Question

Government survey takers determine that typical family expenditures each month in the base year 2010 are as follows: 25 pizzas @ $10 each; rent of apartment at $ 800 per month; Gasoline and car maintenance, $ 50; Basic phone services, $ 50.

In 2011, the survey determines that the price of pizza has risen to $12 each, apartment rent is $850, gasoline and car maintenance, $ 80 and basic phone services have dropped to $ 30 (Tabulate the data given) (6 points)

1. Find the CPI in year 2011 and the rate of inflation between base year 2010 and 2011
2. The family’s nominal income rose by 5% between the 2010 and 2011. Are they worse off or better off in terms of what their income is able to buy?

Answer 1

I have constructed the following table for summarizing the expenditure of the family:

Item	Quantity	Yearly Quantity	Price in 2010	Expenditure in 2010	Quantity in year 2011
Pizza	25	300	10	3000	12	3600
Rent	12	144	800	115200	850	122400
Gasoline and car	1	12	50	600	80	960
Phone expenses	1	12	50	600	30	360
Total				119,400		127,320

We are given the monthly expenses, hence I have made a separate column for annual expenses and computed the total expenditure.

We know:

A) CPI = Expenditure on the given basket in current year/ Expenditure on the given basket in base year

CPI for year 2011 = 127320/119400 = 1.066

This implies that Cost of Living has increased by 6.6% in 2011 compared to year 2010

B) Given the family's income has risen by 5%, the family is worse-off as the cost of living has increased by more than increase in income.

You will be able to better understand it by the following example:

Say, the family's income in year 2010 was $100,

then we can compute the Real Income in 2011 using the formula:

Real Income: Nominal Income/CPI

Since, nominal Income increased by 5%, the new income is $105, CPI = 1.066

Hence, real income in 2011 = 105/1.066 = 98.499

We can see the purchasing capacity has declined to $98.49 from $100

Hence, the family is worse-off