The market demand for a public good, and the optimal quantity to provide

The market demand for a good or service is determined by the sum of the demands for the good or service from each individual consumer. Essentially, you add up the individual consumers' demands to determine the market demand. For a rival good (a good where one person's consumption reduces the amount that is available for everyone else), it is as simple as adding up the quantity demanded at each price. So, if there are only two consumers, and at price P1 the first consumer demands Q1 units and the second consumer demands Q2 units, then market demand at the price P1 is (Q1+Q2).

However, when a good is non-rival, it is no longer quite that simple. Non-rival goods are those where one person consuming the good does not reduce the amount of the good or service available for everyone else. Disney+ is one example. If one person pays for a Disney+ subscription, that doesn't reduce the amount of Disney+ subscriptions that are left for other people. Another example of a non-rival good is a public good. Public goods are goods that are non-rival, and non-excludable (non-excludable means that if they are available for anyone, then they are available for everyone - we'll come back to this point later). Examples of public goods include street lights, or policing.

Now, if we want to know the market demand for street lights, we can't add up the quantity demanded at different prices. That's because two people can consume the same light - remember, it is a non-rival good. The market demand for a non-rival good is found by adding up the marginal private benefit that each consumer gets from the good, to give you the marginal social benefit.

To see how this works, consider the diagram below. There are three people (A, B, and C), and their marginal private benefits for street lights are shown by MPBA, MPBB, and MPBC respectively. The diagram is quite busy, so let's break it down and note what it shows. Person A benefits a lot from street lights. They receive a marginal benefit of P5 for the first little bit of street lighting, and continue to benefit from street lighting all the way out to a quantity of Q4 (this is their marginal private benefit curve, MPBA). Person B benefits less than Person A. The receive a marginal benefit of P3 for the first little bit of street lighting, and continue to benefit from street lighting up to a quantity of Q3 (this is their marginal private benefit curve, MPBB). Finally, Person C receives a marginal benefit of P4 for the first little bit of street lighting, and continue to benefit from street lighting only up to a quantity of Q2 (this is their marginal private benefit curve, MPBB).

What does that mean for the marginal social benefit - the benefit of street lighting to society? The first little bit of street lighting provides Person A with a marginal private benefit of P5, Person B with a marginal private benefit of P3, and Person C with a marginal private benefit of P4. So the marginal social benefit of the first little bit of street lighting is (P3+P4+P5), as shown in the bolder line on the diagram. Now, as the quantity of street lighting increases, the marginal private benefit for each person decreases, until we get to Q2. At that quantity, the marginal private benefit for Person C has fallen to zero. At that quantity, the marginal private benefit for Person A has fallen to P4, and the marginal private benefit for Person B has fallen to P1. So, marginal social benefit at the quantity of Q2 is equal to (P1+P3) - notice that is also equal to P4 (for no reason other than it made it a bit easier to draw the diagram!). Moving on, once we get to the quantity Q3, the marginal private benefit for Person B has also fallen to zero. At that quantity, the marginal social benefit is going to be made up only of the marginal private benefit to Person A, which is equal to P2. And at quantities up to Q4, the marginal social benefit curve is exactly the same as Person A's marginal private benefit curve, MPBA.

Now, we are in a position to consider what happens if we offer street lighting for sale. First, we need to know the price of street lighting. Let's assume that the cost of each unit of street lighting is constant, and equal to P4. That is represented by the marginal social cost curve (MSC) on the diagram below. If we set the price of street lighting equal to its cost (P4), then what would happen? At that price, notice that both Person B and Person C would choose not to pay for street lighting, because the price is above (or equal to) the highest marginal benefit that they receive for the first little bit of street lighting. They would simply opt out of paying for street lighting. Person A is willing to pay more than P4, but they will only be willing to pay for Q1 units of street lighting. The market will provide Q1 units of street lighting, entirely paid for by Person A.

