Increased childcare subsidies will almost certainly raise the price of childcare

The National Party has announced a new childcare policy, called Family Boost, which would be implemented if they are elected later this year. As Stuff reported earlier this week:

If the public service stops hiring so many consultants, National Party leader Christopher Luxon says it could afford greater childcare subsidies.

During his State of the Nation speech on Sunday, Luxon promised he would order the public service to cut $400 million from its consultancy bill. That money, he said, would fund a new childcare policy, giving a 25% rebate to most families’ childcare bills.

The childcare rebates were expected to cost about $250m per year and would be available per household – not per child...

National’s new childcare policy, which it calls Family Boost, would give a rebate of 25% on childcare costs up to an annual limit of $3900 for families earning under $140,000. This would mean up to $75 per week to offset childcare costs.

So far, so good. But then:

 Luxon dismissed concern that giving tax rebates for early childhood fees would lead to an increase in prices, given the majority of children attend for-profit childcare centres. He said the “really competitive” ECE market would mean prices wouldn’t go up.

”I think early childhood education providers will know that they try and pump up fees, they will lose families,” deputy leader Nicola Willis said.

Both Luxon's statement that a competitive market won't raise prices, and Willis' statement that increasing childcare fees following the subsidy will lead childcare centres to lose families, are very likely wrong. To see why, let's consider a model of the market for childcare services, as shown in the diagram below. For simplicity, let's start with no subsidy in the market. [*] Without a subsidy, the market is in equilibrium, with a price of P0, and Q0 hours of childcare are provided. The subsidy, paid to the families (the buyers in this market), is represented by a new curve D+subsidy, which sits above the demand curve. It acts like an increase in demand, and as a result the price that childcare providers receive for childcare services increases to PP. The families pay that price, then receive the rebate back from the government, so in effect they pay the lower price PC. The difference in price between PP and PC is the per-hour amount of the subsidy. [**] So, our model immediately suggests that Luxon's comment about the competitive market not raising prices is incorrect. It is true that the price doesn't go up by the whole amount of the subsidy - the difference between the original price P0 and the new higher price PP is less than the per-hour subsidy (PP - PC).

Next, the number of hours of childcare services provided increases from Q0 to Q1 (because families want to have children in childcare for more hours because of the lower effective price they have to pay, and childcare providers want to provide more hours of childcare because of the higher price they receive). So, even though childcare services have increased in price, the quantity of childcare services demand has increased. So, our model also suggests that Willis' comment about childcare services losing families is also incorrect.

Of course, the model is not the real world. However, what would it take for a subsidy not to increase prices? If the supply curve was horizontal (meaning that supply is perfectly elastic), then prices would not increase. Perfectly elastic supply suggests that there is a large reserve army of childcare providers at the current market price, just waiting for families to call them for childcare services (in fact, it means that there is unlimited supply available at the market price). Any parent who has tried to find a childcare centre for their child at short notice will know that is not the case (see here, for example). And that is just the tip of the iceberg for problems in this sector, as this Stuff article by Michelle Duff documents.

Subsidies increase prices. That happens when the market is competitive, and when the market is not competitive. I'm sorry Mr Luxon - you can't appeal to the competitiveness of a market to argue that subsidies won't increase prices.

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[*] This assumption essentially doesn't change any of the main conclusions. It just makes the market a bit easier to draw.

[**] The actual amount of the subsidy varies between families, but again that doesn't change any of the main conclusions.

Legal access to alcohol, teenage drinking, and crime

Young people do dumb things. Drunk people do dumb things. When people are both young and drunk, they do even dumber things. [*] In other words, when young people gain access to alcohol, their behaviour changes. I've posted before about various studies that compare young people before and after attaining the minimum legal drinking age. Studies have found that gaining legal access to alcohol lowers grades (but only by a little), increases hospitalisations, and increases alcohol-involved motor vehicle accidents.

Add to that list of effects of legal access to alcohol this recent article by Fabian Dehos (RWI-Leibniz Institute for Economic Research), published in the Journal of Health Economics (sorry, I don't see an ungated version online). Dehos looks at the impact of German teenagers attaining the minimum legal drinking age (of 16) on alcohol consumption and crime.

Dehos combines nationally representative survey data from the German Federal Centre for Health Education (covering 2005, 2007, 2008, 2011, and 2015) and from the European School Survey Project on Alcohol and Other Drugs (covering 2007 and 2011). The total sample size is over 20,000 people aged between 14.5 and 17.5 (1.5 years either side of the minimum legal drinking age).

