Value of money and index numbers: construction, problems and uses

1. Value of money

The value of money is its purchasing power: the quantity of goods and services one unit of money can buy. It is the reciprocal of the general price level: V_m = 1/P. When prices double, the value of money halves. The value of money is therefore not the value of the paper or metal but its command over goods.

Two distinctions are often asked:

• Internal and external value. Internal value is purchasing power over domestic goods (measured by domestic price indices); external value is purchasing power over foreign goods, shown by the exchange rate.
• Theories of the value of money. The quantity theory explains it by the supply of money (next note); the cash-balance version by the demand to hold money; Keynes’ income theory by aggregate spending.

Because the general price level cannot be observed directly, changes in the value of money are measured by index numbers.

2. Meaning and definitions of index numbers

An index number is a statistical device that measures the relative change in a group of related variables (prices, quantities, wages) between two periods or places. The base period is given the value 100.

• Croxton and Cowden: “Index numbers are devices for measuring differences in the magnitude of a group of related variables.”
• Spiegel: “An index number is a statistical measure designed to show changes in a variable or a group of related variables with respect to time, geographic location or other characteristics.”

Features: they are expressed in percentages; they measure relative, not absolute, change; they are a specialised kind of average; and they measure changes that cannot be measured directly.

3. Kinds of index numbers

• Price index numbers: wholesale price index (WPI), consumer price index (CPI). In India the WPI is compiled by the Office of the Economic Adviser (DPIIT) and the CPI (rural, urban, combined) by the National Statistics Office, MoSPI. The RBI’s inflation target is set in terms of CPI-combined.
• Quantity index numbers: the Index of Industrial Production (IIP).
• Value index numbers: changes in total value (price × quantity).
• Simple (unweighted) and weighted index numbers.

4. Worked example: simple and weighted indices

Base year prices p₀ and quantities q₀; current year p₁ and q₁:

1. Simple aggregative: Σp₁/Σp₀ × 100 = 53/43 × 100 = 123.26.
2. Simple average of price relatives: relatives are 120, 125, 120, 125; mean = 490/4 = 122.5.
3. Laspeyres (base-year quantities as weights): Σp₁q₀/Σp₀q₀ × 100 = 218/178 × 100 = 122.47.
4. Paasche (current-year quantities as weights): Σp₁q₁/Σp₀q₁ × 100 = 257/210 × 100 = 122.38.
5. Fisher’s ideal index: the geometric mean of the two, √(122.47 × 122.38) = 122.43.

Reading: prices rose by about 22.4 per cent, so the value of money fell to 100/122.43, about 82 per cent of its base-year level. Fisher’s index is called “ideal” because it satisfies both the time-reversal and the factor-reversal tests. Laspeyres tends to overstate a rise in prices (it ignores consumers switching away from dearer goods) and Paasche to understate it.

Consumer price index: methods

A consumer price (cost of living) index measures the change in the cost of a fixed basket of goods and services bought by a defined group (industrial workers, agricultural labourers, urban households). After a family budget enquiry fixes the basket and the weights, it is computed by one of two methods, which give the same answer:

• Aggregate expenditure method: Σp₁q₀ / Σp₀q₀ × 100, that is, Laspeyres with base-year quantities.
• Family budget (weighted relatives) method: ΣIW / ΣW, where I is the price relative (p₁/p₀ × 100) of each item and W its weight, the base-year expenditure p₀q₀. On the figures above: (120×40 + 125×48 + 120×50 + 125×40) / 178 = 21,800/178 = 122.47, the same as Laspeyres.

5. Steps in constructing a price index

1. Purpose. Decide what the index is to measure (cost of living of industrial workers, wholesale prices) because every later choice depends on it.
2. Choice of base year. A normal year, free from war, famine, boom or slump, and not too distant. The base may be fixed or chain (each year on the previous year).
3. Selection of commodities. Representative items, of standard quality, relevant to the group whose prices are measured.
4. Collection of prices. From representative markets and at regular intervals; wholesale or retail as the purpose requires.
5. Choice of average. Arithmetic mean (simple) or geometric mean (more accurate for relatives, but harder).
6. Weighting. Items are given weight by their importance in the budget, by quantity or by value.
7. Choice of formula (Laspeyres, Paasche, Fisher) and computation.

6. Difficulties (problems) in constructing index numbers

• Selecting a normal base year: no year is perfectly normal, and a base grows out of date.
• Selecting commodities: consumption patterns change; new goods appear and old ones disappear.
• Changes in quality: a higher price may reflect better quality, not inflation.
• Collecting prices: prices differ between places and shops; retail data are hard to collect.
• Weighting: weights are arbitrary to some degree and change over time.
• Choice of average and formula: different methods give different results, as the example above shows.
• International comparison: differences in consumption habits make index numbers of different countries hard to compare.

7. Uses (importance) of index numbers

• Measuring the value of money and the rate of inflation or deflation.
• Guide to policy: monetary policy (inflation targeting on CPI), fiscal and trade policy.
• Wage fixation and dearness allowance: DA of government and industrial employees is linked to the Consumer Price Index for industrial workers.
• Deflating national income: converting money income into real income.
• Business decisions: forecasting, studying trends and trade cycles.
• Indexation of contracts and taxes: adjusting long-term payments for changes in prices.
• Measuring changes in output and trade (quantity indices such as IIP).

Limitations. Index numbers are approximations; they measure average changes, not the experience of any one person; they are based on samples; and they may be misused if the base or the items are badly chosen.

How this is examined

For the essay, define, list kinds, then set out the steps and the difficulties side by side (each step has a matching difficulty: base year, commodities, prices, weights, average). For a six-mark “uses of index numbers”, give five or six uses with one line each. If a numerical is set, use the table above: compute p₁q₀, p₀q₀ and so on in columns, show the formula, and state what the result means for the value of money.