That is a problem. The optimal quantity of street lighting is the quantity where marginal social benefit is equal to marginal social cost. That's the quantity Q3. This market isn't going to provide enough street lighting to maximise welfare for society. The problem here is that the good is non-excludable - you can't easily force Person B or Person C to pay for it. If the street lighting is available to anyone, then it is available to everyone. Person B and Person C will benefit from the street lighting paid for by Person A, and won't feel the need to pay for any additional lighting themselves. Person B and Person C are free-riders. This is the reason why public goods are usually provided by the government. [*] The private market would not provide enough. Consider what would happen if the cost of street lighting was higher than P5. Even though marginal social benefit is higher than that, if the cost (and price) of street lighting was higher than P5, nobody would be willing to pay for it!

Finally, let's consider the economic welfare implications of the public good in this example. If the market provides only Q1 units of street lighting, the consumer surplus (the difference between what society is willing to pay for the good, and what is actually paid for the good) is equal to the area ABDC. You may wonder why the consumer surplus isn't equal to the area FDC, which is the surplus that Person A (who is the only one paying for street lighting receives). [**] Remember the free riders Person B and Person C though - they receive benefit (and consumer surplus) from the street lighting, even though they aren't paying anything towards it. So, the consumer surplus is ABDC, not FDC. Moving on, there is no producer surplus (because price is equal to cost for every unit of street lighting). So, total welfare is equal to the area ABDC.

If instead the government provides street lighting, and provides the optimal quantity Q2, then consumer surplus increases to the area AEC. Again, because there is no producer surplus, the area AEC also represents the area of total welfare. There are welfare gains from the government providing street lighting. Or, another way of thinking about it is that if the market was providing street lighting, total welfare would be lower by the area BED - that is the deadweight loss of private provision of this public good.

*****

[*] Of course, the government doesn't necessarily need to provide the public good itself. It can contract and pay a private firm to provide the lighting, up to a quantity specified by the government.

[**] This important question was raised in my ECONS102 class yesterday, so I thank them for the inspiration to address the point.

A lack of supply is not going to increase demand for timber

One of the most abused sayings in folk economics is that "supply creates its own demand", which actually dates back to John Maynard Keynes' summary of Say's Law in his 1936 book The General Theory of Employment, Interest and Money. There are two problems with this saying. The first is that applying the saying to the supply and demand of a single good isn't quite faithful to what Jean-Baptiste Say actually wrote, because Say was really talking about the whole economy. [*] Second, most people interpret Say's Law as supporting a build-it-and-they-will-come approach to business. The ruins of many businesses can trace their origins to a mistaken belief that if you have a cool idea, people will automatically buy it. The number one rule in business is that you actually need to provide something that people value.

Anyway, today's example from the New Zealand Herald isn't quite Say's Law, but it's probably worse:

Carter Holt Harvey has stopped supplying structural timber to Bunnings, ITM and Mitre 10.

Master Builders president Kerry Archer said the move came as a surprise, and was probably because the export market was more lucrative.

Archer said while Carter Holt Harvey was not the only timber supplier, it could mean construction projects cost more as builders try to source supplies elsewhere...

"Timber's already gone a couple of times this year. Once again it's supply and demand, so if there's a lack of supply then demand goes up and unfortunately costs will go up with it."

It is supply and demand, but not in the way that Archer describes. A reduction in supply will not on its own cause demand to increase. At least, it won't cause demand of the same good to increase. Reducing the supply of structural timber will increase the price of structural timber, and that might cause builders to buy more steel framing, which will increase the demand for steel framing. But it's not going to increase the demand for structural timber. And that's supply and demand.

*****

[*] Say, in his 1803 book Traité d'économie politique (A Treatise on Political Economy), wrote (in French, of course, but this is the English translation):

A product is no sooner created, than it, from that instant, affords a market for other products to the full extent of its own value.

Notice that this is about supply of one good creating demand for other goods, which is not how many people interpret it now.

