A Laspeyres Index of prices is commonly used by economists to calculate the cost of buying a given basket of goods that is fixed to a base year, and then compared to its cost in subsequent years.
To most observers, at least at first glance, this may seem like the only sort of calculation necessary for estimating inflation and the changing cost of living. It certainly has the advantage of providing a clear record of changing prices relating to any given basket of goods as time passes.
However, it fails to account for changes in spending preferences as time passes. If consumers never changed anything about their preferred basket of goods, and simply bought more or less of the same items in that basket as their incomes/wealth increased/decreased, then the Laspeyres Index would work perfectly.
In the real world new goods replace old goods all the time, and so any given basket of goods will increasingly fail to account for the true changing cost of living as time passes, because the given basket of goods will become increasingly obsolete over time.
The Laspeyres Index formula is simply expressed as the cost of purchasing a given basket of goods today compared to its cost in a base year. The base year is set to a cost of 100, and subsequent years are compared to that base year.
Basket cost today/Basket cost in base year x 100
For example, if 4 baskets of goods that cost $100 in the base year now costs $640, the Laspeyres Index is calculated as 640/400 x 100 = 160
This gives a 60% increase in the cost of purchasing a basket compared to the base year cost. However, this cost overestimates the true cost of attaining an equal amount of utility, because it doesn't allow consumers to purchase an alternative basket of goods.
Since the Laspeyres index is based on the changing cost of a given basket of goods over subsequent years, it is focused on fixed consumption choices. In other words, it fails to account for changing preferences when the relative prices of individual items in that basket change.
With a spending budget of $100, let's assume that a consumer chooses to purchase 50 servings of cheese and 50 servings of biscuits when the price of either serving is $1. Now, if the price of cheese increases to $2 per serving while biscuits remain $1, it is unreasonable to imagine that consumers will continue to purchase 50 servings of both cheese and biscuits.
Instead the higher relative price of cheese, and lower relative price of biscuits, will lead consumers to prefer less cheese and more biscuits. A Laspeyres Index will simply calculate that the cost of living (i.e. the cost of attaining an equal amount of utility) will rise from $100 to $150 (50 servings of biscuits costing $50 and 50 servings of cheese costing $100) implying a 50% increase in the cost of living.
This gives rise to an upward bias in the true cost of living, for details on this sort of bias see my article about:
In reality, the consumer will prefer to adjust his/her preferred basket of goods given the relative price changes. Perhaps he/she can gain an equal amount of utility from 30 servings of cheese and 80 servings of biscuits, for a total cost of (30 x $2) + (80 x $1) = $140. In other words, an ideal cost of living index would show an increase of 40% rather than the 50% given by the Laspeyres Index.
Yes, the CPI is a Laspeyres Index, at least historically speaking. However, in recent years the CPI basket has tended to be altered more frequently in order to reflect the evolving pattern of consumer preferences when buying goods, so it does not give a perfect Laspeyres index number.
The advantage of amending the basket does outweigh the cost though, and increasingly so if a realistic cost of living index is required. Consumer preferences change all the time, and this needs to be reflected in an updated basket.
Consider, for example, how out-of-date a Laspeyres index would become over a long period of time when a basket of goods from 100 years ago would have been dominated by basic food items, and devoid of modern items like smartphones, foreign travel, online gaming and so on.
While the Laspeyres Index fixes a basket of goods in order to compare how its cost/price changes in subsequent years, the popular alternative is a Paasche Index i.e., an index that focuses on a current preferred basket of goods and look at what its price would have been in previous years.
The Paasche Index suffers from the opposite problem that the Laspeyres Index has i.e., it has a downward bias that tends to underestimate inflation and the cost of living. For more details, see my article about the Paasche Index.
The Fisher Index is simply a geometric average of the Laspeyres Index and the Paasche Index, and while it may or may not result in more accurate estimates, it still fails to give a perfect cost of living index. For details on that, and the difficulty of attaining perfection, see my article about the Fisher Index.