RDP 2020-04: The Apartment Shortage 7. What is the Cost-efficient Height for Apartment Buildings?

Figure 7 compares the cost of building up with the cost of building out for different building heights. For illustration, estimates reflect average values for Sydney, where there is the most scope for changing building heights. The black line shows the marginal cost of adding an apartment on top of a building as a function of height, as calculated in Section 4. The orange line shows the average cost of replacing detached houses with apartment buildings of different heights, as calculated in Section 6. Average cost initially declines with height as the fixed land cost is spread among more apartments. However, this is partially offset by the increase in average cost with height discussed in Section 4.2. Parameter values and equations for the orange and black lines are given in Appendix C. Cheshire and Hilber (2008) discuss several variations on this figure. Chau et al (2007) discuss optimal building height in more detail.

The cost curves in Figure 6 vary height while holding other factors constant. This includes holding the value of land constant at $4,033 per square metre, even though, in practice, land zoned for high-rise apartments is much more expensive than land zoned for low rises. This is because a developer (or town planner examining the project in isolation) must decide where and how high to build, taking the cost of land as given. The average cost curve illustrates the consequences of different decisions. We also hold building and land area constant at 1,173 square metres and 2,397 square metres respectively. In practice, taller buildings tend to occupy more land, so a more intuitive description of the curve may be that it varies density (as measured by FSR).

The vertical line represents the building height of the average apartment, 10.5 storeys. Point A is the marginal cost of building up from Table 3, $519,000. Point B is the average cost of building out from Table 5, $610,000. It is less expensive to go up (point A) than out (point B) until buildings reach 20 storeys, labelled point C, when building out becomes the less costly option. We call point C the ‘efficient’ building height, acknowledging that this is a narrow definition of the term – our estimate ignores externalities and the tendency of price to increase with height, considerations we briefly discuss in Section 9. At this height, it costs $581,000 to supply extra apartments by either approach.

In Melbourne and Brisbane, the average cost curve would intersect with marginal costs much closer to the building height of the average apartment in those cities. The lowest cost at which apartments could be supplied would be $504,000 in Melbourne and $468,000 in Brisbane.

Point C in Figure 7 represents the density of development that a builder or planner would choose if they were free to purchase detached houses at their weighted average price and replace them with apartment buildings of any height. Economists will wonder if profits would be maximized by building up until marginal cost equals the price (not shown). Using the average Sydney sale price in 2018 of $873,000, this would be taller than any building in our database. However, this only applies to a builder or planner with access to a fixed amount of land (for instance, due to land use restrictions that prevent new building). If more land can be bought then costs are reduced by supplying more buildings at the efficient height.

Figure 8 reproduces the solid orange and black lines from Figure 7. The dotted orange line shows an increase in the price of land to $10,703 per square metre, the cost of single-dwelling properties in the Inner Sydney SA3. It would then become economic to build up to 33 storeys (point D). The blue line represents the average variable cost of building up or the limiting case of building out when land is free, as is approximately the case in agricultural areas. Then the least costly apartment buildings would be a single storey.

Figure 9 extends these results for a wide range of locations and land prices. Specifically, we take the average price of land being used for houses in each SA3 from CoreLogic. This tends to vary inversely with distance from the city centre, and the horizontal axis ranks regions on this dimension.^[14] The dark blue squares show implied cost-minimising building heights, given these land prices, as discussed above. The leftmost observation, for Inner Sydney, represents point D in Figure 8. Orange circles show the building height of the average apartment built between 2013 and 2018. We only show estimates within 30 or 40 kilometres of the city centre. As shown in Figure 5, very few apartments are built further out than this. Moreover, the efficient height estimates are for infill. In outlying suburbs development tends to be of greenfield sites where the opportunity cost is less expensive vacant land.

