Question

Suppose there are only two goods in the economy, apples and oranges, and the market basket used to complete the CPI is 8 apples and 4 oranges. Assume the base year is 2018 and suppose you have the following information about prices: January 1, 2018: Price for an apple= $1 Price for an orange= $1 January 1, 2019: Price for an apple= $1.02 Price for an orange= $1.08 Consider an individual receives a fixed income of $36 on January 1st, 2018 and used this to buy 24 apples and 12 oranges.

1. Suppose their income is indexed to the CPI. How much will they receive on January 1, 2019?

2. Since oranges are relatively more costly than apples on January 1, 019, the fixed income recipient may decide to consume more apples. Suppose they choose to consume 30 apples. How many oranges will they consume?

3. Are they happier with the 2018 allocation or the 2019 allocation? Explain.

Answer 1

1. Consumer Price Index or CPI meaures the change in price level of a consumption bundle that is relevant for households

CPI = (cost of consumption bundle in 2019/ cost of bundle in 2018) * 100

Cost of bundle in 2019 = cost of apples * 8 apples + cost of oranges * 4 oranges= 1.02 (8) + 1.08 (4) = 12.48

Cost of the bundle in 2018 = cost of apples * 8 apples + cost of oranges * 4 apples= 1* 8 apples + 1 * 4 apples = 8 + 4 = 12

(Multiplied cost of apple and orange by 8 and 4 respectively as it is given in the question that CPI is computed using this exact no of apples and oranges)

CPI = (12.48/ 12) * 100 = 1.04 * 100 = 104

Next, we need to find the CPI adjusted income of 2019.

In base year 2018, CPI = 100 and income = $36

In current year 2019, CPI = 106, what is the equivalent income of $36 in 2019?

We can find it by setting up a ratio like this

X / 36 = 104 / 100

X = (104 / 100) * 36 = 37.44

Hence the inflation adjusted income is $37.44

2. Fixed income consumer, income = $36

No of apples = 30

Income =( Price of apple * quantity of apples ) + (price of orange * quanity of orange)

36 = ( 1.02 * 30 ) + ( 1.08 * y) = 30.6 + 1.08y

5.4 = 1.08y

y = 3

Hence, 3 oranges are consumed under the new prices.

3. A consumer with fixed income is likely to be happier with the 2018 allocation than 2019 allocation.

In 2018, they could consume total of (24 + 12) = 36 fruits, but in 2019, they could consume only ( 30 + 3) = 33 fruits. Thus the consumer is left worse off in 2019 allocation.