The beauty premium for economists

I've written a number of times about the beauty premium in the labour market (see the list of links at the end of this post). There is robust evidence that more attractive people get paid more. The evidence is neatly summarised Daniel Hamermesh's excellent book Beauty Pays (that I reviewed here).

In the latest contribution to this evidence base, Galina Hale (University of California, Santa Cruz), Tali Regev (Interdisciplinary Center Herzliya) and Yona Rubinstein (London School of Economics) look at the effects of attractiveness on the careers of recent PhD graduates from top PhD programmes in the U.S. They don't have data on these economists' earnings, but they are able to look at the quality of PhD programme they graduate from, where they get their first job (and later jobs), and the quality of their academic output (based on citations). Specifically, they have data on 752 PhD graduates from the top ten economics PhD programmes in the U.S, who graduated over the period from 2002 to 2006, and follow them up to 2017. They find that:

...appearance matters for individuals' academic success in persistent ways. First we observe that among the students in top PhD programs women are more attractive than men, suggesting that attractive women are more likely to get selected into these elite programs. For subsequent career outcomes we find that attractive individuals are more successful than plain looking individuals. They are more likely to be placed in higher-ranking PhD institutions, and upon graduating, they are more likely to be find jobs in the private sector than jobs in academia or the public sector. Within academia, attractive-looking PhD graduates are also more likely to be placed at higher-ranking institutions for the first job as well as subsequent jobs. Appearance doesn't only predict job placement but, more surprisingly, it also predicts actual research productivity on the job. More attractive economists are cited more overall and per publication. All these effects are rather substantial in magnitude, with one standard deviation increase in attractiveness score increasing the probability of an above-median outcome of job placement and citation count by 7-9 percentage points, depending on the outcome considered.

The significant effect on citations is the most difficult to understand theoretically, since in theory attractiveness shouldn't affect the underlying quality of the research. However, Hale et al. offer a suggested explanation, that:

...attractive people become more confident and therefore might be more likely to solicit constructive comments, and, as a result, may produce higher quality papers that are cited more. Due to higher confidence, they might be more likely to submit their papers to conferences and therefore their papers will get higher exposures. They might also be more charismatic when presenting their papers and therefore provide better marketing for their papers and, as \good presenters," might be more likely to be invited to seminars and future conferences.

All of that seems plausible, but I think we need some more research to demonstrate that this is the mechanism that underlies those results. It would also be interesting to know whether it applies to economists that are further down the pecking order, rather than just those who graduated from top-ten PhD programmes (I'm asking for a friend, really). In any case, add this research to the large (and growing) evidence for beauty premiums in labour markets.

[HT: Marginal Revolution]

Read more:

• Blonds have more fun (or rather, they get paid more)
• The beauty premium in undergraduate study is small, and more attractive women major in economics
• The beauty premium in the LPGA
• The beauty and height premiums in the labour market

Some notes on the NZ Government's new housing package

The big news in New Zealand this week was the announcement of the government's new housing package, which included:

• A $3.8 billion fund to accelerate house building;
• Extra support for first home buyers;
• An extension of the 'bright-line' test to ten years, capturing a greater proportion of house sales within what is effectively a capital gains tax;
• Removing tax deductibility of interest payments for residential landlords; and
• Additional support for apprentices.

The goal of the package is to "increase the supply of houses and remove incentives for speculators, to deliver a more sustainable housing market".

The housing market is complex, and the problems associated with high house prices and rents defy simple solutions. A package was always going to be necessary, but the various parts of the package need to work in concert. Let's take a quick look through those five bullet points and think about the effects they might have on the housing markets. I say markets (plural) because the effects may be different on the market for homes (for owner-occupiers and investors) and on the rental market.