Dehos then employs a regression discontinuity design, testing whether there is a discrete jump in alcohol consumption in crime that happens exactly at age 16. In terms of consumption, one of the key insights is summarised in Figure 1 Panel (a) from the paper:

Notice that alcohol consumption jumps up at age 16, both in terms of consumption within the last 30 days, and consumption within the last 7 days. That suggests strongly that young people start drinking more frequently when they get to age 16 (or, at least, they are more likely to report drinking in a survey when they get to age 16). It is especially noticeable that there is no jump in lifetime consumption of alcohol at age 16, which also suggests that drinking becomes more frequent at age 16. Dehos then shows quantitatively that there is:

...a 35% increase... of the overall drinking intensity at age 16. Similarly, there is a 20% increase in the number of drinking days within the last 7 days right at the cutoff...

Turning to crime, the key insights are summarised in Figure 4 Panel (a) from the paper:

Notice again the discrete jump in alcohol-influenced crimes at age 16. There is no such increase in non-alcohol-influenced crimes, which should give us some confidence that there is something special about age 16 that leads to an increase in alcohol-influenced crimes. It should be no surprise what the leading contender is for explaining that change! Quantitatively though, Dehos finds that:

The overall criminal engagement of alcohol-induced crimes increases by 11.7 offenses per 10,000 person-years at age 16... The jump of alcohol-induced offenses at the MLDA, thus interprets as a 15.7% increase... in criminal engagement under the influence.

Those are quite substantial changes in alcohol consumption and alcohol-related crime, and much larger than the effects found in the research I cited in the posts linked earlier. A possible explanation for that is that alcohol access at age 16 has a much greater impact on young people than alcohol access attained at age 21 (as in the US research that found a tiny effect on student academic performance) or at age 18 (as in the New Zealand research on hospitalisations and motor vehicle accidents).

On the other hand, perhaps police change the way that they handle crimes committed by people aged 16 (compared with younger offenders). Dehos tries to rule this out by showing that there is a statistically significant discontinuity at age 16 for a survey question on whether young people "had problems with the police within the last year because they had drunk". That is unconvincing to me (in fact, it makes the case for police treatment of offenders changing at age 16 even stronger). He also looks at a question on whether young people "were involved in a fight because they had drunk", and also finds a statistically significant increase at age 16. In this case, the effect cannot be related to police treatment of offenders, so that provides a little more confidence that Dehos is finding a real effect of alcohol consumption on crime (even though the true effect might be somewhat smaller than what he finds).

Overall, the takeaway messages from this paper are that alcohol consumption increases when alcohol becomes legally available to young people (no surprises there), and that young people are more involved in crime when alcohol becomes legally available to them. That by itself doesn't mean that the drinking age should be increased, only that there are benefits (in terms of lower crime) in doing so, which will need to be carefully weighed up against any costs. On the positive side, with decreasing alcohol use among young people (see here and here), perhaps youth crime will start to decrease?

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[*] Before anyone gets offended, remember that I was young once too. One of my favourite song lyrics is from Adema's The Way You Like It: "Nowadays, no one remembers when they were young and stupid". I do remember being young and stupid, so when I say that young and drunk people do dumb things, I'm speaking from personal experience.

Kūmara prices, consumer decision-making, and the Law of Demand

Yesterday I posted about kūmara prices increasing, and the impact of that on the markets for kūmara and potatoes. This week, my ECONS101 class will be covering constrained optimisation, and the main application of the general constrained optimisation model that we will be looking at is the consumer choice model. So, it seems timely to look at the effect of kūmara prices on consumer decision-making, using that model.

