Question

Essay Question: Consider the following table. Suppose Bureau of Labor Statistics (BLS) conducted the survey in year 2010 and based on the survey the CPI basket is comprised of 20 pound of chicken and 10 pound of beef. But as you see in the table, the price of beef increased too much in 2012 compare to the price of chicken. So rational consumers substituted between chicken and beef in 2012 and consumed 5 pound of beef and 25 pound of chicken to minimize the cost of living.

Year	Beef	Chicken
2010	$3	$3
2011	$4	$4
2012	$7	$5

1. Construct CPI for years 2011 and 2012. Calculate the inflation rate in 2012.
2. Calculate the actual cost living in 2012 and calculate the % increase in the actual cost of living in 2012 compare to 2011. Hint: Actual Consumption basket in 2011 is 10 pound of beef and 20 pound of chicken while consumption basket in 2012 is 5 pound of beef and 25 pound of chicken.

Answer 1

A. Here I have considered 2010 as base year

Consumption basket 2010, 20 lbs chicken and 10 lbs of beef

CPI(2010) = $3*10 + $3*20 = $ 90

Cost of CPI basket in 2011= $ 4*10 + $ 4*20 = $ 120

CPI 2011 = 100*(120/90) = 133.33

Cost of CPI basket 2011 = $ 7*10 + $ 5*20 = $ 170

CPI 2012 = 100*(170/90) = 188.88

Inflation = (188.88-133.33)/133.33 = 41.66%

B. Actual consumption of year 2011 (10 pounds of beef and 20 pounds of chicken)

Cost of basket in 2011 = 4*10 + 4*20 = $ 120

Consumption of 2012 = (5 pounds of beef and 25 pounds of chicken)

Cost of basket in 2012 = 7*5 + 5*25 = $ 160

Percent increase in cost of living

% increase in cost of living = 33.33%

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