Bob Cratchit was NOT making less than the minimum wage.

Bob Cratchit was responsible for maintaining Scrooge’s account books, a job that involved much more than that of a simple bookkeeper today. His salary of 15 shillings a week made him poorly paid. Dickens chose that salary because he knew his readers would know this would be a low salary for such a position.
This salary, however, means he made more than the minimum wage. In today’s currency Cratchit’s annual wage would have a relative earnings value of £32,000 or $43,000. Today full-time work involves 2,000 hours per year (40 hours per week for 50 weeks). If we divide his computed annual relative earnings by 2,000 we find Cratchit’s hourly wage was £16 or $21.44.
The current minimum hourly wage in the United Kingdom is £ 8.91 or 55% of Cratchit’s hypothetical wage there. The current national minimum hourly wage in the United States is $7.25 or 34% of $21.44.
Thirty states, D.C., Guam and the USVI have a higher level. California at $13.00, Massachusetts at $13.50, Washington at $13.00, and the District of Columbia at $15.20 are the highest. None more that 70% of his calculated wage rate of $21.44.

What is the relative value of Bob Cratchit’s 15 shillings a week in 1843?

In Charles Dickens A Christmas Carol, Ebenezer Scrooge paid his clerk Bob Cratchit 15 shillings a week. What is the present-day equivalent of those 15 shillings? The MeasuringWorth comparator gives two answers.

In 2020, the real wage value of 15 shillings from 1843 is £75.28.
In 2020, the relative labour earnings value of 15 shillings from 1843 is £611.30

Why are they so different and what do they mean? The reason is that they are answers to two quite different questions. While they are both measured in British pounds, they should NOT be compared to each other.

The real wage is computed using a retail consumer price index of a basket of goods and services. In principle, by inflating the collection of goods (e.g., a goose) the average family could buy with 15 shillings, the index says that would be similar to a collection of goods an average family in today’s London could buy with £75.28. This is a totally unrealistic number!

Today a family of six could not afford the groceries to make a Christmas dinner for £75.28, let alone live for week. If we assume that Cratchit worked 10 hours a day for six days each week, that £75.28 rate would be £1.26 an hour. The current national minimum or living wage rate in the UK is £8.91 per hour. Even for workers under the age of 18 it is £4.60.

Price indexes do not reflect the actual increases in the cost of living over long periods of time because the market baskets purchased by representative consumers have changed so much. For example, food purchases constituted roughly 50% of the index in the 1840s; food is less than 10% today.* The Cratchits could not have purchased most of the goods in today’s basket because they didn’t exist in 1843.

The relative labour earnings is computed using an index of average earnings paid to workers. Thus, the “relative” wage of a worker who earned 15 shillings a week in 1843 is £611.30 today. At 52 weeks of work, that would correspond to about £32,000 a year. Bob Cratchit was responsible for maintaining Scrooge’s account books. The average UK accountant today earns a salary of £62,042 per year; the average bookkeeper, £26,848 per year. While Cratchit’s job may not have required a CPA, it involved much more than the tasks required of the average bookkeeper today. The fact Scrooge was paying Cratchit an amount slightly above that of an average bookkeeper speaks to Scrooge’s miserliness.

*The CPI and RPI are better designed to compute inflation rates than the “cost of living” over long periods on time.