Question

7. LounchPad . Consider an economy that produces and consumes hot dogs and ham- burgers. In the following table are data for two different years 2013 2015 Good Hot dogs Hamburgers Quantity Quantity Price 250 $4 500 $4 200 $$2 200 $3 a. Using 2010 as the base year, compute the following statistics for each year: nominal GDP, real GDP, the implicit price deflator for GDP, and a fixed-weight price index such as the CPI. b. By what percentage did prices rise between 2010 and 2015? Give the answer for each good and also for the two measures of the overall price level. Compare the answers given by the Laspeyres and Paasche price indexes. Explain the difference.

Answer 1

a.

	2010		2015
	Quantity	Price	Quantity	Price
Hot dogs	200	2	250	4
Hamburgers	200	3	500	4
Nominal GDP	1000		3000
Real GDP	1000		2000

GDP deflator = (Nominal GDP/Real GDP)*100
GDP deflator for 2010 = (1000/1000)*100 =100
GDP deflator for 2015= (3000/2000)*100 =150
CPI = (GDP deflator 2015- GDP deflator 2010)/ GDP deflator 2010
= ((150-100)/100)*100 =50

b.

Price rise,
Inflation,
Price rise for Hot dogs = ((4-2)/2)*100 = 100 percent
Price rise for Hamburgers = ((4-3)/3)*100 = 33.33 percent
CPI
Price rise for Hot dogs =((250*4-200*2)/(200*2))*100= 150 percent
Price rise for Hamburgers = ((500*4-200*3)/(200*3))*100= 233.33 percent

Laspeyers Price Index = ((current price* base quantity commodity)/ ( base price * base quantity))*100
For 2010 = ((200*2+200*3)/(200*2+200*3))*100 = 100
For 2015 = ((200*4+200*4)/(200*2+200*3))*100 = 160

Paasche Price Index = ((current price* current commodity)/ (base price*current quantity))*100
For 2010 = ((200*2+200*3)/(200*2+200*3))*100 = 100
For 2015 = ((250*4+500*4)/(250*2+500*3))*100 = 150

Laspeyers overstate the prices because as price changes, consumers change their purchasing behavior and paasche understates price changes as some of the changes are affected in consumption pattern