Prices

1.2.1: Using your loaf

Cade: There shall be in England seven halfpenny loaves sold for a penny; the three-hooped pot shall have ten hoops; and I will make it felony to drink small beer.

(William Shakespeare, Henry VI, Part 2, written in 1594)

In this quotation, the character Cade anticipates the good times that are sure to follow after the revolution. The notion of the ‘halfpenny loaf? is interesting, as is the question of whether most people in Shakespeare's Elizabethan England were able to afford it. It raises the general question of how well-off different people actually were in the late sixteenth century when the play Henry VI, Part 2 was written, and whether, in material terms, people are much better off now. This is the central question which drives this Unit.

This is a problem-solving process: you will work through a series of stages to try to answer the question ‘Are people getting better off?? The first stage here is to try to specify the problem more precisely.

Activity 1: Using your loaf

Can you think of a way of using the loaf of bread as a very rough measure of how the standard of living has changed between the late sixteenth century and today? What information would you need? How would you go about finding the necessary information? What problems of measurement and comparison do you foresee?

Take a few minutes to write down your ideas before reading on.

Clearly, the price of a loaf of bread has greatly increased since 1594. However, prices and earnings have both increased, so simply looking at prices alone will not provide a useful basis of comparison. Better measures are the proportion or percentage of someone's daily or weekly earnings required to buy a loaf of bread. Making such a comparison requires further pieces of data: for example, the price of a loaf of bread today, and typical earnings in 1594 and today.

With this formulation of the problem, there is a need to collect some appropriate data. Note the use of the word data. In this context, data means information, usually appearing in the form of numbers. Data is a plural word (the singular, a datum, refers to a single fact or figure). In everyday usage, the word ‘data? is often used in the singular, but this Unit treats the word as a plural noun.

But collecting the data raises further questions. First, what about the price of a loaf of bread today? In shops selling bread, there are many types—white, brown, granary, wheaten, baps, batches, French sticks, and so on—and a variety of sizes—large, medium and small. Not surprisingly, each of these many options comes at a different price. So, what is the price of a loaf of bread today? The comparison perhaps requires choosing a loaf that corresponds most closely to the sort of loaf that people were buying four hundred years ago. Did they go in for giant loaves that would see a family of twelve through the entire week or were Elizabethan loaves gobbled up in a single bite?

Suddenly this is getting much harder! This is rather specialised knowledge that most people are unlikely to have. However, exact figures are not necessarily appropriate here, so let us choose the most popular large loaf that most people these days seem to put in their shopping trolleys: a large white sliced loaf. In 2005, this was priced at 60p in a local UK supermarket.

Next, what was a typical wage in 1594? This required a library search, and, with a little help from the computer, a journal article by E.H. Phelps-Brown and Sheila V. Hopkins, called Seven Centuries of Building Wages, came to light. It revealed that the daily wage of a building labourer in southern England between 1580 and 1629 was 8 old pence (there were 240 old pence in a pound).

Finally, what could stand for a typical wage today? For reasons of comparability, it seems to make sense to choose a modern UK building labourer and a figure of roughly £360 per week seems a reasonable ‘estimate? in 2005. This £360 figure is based roughly on data from the UK Government New Earnings Survey.

Now that all the required data are collected, the next stage in solving the problem is to analyse them. This will involve calculating the proportion or percentage of daily earnings required to buy a loaf of bread both in 1594 and in 2005.

Let's summarise the data we have in a table.

Table 1 Summary of wages and the price of a loaf, 1594 and 2005

Activity 2: Taking in the table

Pause for a few moments and reflect on what this table of data means to you.

• ♦ Write down briefly in your own words what the table is telling you.

• ♦ Make a brief note of anything that puzzles you.

When constructing a table of this kind, one of the first checks to make is to ensure that the units are compatible. Clearly, one old penny in 1594 was worth much more in terms of what it could buy than one new penny today. However, since the necessary calculations will run down the columns of the table, there are no direct comparisons between old money and new money, so the relative worth of the coinage will not cause a problem. However, the money units within a column need to be the same. In the 1594 column they already are, but for 2005 we need to use either pounds or pence, not both.

