PLEASE SHOW THE WORK The CPI is calculated for a fixed market basket . It measur
ID: 2505623 • Letter: P
Question
PLEASE SHOW THE WORK
The CPI is calculated for a fixed market basket . It measures the change in the cost of the market basket from the base year until the current year . An index with the market basket fixed in the first year , like the CPI, is called a Laspeyres index. An alternative index , the Paasche index, is based on a market basket in the end year. Suppose that the base year is 2003 . Suppose that the market basket contains only two items , peanut butter and gasoline, and the quantities consumed in 2006 and 2007 are
Peanut Butter
Gasoline
2006
100 jars
50 gallons
2007
150 jars
45 gallons
Suppose that the price of peanut butter increases from $1 per jar in 2006 to $1.20 per jar in 2007 and the price of gasoline increases from$0.50 per gallon to $2.00 per gallon
A: Calculate the rate of inflation for the Laspeyres (CPI) index and the Paasche index
B: will inflation calculated using the Laspeyres index always exceeds inflation calculated with the Paasche index? (Using standard indifference curve analysis)
C: Workers often receive an adjustment in their wages equal to only a fraction of inflation as calculated using the CPI. In view of the preceding analysis, explain why workers would likely be better off than they were before if they were fully compensated for inflation. Would this also be the case if inflation was calculated using the Paasche index?
Peanut Butter
Gasoline
2006
100 jars
50 gallons
2007
150 jars
45 gallons
The CPI is calculated for a fixed market basket. It measures the change in the cost of the market basket from the base year until the current year. An index with the market basket fixed in the first year , like the CPI, is called a Laspeyres index. An alternative index , the Paasche index, is based on a market basket in the end year. Suppose that the base year is 2003. Suppose that the market basket contains only two items , peanut butter and gasoline, and the quantities consumed in 2006 and 2007 are Suppose that the price of peanut butter increases from $1 per jar in 2006 to $1.20 per jar in 2007 and the price of gasoline increases from$0.50 per gallon to $2.00 per gallon Calculate the rate of inflation for the Laspeyres (CPI) index and the Paasche index will inflation calculated using the Laspeyres index always exceeds inflation calculated with the Paasche index? (Using standard indifference curve analysis) Workers often receive an adjustment in their wages equal to only a fraction of inflation as calculated using the CPI. In view of the preceding analysis, explain why workers would likely be better off than they were before if they were fully compensated for inflation. Would this also be the case if inflation was calculated using the Paasche index?Explanation / Answer
1. Laspeyres2007 = 100*(100*1.2 + 50*2)/(100*1 + 50*0.5) = 176
inflation = Pneew - Pold/Pold = 176-100/100 = 0.76%
Paashe2007 = 100*(150*1.2 + 45*2)/(150*1 + 45*0.5) = 156.5
Inflation = 156.5-100/100 = 0.565%
2. Yes, in general. Consumers will substitute away from goods that are relatively more expensive to
goods that are relatively cheaper. Therefore, it will be more expensive to buy the original basket
than the new basket and so Laspeyres will exceed Paasche when there is inflation.
3. If we compensated workers for inflation using the Laspeyres index, the argument in part (b)
shows that they
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