We must fight shrinkflation – but let’s get the maths right first

Have you noticed how chocolate bars don’t seem to be as big as they were when you were a kid? Perhaps, as some companies suggest, it’s just that they feel smaller now that you’re bigger. But no, in fact, things really are getting smaller.

Previously, as prices for commodities like oil and wheat have surged, producers have been faced with a difficult choice to maintain their profit margins – hike the price of their product, or shrink its size (or sometimes both at once). Increasing the price is often seen as an unattractive option – consumers notice all too readily the increase in their shopping bill. Reducing the size of the product itself is more subtle and perhaps goes unnoticed – at least at the check-out.

Famously in 2016, Toblerone resected some of its famous ridges – increasing spacing between the remaining triangles – citing higher ingredient costs and a desire to maintain their signature product’s price for the consumer. With the box size staying the same, unwitting customers didn’t discover the missing triangles until after opening the prismatic cardboard container. But when they did, many were furious. One consumer described the new-look bars as “obscene” while another suggested Toblerone now resembled “a weird knock-off of itself”.

Other notable examples of shrinkflation from the last few years include Birds Eye reducing the number of fish fingers in a packet from 12 to 10 and Cadbury’s selling Creme Eggs in boxes of five rather than six. Reducing the number of items might be viewed at least as being an obvious change, but other shrinkages are perhaps more subtle – a WKD Original Vodka bottle shrinking in size from 330ml to 275ml is harder to pick up as the bottle essentially looks the same, just slightly scaled down. Similarly, most consumers probably wouldn’t notice the difference between a 1.5kg bag of frozen chips and a 1.25kg bag without looking carefully at the packaging, especially if the price stays the same.

Recently, Allison Pearson wrote a column in The Daily Telegraph suggesting many firms might be hiding behind “the climate” as an excuse to reduce packaging and to surreptitiously reduce the products inside at the same time.

Responding to a recent Office for National Statistics (ONS) study, which demonstrated that the lowest-priced supermarket items have risen in cost by 17 per cent in the year ending September 2022, Pearson suggested that “the metric system makes it a lot easier for manufacturers to con consumers”. As evidence, she suggested that “1lb down to 14oz would be picked up quickly, but 454g to 425g is less noticeable”, which is, of course, complete nonsense.

A drop from 100g to 95g would be just as noticeable as 1lb 4oz to 1lb 2oz. If anything the drop from 1lb to 14oz, or from say one pint to 18 fluid ounces, relies on consumers knowing that in the esoteric, non-uniform imperial system there are 16 ounces in a pound and 20 fluid ounces in a pint. I am confident that there is almost nothing for which the imperial system is better than the metric system.

Despite her outrage at “virtue-signalling companies” “diddling” consumers, a mathematical misunderstanding means that Pearson fails to properly expound the full extent of the issue of shrinkflation. She writes “So, Sensodyne toothpaste is the same price, but tubes are now 75ml instead of 100ml. That’s a 25 per cent price increase.”

No, it’s worse than that – it’s more like 33 per cent. Imagine the toothpaste cost £1, then previously consumers were paying £1 per 100ml. With the tube shrunk down to 75ml and the price kept the same, you’d need to add an extra 25ml to make up the 100ml volume. That’s a third more again than the 75ml size, meaning consumers would pay £1.33 per 100ml – a 33 per cent increase.

This is a common mistake. One of the factors that can catch us off guard when dealing with rises and falls in prices is the asymmetry in the percentage increase needed to recoup a decrease – or the increase in price per unit volume when the volume decreases. Perhaps surprisingly, even a small percentage fall always needs to be offset by a larger percentage rise. Similarly, a seemingly big percentage rise can be wiped out by a smaller percentage fall.

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If we invest £100 in a company and its share price falls by 10 per cent to £90, a 10 per cent rise from that position only takes us back up to £99. The rise required to get us back to £100 is just over 11 per cent.

For bigger percentage losses, the commensurate rise required to level up is even larger. For a fall in share prices of a quarter, the corresponding rise to recoup the loss is a third. For a fall of 50 per cent, the share price must double – a rise of 100 per cent – to leave us even.

But despite her maths mistake, Pearson is right to point out the extent of shrinkflation. Strangely though, she fails to mention the weakness of the pound as a possible reason for the increased price of many goods, particularly those that rely on imported commodities. While the pound remains weak and pay fails to rise in line with inflation, we can expect more shrinkflation, as companies seek to part us from our increasingly stretched budgets by stealth.

Kit Yates is a senior lecturer in the Department of Mathematical Sciences and co-director of the Centre for Mathematical Biology at the University of Bath