Another difficulty still to be dealt with is the basic wage unit. This is quoted at a daily rate for 1594 and at a weekly rate for ‘now?. In order to be able to make proper comparisons, the same period of time should be used. So one of the rates must be converted. It does not really matter which, so, to keep the numbers small, let us use a daily rate.

However, the best procedure for working out a daily rate is not obvious. Although there are seven days in a week, how many working days are there in a working week now and how many were there in Elizabethan times? It could be five, six or seven or something between. Elizabethan workers probably had Sundays off, so their week?s wage was probably six times their daily wage. So, on balance, it makes sense to divide the weekly rate ‘now? by six to get a daily rate. However, it is worth pausing to observe that this is one of many situations where ambiguity and uncertainty crop up in statistical work. In general, problems and investigations which involve these sorts of subjective judgements are not so much ‘solved? as ‘resolved?.

A weekly wage of £360 works out at £360 ÷ 6 which is £60 or 6000p per day.

Table 2 Summary of wages and the price of a loaf, 1594 and now-daily rates

Note that Table 2 shows the same information as Table 1 but with daily rates quoted in pence in each case. Now express the cost of a loaf as a percentage of a typical daily wage.

The cost of a loaf in 1594 as a proportion of a typical daily wage is:

The cost of a loaf in 1594 as a percentage of a typical daily wage is 100 times this:

This means that if, in 1594, a worker chose to buy a loaf of bread, it would have cost him about 6% of his daily wage.

Activity 3: Today's figures

Calculate the cost of a loaf today as a proportion and as a percentage of the typical current daily wage. Compare the result for today with the corresponding figure for 1594. Do the results suggest people are better off today than then?

Discussion

The cost of a loaf today as a proportion of a typical daily wage is:

The cost of a load today as a percentage of a typical daily wage is:

This is considerably less than in 1594, suggesting that people are better off now.

Having collected and analysed the data, the next task in the problem-solving process is to interpret the results. The percentage figure for 1594 at 6.25% is just over six times the corresponding figure for 2005 of 1%. In other words, as a percentage of earnings, the cost of a loaf of bread has dropped to about one sixth in real terms over the past four hundred years. This seems to suggest that people have got better off—about six times as well-off, in fact.

Comparison over time based on the cost of a simple item such as a loaf of bread is relatively straightforward. But is it appropriate as a way of measuring how well-off people are? It is possible that the price of bread is untypical of price changes and so some other goods should be used. But what else might you choose? Clearly, to choose items whose existence are exclusive to recent times, such as cars, computers and electricity bills, is inappropriate. Yet to exclude these items will have the effect of denying their contribution to how well-off or otherwise you may feel today. For similar reasons, the price of quill pens, ox-drawn ploughs and hunting spears should probably be excluded.

Even things which existed both then and now, like houses, clothing and heating, are so different in nature as to be, essentially, different items. Furthermore, it is quite possible that many of the goods and services that made living in Elizabethan times bearable, if not pleasurable (the acquisition of fresh vegetables, child care, and so on), were not bought with cash but ‘paid for? in kind or by favour or grown for personal consumption. The tax system has also altered considerably over the period, as has the range of services provided subsidised or free by the state (health, education, social welfare, etc.), which were largely absent in this form four hundred years ago.

A final complication is that the data on which the previous analysis was based were restricted to a particular group within Elizabethan society. The workers were building labourers in southern England. This is a very particular group and it would be dangerous to draw universal conclusions covering other people of the time. Today, earnings vary enormously both within and between occupations and similar inequalities certainly operated in the late sixteenth century.

In summary, this investigation which started out with a deceptively simple question has become something of a puzzle! There is a lot of information that we simply do not know and have had to make sensible guesses about. This is a more common state of affairs than is popularly realised! How much of the quantitative information supplied by government, advertisers and the media might have been constructed in this way? Try to develop a habit of considering whether facts presented to you are sensible and consistent, and checking other people?s sources of information.

An important thread that has run through this subsection has been problem solving. You have started to learn about some ideas in statistics through addressing this problem. A number of key stages in the solving of a problem have been employed. They concern clarifying the problem, the collection and analysis of the data, and their interpretation. These stages are used from time to time in this Unit.

Except for third party materials and otherwise stated (see terms and conditions), this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence