Sunday 13 February 2022

Quibans 104: Basket Case

This Quibans comes from a BBC story (widely reported elsewhere too) about the rise in price of a basket of items.

Cost of pasta and tinned tomatoes jumps as shop prices rise

The price of pasta, tinned tomatoes and strawberry jam jumped last year as the cost of supermarket staples rose, new figures for the BBC suggest.

Overall, the price of a basket filled with 15 standard food items rose by £#.## or 8%, in just one year.

Changes in the average cost of the food items at Asda, Morrisons, Sainsbury's and Tesco were tracked by retail research firm Assosia.

Some items fell in price, with carrots and mild cheddar seeing small declines.

The same basket of food made up of items from the cheaper "value" ranges at the supermarkets recorded an overall fall in price, down 45p, or 4%. But within that, items such as pasta and vanilla ice cream saw rises of more than 6%.

Other items the firm tracked in the new research for BBC News included tortilla chips, fish fingers, honey, blueberries, carrots and lemons.

Although official figures suggest that the overall cost of living increased by 5.4% in the year to December, this number - known as the inflation rate - can mask some steep rises seen at the tills, especially on everyday items.

There are many factors that can make it difficult to track how prices are changing for households, such as promotions at supermarkets or a lack of availability of certain products.

 

Questions

1)  Some of the numbers/percentages in the first half of the graphic have been hidden.  Work them out.

2)  There are two errors in the numbers in the second half of the graphic.  Can you spot them without needing to use a calculator?

3)  What is odd about the value range potatoes?

4)  What percentage of the cost of a standard range basket of goods in 2022 is each of the items?

5)  Which of the three products in each range is the most expensive compared to its weight?

6)  If the baskets of goods had only consisted of the three products shown here, what would the percentage change in the cost of the basket have been?

7)  If (from the standard range) you bought an equal weight of spaghetti and potatoes, what would the percentage increase in price be?

8)  The standard range potatoes have increased by 2p and by 2%.  You would expect these two numbers to be the same only if the original price was £1.  Can you explain why it is still possible here?  What is the smallest original price that would mean a 2p increase is also a 2% increase?  What the biggest original price that would work?

9)  What if we wanted an increase of 20p and an increase of 20% ?  What is the smallest price that works?

10) The article mentions some of the items that were used to form the basket of food.  What do you think of their decisions? 

 

Answers

Q1)  Some of the numbers/percentages in the first half of the graphic have been hidden.  Work them out.  A1)  The original graphic (without the hidden numbers) is below.

Q2)  There are two errors in the numbers in the second half of the graphic.  Can you spot them without needing to use a calculator?  A2)  The total basket has gone from £11.24 to £10.80, which looks like a fall of 44p, but the change is given as 45p.  If the numbers have been rounded to give £11.24 to the nearest penny, but the original values have been used to work out the 45p difference (which is possible) then that means the researchers are using 5 significant figures in their calculations, which seems unlikely to be appropriate/accurate!

If tomatoes going from 28p to 29p gives a 4% increase, then an increase from 27p to 28p in the cost of pasta seems unlikely to be 6%.  (It is actually an increase of 3.7%, compared to the 3.6% for tomatoes.)

Q3)  What is odd about the value range potatoes?  A3)  They cost more than the standard potatoes! 

Q4)  What percentage of the cost of a standard range basket of goods in 2022 is each of the items?  A4)  Pasta is 4%, tomatoes are 3% and potatoes are 6%.

Q5)  Which of the three products in each range is the most expensive compared to its weight?  A5)  In 2022, in the standard range, 1kg of pasta costs 144p, 1kg of tomatoes is 112.5p and 1kg of potatoes is 39.2p (pasta is the most expensive).  In the value range, 1kg of pasta costs 56p, 1kg of tomatoes is 72.5p and 1kg of potatoes is 36.4p (tomatoes are the most expensive). 

Q6)  If the baskets of goods had only consisted of the three products shown here, what would the percentage change in the cost of the basket have been?  A6)  Standard: 18% increase.  Value: 6% decrease.

Q7)  If (from the standard range) you bought an equal weight of spaghetti and potatoes, what would the percentage increase in price be?  A7)  I multiplied the pasta figures by 5 to give the same weight as the potatoes.  The increase is 30.5%.

Q8)  The standard range potatoes have increased by 2p and by 2%.  You would expect these two numbers to be the same only if the original price was £1.  Can you explain why it is still possible here?  What is the smallest original price that would mean a 2p increase is also a 2% increase?  What the biggest original price that would work?   A8)  A 2p increase on 96p is a 2.0833% rise.  This is rounded (reasonably) to 2%.  If the price goes from 80p to 82p then the percentage increase is exactly 2.5%, so 81p is the smallest price that would see a 2p rise also being a 2% (rounded to the nearest whole number) increase.  The biggest price that works is £1.33

Q9)  What if we wanted an increase of 20p and an increase of 20% ?  What is the smallest price that works?  A9)  98p

Q10) The article mentions some of the items that were used to form the basket of food.  What do you think of their decisions?  A10)  I was surprised to see lemons and blueberries were included.  I expected to see the basket include the 15 most common items bought (so apples and bananas might be included?)  Are tortilla chips really more commonly bought than crisps?  

Source: https://www.bbc.co.uk/news/business-60290236

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