095.4
2010	$14958.3	110	$13598.5

Method 1: Using the Elementary Growth Rate formula

(Existent GDP in 2010 – Real GDP in 2005) / Existent GDP in 2005 = Growth of Real Gdp

Plugging in the numbers gives

($13,598.5- $13,095.4) / $13,095.5 = 4%

Method 2: Using the Math Trick

Growth of Nominal GDP – Growth of GDP Deflator = Growth of Real Gross domestic product

Plugging in the numbers and using the Unproblematic Growth Charge per unit formula gives

[latex]\frac{($14,958.3-$13,095.4)}{$13095.4}-(\frac{(110-100)}{100})=14.2\%-x\%=4.2\%[/latex]

Notation that Method two is just a quick approximation to Method ane.

Try It

Contribute!

Did you take an thought for improving this content? We'd love your input.

Better this pageLearn More

Source: https://courses.lumenlearning.com/wm-macroeconomics/chapter/converting-real-gdp/

Posted by: espinozaexuld1949.blogspot.com

Share this post