Question

5. The economy of Britannica produces three Year Computers DVDs Pizzas goods: computers, DVDs, and pizza. The Price Quantity Price Quantity Price Quantity accompanying table shows the prices and 2010 $900 10 $10 100 15 2 output of the three goods for the years 2011 1,000 10.5 12 105 16 2 2012 1,050 12 14 110 2010, 2011, and 2012. a. Calculate nominal GDP in Britannica for each of the three years. What is the per- cent change in nominal GDP from 2010 to 2011 and from 2011 to 2012? b. Calculate real GDP in Britannica using 2010 prices for each of the three years. What is the percent change in real GDP from 2010 to 2011 and from 2011 to 2012? c. Calculate the aggregate price level (with a base year of 2010) using the Laspeyres (CPI- style) price index, measured to the nearest one-hundredth, d. Calculate the aggregate price level (with a base year of 2010) using the Paasche (GDP- deflator-style) price index, measured to the nearest one-hundredth. Compare to the Laspeyres - which index implies there is a greater rate of inflation? Why is it greater?

Answer 1

a).

Consider the given problem here Britannica produces three goods and there price and quantity are given for different years. Now, the nominal GDP is the market value of all goods and services produce by a nation in a particular period or year. Here in 2011 Britannica produce “10.5 computers”, “105 DVD’s” and “2 Pizzas” and their respective price are “$1,000”, “$12” and “$16”. So, the nominal GDP of 2011 is “1,000*10.5+12*105+16*2 = $11,792”. Similarly, we can get the nominal GDP for 2010 and 2012, the following shows the nominal GDP for different years.

Nominal GDP Calculation % change in nominal GDP Calculation Computers Year Price Quantity Price 2010 900 10 2011 1000 10.5 2012 1050 12 DVS's Quantity Price 100 12 105 110 Pizzas Quantity 2 16 2 $10,030 "900*10 + 10* 100+ 15*2" $11,792 "1000*10.5 + 12*105 + 16*2" $14,191 "1050*12 + 14*110 + 17*3" 14 17.57% "(11,792-10,030)*100/10,030" 20.34% "(14,191-11,792) *100/11,792" 17

Now, the nominal GDP of 2010 and 2011 are “10,030” and “11,792”, => the % change in nominal GDP from 2010 to 2011 is [(11,792-10,030)*100/10,030]= 17.57%. Similarly the above table shows the % change in nominal GDP from 2011 to 2012.

b).

The real GDP is the market value of all goods and services produce by a nation in a particular period or year in base price. Here in 2011 Britannica produce “10.5 computers”, “105 DVD’s” and “2 Pizzas” and their respective price in base year 2010 are “$900”, “$10” and “$15”. So, the Real GDP of 2011 is “900*10.5+10*105+15*2 = $10,530”. Similarly, we can get the real GDP for 2010 and 2012, the following shows the real GDP for different years.

Real GDP Calculation % change in nominal GDP Calculation Computers DVS's Pizzas Year Price Quantity Price Quantity Price Quantity 2010 900 10 10 100 15 2011 1000 10.5 12 105 16 2012 1050 12 14 110 17 $10,030 "900*10 + 10* 100 + 15*2" $10,530 "900*10.5 + 10*105 + 15*2" $11,945 "900*12+10*110 + 15*3" 4.99% "(10,530-10,030) *100/10,030" 13.44% "(11,945-10,530)*100/10,530"

Now, the real GDP of 2010 and 2011 are “10,030” and “10,530”, => the % change in real GDP from 2010 to 2011 is [(10,530-10,030)*100/10,030]= 4.99%. Similarly the above table shows the % change in real GDP from 2011 to 2012.

c).

To get the aggregate price level in Laspeyres method, we have get CPI. Now, in CPI we have to fixed the bundle of goods and services. Here in 2010 the quantity of computer, DVD and pizzas are “10”, “100” and “2” respectively. So, here we will get the value of this bundle in different year with different price levels.

Value of bundle Calculation CPI Calculation Inflation Calculation Computers Year Price Quantity Price 2010 900 10 2011 1000 10.5 2012 1050 12 DVS'S Pizzas Quantity Price Quantity 10 100 15 2 12 105 16 2 14 110 17 3 $10,030 "90010 + 10* 100 + 15*2" $11,232 "1000*10 +12*100 + 16*2" $11,934 "1050*10+14*100 + 17"2" 100 "(10,030/10,030) *100" 111.9840 "(11,232/10,030) *100" 118.9831 "(11,934/10,030) *100" 11.98% "(111.9840-100)*100/100" 6.25% "(118.9831-111.9840) *100/111.9840"

Here the above table shows the CPI as well as inflation for different years.

d).

To get the aggregate price level in Paasche method, we have get GDP-deflator. GDP deflator is the ratio of nominal to real GDP. The following table shows the GDP-deflator for different years.

Inflation Year 2010 2011 2012 Nominal GDP Real GDP GDP-deflator Calculation 10,030 10,030 100 "(10,030/10,030) *100" 11,792 10,530 111.9848053 "(11,792/10,530)*100" 14,191 11,945 118.8028464 "(14,191/11,945)*100" 11.98% 6.09%

If we compare the price index in both the method then we get that the CPI and GDP-deflator are same for 2011 but CPI is more in 2012, the one most important reasons is CPI fixe the bundle on the other hand GDP-deflator takes into account the total goods produced in different years.