This week my ECONS101 class has been covered constrained optimisation, with a particular focus on consumer choices. So, I was interested to see this article by Puneet Vatsa and Alan Renwick (both Lincoln University) in The Conversation yesterday, talking about food price rises:
The rising price of food has been making headlines for the past decade. But prices have not been rising consistently across all food groups – and this has major health implications for New Zealanders...
Although food price increases have been noticeable over the long term, the change in relative prices — the cost of one food category compared to another — often goes unnoticed. Nevertheless, these relative price changes are crucial as they influence consumer choices, often subconsciously.
Our new research examines Stats NZ data between 2014 and 2023 on the price of 85 food items collected from 560 retail outlets – supermarkets, greengrocers, fish shops, butchers, convenience stores, restaurants, and outlets selling breakfast, lunch, and takeaway foods – in 12 urban areas.
Between July 2014 and March 2023, prices of some sweetened, processed foods and drinks such as boxed chocolate, ice cream, soft drinks and sports energy drinks have risen by around 14%. At the same time, price of some fruits and vegetables have risen by around 45%.
When sweetened processed foods are cheaper relative to fruits and vegetables, people tend to buy more of the former. This can lead to poor dietary habits, increasing the prevalence of obesity and related health issues.
Changes in relative prices are something that we can examine theoretically using the consumer choice model (otherwise known as the constrained optimisation model for the consumer). I've used this model to describe consumer choices before (see here and here), but this application is slightly more difficult, as the price of both goods is changing over time. I'm not going to go into the basics of the model. It has two components - budget constraints (which I explain here) and indifference curves (which I explain in some detail here).
Consider a model of consumer choices, where the consumer can choose between two goods: sweetened processed foods (S) and fruits and vegetables (F). This model is shown in the diagram below. The consumer has income of M, the price of sweetened processed foods is PS0, and the price of fruits and vegetables is PF0. The consumer's budget constraint is shown by the straight, downward sloping line. The slope of the budget constraint is equal to [-PF0/PS0] (which is the relative price of the two goods). The consumer's best affordable choice (the consumer's optimum) is the bundle of goods E0, which is on the highest indifference curve that they can reach, I0. That bundle of goods includes S0 units of sweetened processed foods, and F0 units of fruits and vegetables.
Now consider changes in prices. The price of sweetened processed foods increases (to PS1), and the price of fruits and vegetables increases (to PF1), but the increase in the price of fruits and vegetables increases by more than the increase in the price of sweetened processed foods. The consumer's budget will not be able to buy as much as before (their income is still equal to M [*]), so the budget constraint will move inwards. The budget constraint will also become steeper, because the relative price has changed. The price of both goods has increased, but the price of fruits and vegetables has increased by more than the price of sweetened processed foods. So, the new slope of the budget constraint, which is equal to [-PF1/PS1], must be a larger number (because PF is increasing faster than PS), meaning that the budget constraint is steeper.
This change is shown in the diagram below. The new budget constraint is the red line - it is steeper and moved inwards from the original black budget constraint. The consumer can no longer buy the bundle of goods E0, because it is outside the budget constraint (the consumer cannot afford to buy E0 anymore). The consumer's new best affordable choice is the bundle of goods E1, which is on the highest indifference curve that they can reach now, I1. That bundle of goods includes S0 units of sweetened processed foods, and F0 units of fruits and vegetables.
Notice that the consumer buys less of both goods, but the impact on the quantity of fruits and vegetables is greater than the impact on the quantity of sweetened processed foods, which is what Vatsa and Renwick found in their research. [**]
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[*] To make life a bit easier, we're assuming that the consumer's income has not changed. Effectively, this reflects an assumption that the price of both goods is increasing faster than incomes have increased, which is probably not too far from recent experience in New Zealand, where food price inflation has been higher than wage inflation.
[**] It is also possible to draw this diagram in such a way that the impact on the quantity of fruits and vegetables is less than the impact on the quantity of sweetened processed foods. The only difference in the diagram would be the placement of the new highest indifference curve I1 and the new best affordable choice E1, which would be further to the right on the diagram. I'll leave that as an exercise for any interested reader to do for themselves.
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