First, $3.8 billion to accelerate house building sounds good on the surface. However, remember that the government isn't a builder of houses, and that's not what this fund is for. The $3.8 billion is to fund infrastructure such as roads and water. This will (hopefully) make it less costly for local councils to zone additional land for development, and for developers to develop the land, since presumably it means that the developers will get to pay lower development contributions. At least, that's how I assume it will work, and if that's the case, then the costs of development will fall, and that should reduce the costs of newly built houses. Some of that reduction in cost will be passed onto new home buyers in the form of lower prices. However, if there is no change in development contributions, then any effect on new house prices is likely to be a lot smaller.

Lower house prices for new builds should lower house prices for existing homes as well, because the two types of homes are substitutes - if more people are buying new builds, there will be less demand for existing homes. Lower house prices mean lower costs for landlords (because their mortgage payments, as well as potentially insurance and rates, will be lower).

Second, extra support for first home buyers is going to undo some of the price effects of the infrastructure fund. Increasing home grants (as noted here) "from $85,000 to $95,000 for individuals and from $130,000 to $150,000 for two or more buyers" is essentially increasing the size of the subsidy for home buyers. Subsidies tend to push up prices, because more buyers are going to be looking for homes, and all the effects on prices noted above will work in reverse.

Third, the extension of the 'bright-line' test to ten years will make a difference at the margin for some existing home owners. They will be more reluctant to sell within ten years, if their home has been rented out at any time. This will reduce some speculator demand in the house market, and act to reduce house prices. However, most speculators were probably being captured by the previous five-year bright-line test anyway.

Fourth, removing tax deductibility of interest payments for residential landlords possibly has the biggest effect, and is considered by many people to be the most consequential of the changes (e.g. see here). This change will reduce the 'profitability' of being a residential landlord. Investors will want to get out of the market, shifting some houses out of the rental sub-market and into the owner-occupier sub-market. This will reduce house prices, but increase residential rents because landlords will now need to cover more expenses across the year as they will be paying more tax (or, more likely, paying tax as opposed to offsetting rental losses against their other income, or carrying losses forward to future years).

Alternatively, some landlords might seek to shift their residential properties into the commercial market, especially if they are zoned in mixed-residential or commercial zones. If you rent a house out to a business to use as an office and/or workshop, it is likely that this is a commercial rental and interest would still be tax deductible. Similarly, landlords might shift their houses onto Bookabach or AirBnB, accelerating an existing trend. That is particularly likely as borders re-open and tourist flows resume. Again, that makes the house rental commercial rather than residential and interest would likely be tax deductible. It will be interesting to see what (if anything) the government tries to do to prevent this type of activity. However, to the extent that landlords move houses out of the residential and into the commercial or short-term accommodation markets, the supply of rental houses will reduce and residential rents will increase.

Finally, additional support for apprentices will only have a small effect on the housing market. More apprentices now isn't going to make much difference to the number of builders and tradesmen available now, but will do in the future.

Overall, what can we conclude? On balance, house prices are probably going to fall a little, but it depends on how much demand is stimulated by first home buyers, and how many landlords look to exit the market, rather than shifting their houses into commercial uses. Residential rents are almost certainly going to increase.

Who really benefits from this package? The government wanted to help first home buyers, and this package will likely succeed. Property developers also benefit (if the development contributions that they would usually be required to pay are reduced).

Who is paying the costs? The taxpayers is picking up some of the cost, including the increased support for home buyers and apprentices, and the $3.8 billion infrastructure package. Landlords are going to be worse off due to their higher tax liability, and many of them will no doubt be seriously considering exiting the market. However, the group that may be most hurt by this package will be low income renters. Families whose income is too low to be able to contemplate saving a house deposit are almost certainly going to be paying higher rents.

Of course, as I said earlier, the housing market is complex, and there is a lot going on. The local and global economies are recovering from the pandemic, interest rates are currently at all-time lows, and international migration (inward and outward) has slowed to a trickle. None of those situations are going to persist forever, and as they change they will also have effects on the housing market. It will be interesting to see how it all plays out.