Question

plz solve step by step and clearly show which formula you used

Q1 The Consumer Price Index is a measure of the average price of goods that a typical household consumes. To calculate the CPI, a basket of 700 goods and services that reflects the U.K. Society's buying habits is used to construct the index. Assume that U.K. Consumers buy only meat and movie tickets as their basket of goods and services. Below is a representation of the kind of data that the Office for National Statistics collects to construct the consumer price index. In the base year, 2010, both the prices and quantities of goods and services purchased are collected. In subsequent years, price changes are calculated for the same set of goods and services. The Office uses the Inflation Calculator to measure by how the cost of goods and services has changed over time. The Inflation Calculator can calculate the future cost of goods and services based on price changes from a date in the past. Alternatively, it can calculate the past cost of goods and services based on price changes from a date in the future. The data: In an average week in 2010, the Office for National Statistics searches thousands of households and determines that the average consumer purchases two pounds of meat and one ticket in a month. In subsequent years, the price per pound of meat and per movie ticket are found below. Q1 £4,8 £2 £5 £5,2 Year Price of Meat Price of Movie Ticket 2010 2011 £1,9 2012 £2 £4,9 2013 £2 2014 2015 £2.1 £5,3 What is the cost of the consumer price basket in 2010? What is the cost of the consumer price basket in 2011 and in subsequent years? Represent the cost of the consumer price basket as an index number in the year 2010 to 2015. Set the value of the index number equal to 100 in 2010. Calculate the annual rate of inflation using the percent change in the value of the index number between each year from 2010 through 2015. You would find it helpful to fill in the table below

Answer 1

CPI is calculated by the price of the basket. The price of the basket is the sum of the current market prices multiplies by the quantity of the goods.
CPI = $\tiny \sum$ ( current Market Price * Quantity )

a) For 2010,
( 2 * 2 ) + 5 = 9

b) For 2011,
( 2 * 1.9 ) + 4.8 = 8.60

Year	Meat	Movie Ticket	Basket
2010	2	5	9.00
2011	1.9	4.8	8.60
2012	2	4.9	8.90
2013	2	5	9.00
2014	2	5.2	9.20
2015	2.1	5.3	9.50

c) Now the cost of the basket in 2010 is the base year CPI value
CPI in 2010 = 100

CPI_t = ( Basket Cost in Year t * 100 ) / ( Base Year Basket Cost )
2011,
( 8.6 * 100 ) / 9 = 95.56
2012,
(8.9 * 100) / 9 = 98.89

Year	Meat	Movie Ticket	Basket	CPI
2010	2	5	9.00	100.00
2011	1.9	4.8	8.60	95.56
2012	2	4.9	8.90	98.89
2013	2	5	9.00	100.00
2014	2	5.2	9.20	102.22
2015	2.1	5.3	9.50	105.56

d) Inflation can be calculated by the following method
Inflation = ( (Current CPI Value / Previous Year CPI Value) - 1) * 100

for 2011,
((95.56 / 100) -1) * 100 = -4.44%
2012,
((98.89 / 96.56) - 1) * 100 = 3.49%

Year	Meat	Movie Ticket	Basket	CPI	Inflation %	Inflation Base 2010
2010	2	5	9.00	100.00	N.A.	N.A.
2011	1.9	4.8	8.60	95.56	-4.44	-4.44
2012	2	4.9	8.90	98.89	3.49	-1.11
2013	2	5	9.00	100.00	1.12	0.00
2014	2	5.2	9.20	102.22	2.22	2.22
2015	2.1	5.3	9.50	105.56	3.26	5.56