The Formula to Calculate CPI Between a Base Year (Say

question 53

Essay

The formula to calculate CPI between a base year (say, Year 0) and another, specified year, say Year 1, is CPI=(Expenditure on basket in Year 1)/(Expenditure on basket in Year 0). Suppose an economy produces only two goods, food (f) and clothing (c). Let quantities and prices in Year 0 be q^f0, q^c0, p^f0 and p^c0, respectively, and let us adopt similar notations for Year 1, with the caveat that, for CPI, the quantities remain the same as in Year 0.
a.Calculate, using the notations in the problem, the expenditure on the basket in Year 0, the expenditure on the basket in Year 1, and the CPI.
b.Find the formulas for the share of each of the two goods in the expenditure on the basket in Year 0. Let w^f and w^c be the two shares. Show that the sum of the two shares is equal to 1. Let us multiply each of these shares by 100 and call them weights. Check that their sum is equal to 100.
c.Using the notations w^f and w^c for the two weights, re-write the CPI formula.
d.Replace w^f and w^c in the formula that you just wrote and compare the result to the formula of definition for CPI. Are they identical? If not, what changes do you need to operate in order to make them identical?
e.Did you need to know quantities in Year 1 in order to compute CPI?

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