The deadweight loss of a pillow tax

For those of you who have missed the news over the last couple of weeks, Auckland mayor Phil Goff has proposed a targeted rate for accommodation providers in Auckland, to be used to fund Auckland Tourism, Events and Economic Development (ATEED) in its role of promoting the city to tourists. At first glance, this might seem like a useful user-pays charge. After all, the accommodation industry receives benefits from the increased tourism, so why shouldn't they pay the costs rather than the ratepayers at large?

The New Zealand Herald has several stories on this topic, including this one from Tuesday:

As part of its annual budget, Auckland Council wants to shift the funding of Ateed from ratepayers to 330 accommodation providers, ranging from backpackers to camping grounds to big hotels.

Auckland mayor Phil Goff says the accommodation sector has profited from the boom in tourism and increased room rates so it was fair it should pay for Ateed rather than ratepayers.

Money saved could be redeployed to fund infrastructure such as roads, which also benefited the tourism sector.

But the accommodation sector says it has been unfairly singled out and should not be the only sector of businesses to pay for the cost of Ateed.

In its submission it says that it gets 9 per cent of visitor spend in Auckland but is being asked to fund 100 per cent of council efforts through Ateed to increase this spend.

On average rates will increase 150 per cent for the affected accommodation providers and in some cases by more than 300 per cent.

The accommodation sector is right in its criticism of this targeted rate. There are two lines of criticism though, and the sector has struck on only the first: fairness. If a commercial business benefits from the activities of ATEED, they should be paying towards its costs. To be equitable, all businesses would pay proportionally to the benefits received, but that is clearly infeasible. Paying proportional to current property value might be a second-best option. Clearly, some sectors (e.g. finance, law firms) would pay vastly more than necessary due to high property values and low benefits received, while others would pay less relative to benefits received. I would argue that including residential ratepayers in this system would be inequitable (but others might argue the opposite, since the activities of ATEED creates jobs that benefit ratepayers).

The second line of criticism, which is missed by the accommodation sector, is efficiency. If the government has a targeted amount of funding they want to raise (e.g. $27.8 million to fund ATEED), then a small tax (like rates) on a wide number of taxpayers generates a much smaller deadweight loss than a larger tax on a smaller number of taxpayers.

To see why, consider the market diagrams below. There are two sectors (A, on the left; and B, on the right). Without the tax, both markets operate at equilibrium (prices P0 and Pa, quantities Q0 and Qa), and total welfare (a measure of benefits to buyers and sellers in these markets, combined) is the area AED in Sector A, and the area FKJ in Sector B. If the government taxes the firms in both sectors a similar amount, we represent this by a new curve (S+tax) [*]. The per-unit amount of the tax is equal to the vertical distance between the S and S+tax curves (the distance BC in Sector A, or GH in sector B). The quantities traded fall to Q1 and Qb. The prices paid by customers in the two sectors increase to P1 and Pb, while the effective prices for the sellers (the price after paying tax to the government) fall to P2 and Pc. Total welfare falls to ABCD in Sector A (with a deadweight loss, or lost total welfare, equal to the area BEC) and FGHJ in Sector B (with a deadweight loss equal to the area GKH).

Now consider what happens if the government wants to raise the same tax revenue, but by taxing only one sector instead of both sectors. This is shown in the diagrams below. Notice that there is no tax in Sector A, and total welfare is maximised at AED. However, in order to earn double tax revenue from Sector B, the government must more than double the tax rate, to the distance LM. [**] The quantity traded in Sector B falls to Qc (instead of Qb). The total welfare in Sector B falls to FLMJ, and the deadweight loss increases to LKM.

Now compare the size of the deadweight losses in the first pair of diagrams (BEC+GKH) to the deadweight loss in the second pair of diagrams (LKM). It should be clear that the size of the deadweight loss in Sector B is more than four times bigger when it is the only sector that is taxed, than when both sectors are taxed. The combined deadweight loss (when you factor in that there would no longer be any deadweight loss in Sector A in the second pair of diagrams) is more than doubled. Total welfare is therefore much lower if the tax is targeted on only one sector.

So, there are both equity and efficiency arguments against the proposed targeted rate for accommodation providers in Auckland. It probably needs a careful re-think.

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[*] Strictly speaking, the targeted rate is different to the specific excise tax that is shown in these diagrams. The difference is that the S+tax curve should be curved in towards the supply curve (but not ever quite touch the supply curve) to represent that the average cost of the targeted rate would reduce, the greater number of accommodation nights provided by the industry. However, I have kept the diagrams simple, as this fact makes no qualitative difference to the discussion.

[**] The government needs to more than double the tax rate, because as the tax increases the quantity sold in the market decreases, so simply doubling the tax would not raise enough tax revenue.