Consider the decision-making of a single consumer. [*] The model is shown in the diagram below. The consumer can choose to buy kūmara (measured along the x-axis) or 'all other goods' (AOG; measured along the y-axis). All of the points within the space on the diagram are combinations of kūmara and AOG, which we will refer to as bundles of goods. Now, the consumer's choice of how much of each good (kūmara and AOG) they will buy is constrained by their income (M). This is represented on the diagram by the straight-line budget constraint. The budget constraint starts at a bundle of goods with only AOG and no kūmara at all. At that point (at the top of the budget constraint), the consumer is spending all of their income on AOG, and nothing on kūmara. The maximum amount of AOG the consumer can buy is M/Pa (where Pa is the price of AOG). At the other end of the budget constraint is a bundle of goods with only kūmara and no AOG at all. At that point (at the bottom of the budget constraint), the consumer is spending all of their income on kūmara, and nothing on AOG. The maximum amount of kūmara the consumer can buy is M/Pk0 (where Pk0 is the price of kūmara). Now, the consumer can afford any bundle of goods (kūmara and AOG) that is on the budget constraint or underneath it (we refer to this as the feasible set). Now, for reasons we won't go into here, the slope of the budget constraint is equal to -Pk0/Pa (the relative price of the two goods). Any bundles of goods outside of the budget constraint cost too much for the consumer to afford. Next, we assume that the consumer is trying to maximise their utility. We represent utility on the diagram using indifference curves. So, the consumer is trying to get to the highest possible indifference curve, while choosing a bundle of goods that is in the feasible set. That happens at the bundle of goods E0, which is on the highest indifference curve I0, and which includes K0 of kūmara and A0 of AOG. The consumer can't get to any higher indifference curve than I0, because any higher indifference curve than I0 wouldn't be touching the budget constraint (and so there would be no bundles of goods on the higher indifference curve that are within the feasible set). That is the basic setup of the consumer choice model, and it shows what the consumer will buy given their income (M), the prices of the goods (Pk0 and Pa), and the consumer's preferences for the two goods (shown by the indifference curves).

Now, consider what happens when the price of kūmara increases (as discussed in yesterday's post) from Pk0 to Pk1. The budget constraint is affected first. If the consumer was only buying AOG and no kūmara at all, then the change in the price of kūmara would not affect them. The point at the top of the budget constraint remains the same. However, if the consumer were only buying kūmara (and no AOG at all), then they would now be able to buy less kūmara. This is represented by the new point M/Pk1, which is a smaller quantity of kūmara than M/Pk0. The budget constraint pivots inwards and becomes steeper. The steeper budget constraint makes sense, because its slope is now equal to -Pk1/Pa, which is a larger number (in absolute terms) than -Pk0/Pa (and larger numbers mean steeper slopes). The problem for the consumer is that they now can't afford the bundle of goods E0, because it is outside of the new feasible set (it is outside the budget constraint - the consumer can't afford to buy E0 any more). Instead, the consumer will choose the bundle of goods on the highest indifference curve that they can now reach. That is the indifference curve I1, and they will buy the bundle of goods E1, which includes K1 of kūmara and A1 of AOG.

In the consumer choice model, after the price of kūmara increases, the new bundle of goods that the consumer chooses to buy contains less kūmara. So, consumers will respond to the increase in the price of kūmara by buying less kūmara. This is what economists refer to as the Law of Demand, one of the most important empirical regularities in economics.

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[*] I haven't explained all of the moving parts of the consumer choice model here. In particular, I'm leaving a detailed discussion of indifference curves for a future post. However, if you need a bit more detail, try this explainer.

Storm damage, and the price of kūmara and potatoes

The New Zealand Herald reported earlier this week:

The price of some vegetables like kūmara and broccoli has doubled since Cyclone Gabrielle swept through New Zealand and decimated vast areas of crops.

Customers should get used to the higher prices, which could linger until after next year’s harvests, some supermarkets say...

At Auckland greengrocer Point Chev Fresh on Tuesday, assistant manager Manni Singh said he had never seen such a big increase in such a short time.

“The kūmara price has gone up to $9 a kilo,” Singh said.

“Normally, we were selling it for $4.50.”

Why has the price of kūmara gone up so much? The effects of storm damaged kūmara on the market for kūmara can be explained using the supply and demand model (that my ECONS101 class will cover later this trimester). This is shown in the diagram below. The kūmara market was initially in equilibrium, where demand D0 meets supply S0, with a price of P0 and Q0 kūmara is traded. Storm damage reduces the amount of kūmara available to harvest, decreasing supply to S1. This increases the equilibrium price of kūmara to P1, and reduces the quantity of kūmara traded to Q1.

The consumer response to higher kūmara prices will likely cause the price of other root vegetables to increase as well. Potatoes are a substitute for kūmara. If the price of kūmara has increased, that makes potatoes a relatively cheaper alternative, and , some consumers will switch to potatoes. The effect on the market for potatoes is shown in the diagram below, where the market is initially in equilibrium with a price of PA, and a quantity of potatoes traded of QA. Consumers switching to potatoes increases the demand for potatoes from DA to DB, increasing the equilibrium price of potatoes from PA to PB, and increasing the quantity of potatoes traded from QA to QB.

Even consumers who don't like kūmara, and prefer potatoes, are likely to be affected.