Question

19. (16 POINTS) Suppose that the representative basket of goods consumed in the economy in a year is made of: 150 lbs of bread, 80 bottles of water and 50 T-shirts. Prices (in USD) of each of these items, across different years, are reported in the following table Year 1 lbs of bread 1 bottle of water 1 T-shirt 2008 S2 2009 $2.3 2010 $2.6 2011 $2.8 2012 S3 $1.2 $1.2 $1.35 $1.8 $1.8 $15 $18 $18 $18 $25 (a) Compute the value of the basket in each year (b) Compute the CPI price index for each year, using 2008 as base year (c) Compute the CPI price index for each year, using 2010 as base year (d) Compute the inflation rate of 2009, 2010, 2011 and 2012

Answer 1

A consumer price index (CPI) is used to measure changes in the price level or cost of living of the people in a country by comparing the cost of a given basket of goods purchased by a consumer in a year with the price of the same basket in some base year.

The methods of constructing a consumer price index are:

1. Choose a fixed basket of goods the consumer purchase.

2. Choose a base year.

3. Find the price of each item in the basket. (For base year and the year of comparison)

4. Find the total cost of basket of goods in base year and the year of comparison (Multiply the price with quantity of items purchased)

5. Divide the cost of basket in the year of comparison with the cost of basket in the base year.

6. Multiply the result with 100 in order to get percentage changes in the cost of basket between the base year and the year of comparison.

a. The Value of basket in each year.

Year	Price of bread(in $)	Quantity of bread purchased	Total amount	Price per bottle of water(in $)	Quantity of bottle purchased	Total amount	Price of T-shirt (in $)	Quantity of T-shirt purchased	Total Amount	Total cost on the basket in each year
2008	2	150	300	1.2	80	96	15	50	750	1146
2009	2.3	150	345	1.2	80	96	18	50	900	1341
2010	2.6	150	390	1.35	80	108	18	50	900	1398
2011	2.8	150	420	1.8	80	144	18	50	900	1464
2012	3	150	450	1.8	80	144	25	50	1250	1844

b. Consumer Price index for each year taking 2008 as base year.

Consumer Price index for the year 2009 is 1341/1146×100=117.2

Consumer Price index for the year 2010 is 1398/1146×100=121.9

Consumer Price index for the year 2011 is 1464/1146×100=127.8

Consumer Price index for the year 2012 is 1844/1146×100=160.9

c. Consumer Price index for each year by taking 2010 as base year.

Consumer price index for the year 2008 is 1146/1398×100=81.97

Consumer price index for the year 2009 is 1341/1398×100=95.92

Consumer price index for 2010 is 121.9 (as per 2008 base year)

Consumer price index for the year 2011 is 1464/1398×100=104.72

Consumer price index for the year 2012 is 1844/1398×100=131.90

d. Inflation Rate taking 2010 as base year .

To find the inflation rate, minus the previous year CPI from the current year CPI and divide it with previous year CPI and multiply with 100.

The inflation rate for the year 2009 is 95. 92-81.97/81.97×100=17.01

The inflation rate for the year 2010 is 121.9-95.92/95.92×100= 27.8

The inflation rate for the year 2011 is 104.72-121.9/121.9×100= 14.09

The inflation rate for the year 2012 is 131.90-104.72/104.72×100= 25.95