Question

Suppose a consumer only buys the three products given below:

Item	2013 Quantity	2013 Price	2019 Quantity	2019 Price
Haircuts	2	$10.00	2	$16.00
Hamburgers	5	$4.00	4	$5.00
DVDs	4	$15.00	10	$14.00

a.         Calculate the Consumer Price Index for 2019, using 2013 as the base year.

b.        Suppose that the price of gasoline in this country was $3.40 a gallon in 2019. What is the real price of gasoline in 2012 dollars?

c.         You decide to ask for a raise based on the rate of inflation as measured by the CPI. If the CPI in 2021 is expected to be 120, what percentage raise for 2021 should you ask for?

d.        You ask for the raise to protect yourself from inflation. What problems with the calculation of the Consumer Price Index might make the raise you asked for inaccurate measure of what is happening to prices?

Answer 1

a. For 2019, Cost of basket of goods = 2 * 16 + 4 * 5 + 10 * 14 = 32 + 20 + 140 = 192

Considering the same basket of goods and finding the price in 2013 dollars, 2*10 + 4 * 4 + 10 * 15 = 20 + 16 + 150 = 185

So CPI for 2019 = 192/186 * 100 = 103.22

b. Since 2012 prices are not mentioned, I will do the calculation for 2013.

Price of Gasoline in 2019 = 3.4

CPI = 103.22

So Price of Gasoline in 2013 = 3.4 / 103.22 * 100 = 3.29 per gallon

c. If the CPI of 2021 is 120 and the CPI of 2019 is 103.22, so the increase of CPI is (120 / 103.22) - 1 = 16.26%

So I would ask for a raise of 16.26% if there was no raise in 2020.

d. There are 3 issues which are not factored in while calculating for the CPI.

1. Substitution Effect: the change in consumer reaction towards change of prices of substitution goods

2. Introduction of new products.: Newer products change the perception of the consumers towards the old basket of products

3. Unmeasured Quality Changes: Change in quality which might increase or decrease the price of a good.

Because of this the CPI cannot be accurately calculated and thus the raise may not be in line.

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