Question

Recall the method of calculating real GDP detailed in the chapter. As you may already have​ noticed, this method has a​ problem: in calculating aggregate​ output, this method weights the output of the various goods and services by their relative prices in the base year. ​Say, for​ example, a textbook costs​ $100 in the base​ year, and a laptop costs​ $2,000. This means that the laptop would have 20 times the weight of a book in calculating aggregate output. But what happens when relative prices​ change? As you​ know, the prices of most​ high-tech items, including​ laptops, have generally been decreasing over time. Suppose the price of a laptop declined from​ $2,000 to​ $1,000 in the period from the base year to the current year.​ Now, a laptop costs only 10 times as much as the book.​ So, using​ base-year relative prices would overweight laptops in calculating real GDP in the current year. In response to this​ problem, in 1996 the BEA switched to what is called a ​chain-weighted method of calculating real GDP. Say the base year is 2008. To calculate the growth rate of real GDP between 2008 and​ 2009, for​ example, the BEA calculates real GDP for 2008 using 2008 as the​ base, and then real GDP for 2008 using 2009 as the base.​ Then, the bureau calculates real GDP for 2009 using 2009 as the​ base, and real GDP for 2009 using 2008 as the base. For each​ base, the growth rate is then calculated​ as: StartFraction 2009 GDP Subscript left parenthesis font size decreased by 1 2008 Base right parenthesis Baseline minus 2008 GDP Subscript left parenthesis font size decreased by 1 2008 Base right parenthesis Over 2008 GDP Subscript left parenthesis font size decreased by 1 2008 Base right parenthesis EndFraction and StartFraction 2009 GDP Subscript left parenthesis font size decreased by 1 2009 Base right parenthesis Baseline minus 2008 GDP Subscript left parenthesis font size decreased by 1 2009 Base right parenthesis Over 2008 GDP Subscript left parenthesis font size decreased by 1 2009 Base right parenthesis EndFraction ​So, they end up with two different growth​ rates, which are then averaged. Given this averaged growth​ rate, and the level of GDP in 2008 at 2008​ prices, the bureau then calculates real GDP for 2009 as one plus the average growth rate previously​ calculated, times 2008 output in 2008 dollars. The growth rate between 2009 and 2010 is then calculated similarly.   Suppose that​ laptops, economics​ textbooks, and energy drinks are the only three goods produced in the United States. The following table gives the quantity of each produced​ (in millions) and their price in the years from 2010 to​ 2012:

Laptops Textbooks Energy Drinks Price Quantity Price Quantity Price Quantity

2010 ​$1,800 8 ​$170 6 ​$2 20

2011 ​$1,500 10 ​$180 8 ​$4 25

2012 ​$1,300 10 ​$200 9 ​$4 30

Complete the following table by calculating nominal GDP and real GDP​ (using 2010 as the base​ year) for each year. ​(Enter your responses as integers​.)

Nominal GDP & Real GDP​ (2010 Base​) 2010 ​$__ $__ 2011 $__ $__ 2012 $​__​ $__

Using the​ chain-weighted method outlined​ above, real GDP for 2011 is ​$__ . ​(Round your response to the nearest dollar​.) Using the​ chain-weighted method​ again, real GDP for 2012 is ​$__ . ​(Round your response to the nearest dollar​.)

Answer 1

Nominal GDP for 2010 = (1800 *8 ) + ( 170 *6 ) + ( 2* 20 ) = 15,460

Nominal GDP for 2011 = (1500 * 10) + ( 180 *8) + (4*25) = 16,540

Nominal GDP for 2012 = (1300 *10 ) + (200 * 9) + ( 4* 30) = 14,920

Real GDP in 2010 = 15,460

Real GDP in 2011 = (1800 *10 ) + (170 *8 ) + (2*25) = 19,410

Real GDP in 2012 = (1800 *10) + (170 *9) + ( 2*30) = 19,590

chain weighted method real GDP for 2012 .

the ratio of year 2011 real GDP to year 2010 real GDP equals g1 = 19410 / 15460 = 1.255

Real GDP of 2011 at 2011 price is same as nominal GDP in 2011 = 16540

2010 GDP at 2011 price = (1500 * 8 ) + (180 *6 ) + 4*20) = 13160

The ratio of year 2011 GDP at year 2011 prices to year 2010 GDP at year 2011 prices equals g2 = 16540 / 13160 = 1.256

The chain-weighted ratio of real GDP in the two years therefore is equal to gc =

gc = = 1.255