Strikingly, newly completed apartment buildings have been shorter than the lowest cost height in almost every area. The gap is most pronounced in central regions of Sydney: the Inner City, North Sydney, Eastern Suburbs and Leichhardt would reduce average apartment costs by increasing building heights by about 20 storeys. In contrast, buildings have been built up to their efficient height in inner areas of Brisbane and even higher in central Melbourne. Taken at face value, the result for central Melbourne would imply that developers would increase profits by building more but shorter buildings. We think this is unlikely and illustrates a limitation of our approach. We estimate building heights based on the average value of detached housing in each SA3. However, tall buildings are more likely to be located on the most expensive land, rather than the average. We suspect that a finer level of disaggregation would result in a higher efficient height for inner Melbourne. Other pockets of high-density building that may be interesting to note include Auburn, Parramatta and Liverpool in Sydney and Knox in Melbourne.

Although Figures 4 and 9 both show results disaggregated by SA3, they address different questions. Figure 4 compares costs with prices to ask: whether to build apartments in different locations? Figure 9 compares the cost of building up with the cost of building out to address the question: if apartments replace houses, how high should they be?

A striking feature of Figures 7 and 8 is how costly it is to supply medium-density housing. As shown by the solid orange line, it costs about $894,000 per apartment to replace detached houses with a three-storey building in Sydney.^[15] Two-storey apartments would cost much more.^[16] This is considerably more costly than providing high density. The reason is that land costs represent a large component of overall costs for low-rise apartments.

The extra cost of low-rise buildings can be compared to the extra amount that home buyers are prepared to pay to live in them. Real estate advertisements rarely mention being in a low-rise building as a selling feature, suggesting the value of this is small. To gauge this more precisely we regress Sydney apartment prices on a wide range of hedonic controls, including suburb dummies and the number of bedrooms and bathrooms. We include the number of dwellings at an address, constructed from the PSMA's Geocoded National Address File (G-NAF), as a measure of density. The most attractive density, as determined by willingness to pay, is buildings with fewer than ten dwellings, for which buyers pay a premium of 6.3 per cent (p-value < 0.01) or about $55,000. However, the cost of supplying housing at this density is hundreds of thousands of dollars more than at average building heights. We note that our regression has some puzzling features. For example, we expected proximity to train stations and light rail stops to significantly boost values but they do not. We also did not expect proximity to education facilities (e.g. TAFEs) and swimming pools to significantly reduce values but they do. Moreover, we are not aware that the G-NAF data have been used like this before. So our estimates should be treated cautiously. Regression output and further details are in Appendix D.

These results have important implications for debates over urban planning. The Grattan Institute (Daley et al 2018, pp 53, 56) suggests that planners should prioritise medium-density housing in the middle ring of our cities, which they say is ‘under-supplied’. Many planners and policymakers call for developing the ‘missing middle’ with terraces, townhouses and low-rise apartments. According to then NSW Minister for Planning Rob Stokes (2016),

Medium density homes such as terraces are highly sought after, efficient and versatile forms of housing, but are in short supply compared with traditional quarter-acre blocks and high-rise apartments.

However, as noted above, expensive land makes medium-density housing considerably more costly than high density. And home buyers are largely indifferent between these options. So, on these narrow criteria, high rises would be more efficient. A free market would provide infill in the form of high density rather than medium density. Though, of course, policy decisions should also take externalities into account.

Medium-density housing is sometimes supported by reference to Kelly et al ((2011); updated by Daley et al (2018, Table 3.2)). This study surveyed home buyers about their preferences for different levels of density. For equivalent costs, survey respondents expressed a strong preference for more medium-density housing relative to detached housing. However, an under-emphasised finding of this survey is that respondents also expressed a strong preference for more high-density housing.

Footnotes

SA3 proximity to the CBD is calculated by averaging the mean distance to the CBD of all properties sold within that SA3 during 2016, rather than the geographic centre of SA3 boundaries. [14]

This assumes new buildings are located near where other apartments have recently been built. If we instead assumed the new housing was located randomly in the Sydney metropolitan area (and hence the land was valued at the unweighted average price of detached housing), the cost would be $673,000 per apartment. [15]

It is difficult to be more precise about low-rise apartments because the ABS aggregate buildings of one and two storeys. [16]