(a) Using the data in Problem 10.3, calculate the expenditure shares on each fuel in 1984 and the individual price index number series for each fuel, with 1984 = 100.

(b) Use these data to construct the Laspeyres price index using the expenditures shares approach. Check that it gives the same answer as in Problem 10.3(a).

Problem 10.3

The following data show energy prices and consumption in 1984–88 (analogous to the data in the chapter for the years 1999–2003).

(a) Construct a Laspeyres price index using 1984 as the base year.

(b) Construct a Paasche price index. Compare this result with the Laspeyres index. Do they differ significantly?

(c) Construct Laspeyres and Paasche quantity indices. Check that they satisfy the conditions that Eⁿ = P_L × Q_P etc.

Prices Coal (/tonne) Petroleum (/tonne) Electricity (/MWh) Gas (/therm) 1984 49.60 149.70 28.89 0.2634 1985 51.00 151.75 30.02 0.2841 1986 49.64 72.98 30.07 0.2378 1987 47.50 78.10 28.92 0.2196 1988 43.10 55.04 30.02 0.2175