1) Am I to assume the entire economy consists of CDs and Tennis Racquets? I presume yes.
2) Is the Tennis Racquets production in 2006 really 90 -- should it be 190? I will assume 190.
3) You are asked to calculate a price index. There are 2 general methodologies: the Laspeyres index and the Paasche index. As the CPI is a Laspeyres index, I will assume you want the Lapeyres price index.
3) Most people calculate percentage change as (Xt/X0 - 1) (0 is the base y ear's value and t some time in the future or past). However, some economists prefer the mid-point method. I presume you want the "common" method over the mid-point method.
Now then GDP = sum(P*Q) over all goods so:
2005 GDP is 18*90 + 100*180 = 19620
2006 GDP is 20*100 + 110*190 = 22900
2006 GDP at 05 prices is 18*100 + 100*190 = 20800
Q1) Real GDP grew by 20800/19620 = 1.06 = 6%
The price index (Laspeyres method) is 100*(P2*Q1)/(P1*Q1)
CPI05 = 100
CPI06 = (20*90 + 110*180) / (18*90 + 100*180) = 100*(21600/19620) = 110
Q2) price index for 2006 is 110
Q3) Real 2006 GDP using 06 prices (e.g., deflate by CPI) is 22900/1.10 = 20818. Percent change in Real GDP is 20818/19620 = 6.1%
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