Question

Suppose that the Statistical Institute uses information about three goods to construct the basket to be used for construction of Consumer Price Index (CPI). The set of prices and the set of quantites describing the basket of goods at the year of t respectively is the following: Pt = {Pat , Pbt , Pct } ; Qt = {Qat , Qbt , Qct }
i) Please show the CPI for the year of t = 2 (2 years after base year- at the base year t=0) which would contain elements belong to sets of Pt and Qt. (Hint: The formulation should include summation over goods for t = 0 and t=2 ).   

ii)Suppose at the base year (t=0) all prices are doubled. Construct the CPI under the new setting for the year of t=2. (5 points)

iii) Suppose that a year after the base year (at t=1) all prices are freezed, was not allowed to change. Additionally, suppose that all price controls were lifted at the second year after the base year (at t=2). Pta increased by %150, Pbt increased by %100 and Pct increased by %200 at the year of t=2. Under these settings calculate the inflation from the year of t=0 to the year of t =1 and the inflation from the year of t=1 to the year of t =2. (Please solve (only) 1.iii) by assigning numbers to elements for the set of Pt and for the set of Qt ) (10 points)

Answer 1

Only 3 products , i.e. a,b,c are used in contruction of CPI

Prices and Quantities are as follows

Prices	Quantities
Pat	Qat
Pbt	Qbt
Pct	Qct

For Base year t =0, next year t=1, and next to next year t=2

For t=0	For t=1	For t=2
Prices	Quantities	Prices	Quantities	Prices	Quantities
Pa0	Qa0	Pa1	Qa1	Pa2	Qa2
Pb0	Qb0	Pb1	Qb1	Pb2	Qb2
Pc0	Qc0	Pc1	Qc1	Pc2	Qc2

Price of basket in base year (t =0)
P(Basket0)	= Pa0*Qa0+Pb0*Qb0+Pc0*Qc0
Price of basket in first year (t =1)
P(Basket1)	= Pa1*Qa1+Pb1*Qb1+Pc1*Qc1
Price of basket in Second year (t =2)
P(Basket2)	= Pa2*Qa2+Pb2*Qb2+Pc2*Qc2

Answer to first question
CPI for Year 2	= (P(Basket2)/P(Basket0))*100
	= ((Pa2*Qa2+Pb2*Qb2+Pc2*Qc2)/(Pa0*Qa0+Pb0*Qb0+Pc0*Qc0))*100

Answer to second question

If prices in base year are doubled, new prices will be as follows

For t=0
Prices	Quantities
2*Pa0	Qa0
2*Pb0	Qb0
2*Pc0	Qc0

CPI for Year 2	=(P(Basket2)/P(Basket0))*100
	=((Pa2*Qa2+Pb2*Qb2+Pc2*Qc2)/(2*Pa0*Qa0+2*Pb0*Qb0+2*Pc0*Qc0))*100

For third question, assuming the prices to be 10 for all the three products in the base year.

Also, keeping the quantities as 10 for all the three products.

For t=0	For t=1	For t=2
Prices	Quantities	Prices	Quantities	Prices	Quantities
10	10	10	10	25	10
10	10	10	10	20	10
10	10	10	10	30	10

Price of basket in base year (t =0)
P(Basket0)	10*10+10*10+10*10	300

Price of basket in first year (t =1)
P(Basket1)	10*10+10*10+10*10	300
Price of basket in Second year (t =2)
P(Basket2)	25*10+20*10+30*10	750

CPI for Year 2	=(P(Basket2)/P(Basket0))*100
	=(750/300)*100
	250.00