The Law of Diminishing Marginal Utility — An Empirical Evidence in Housing Provisions
Law of Diminishing Marginal Utility
The Law of Diminishing Marginal Utility is one of the most well-known economic laws. As it is intuitively logical and plausible that there have been very few empirical tests on it. Investopedia states it as the following: “all else equal as consumption increases the marginal utility derived from each additional unit declines.” It is often explained by using our experience of over-eating. For example, when you are very hungry, the first banana you eat would be lovely, but the second and the third ones may gain less satisfaction. The fourth and the fifth ones may even be considered negative, when the stomach is full or overloaded. The cartoon below explains it well.
However, it is just because we have the physiological capacity and hormone responses towards foods and eating, it may not be true for other consumable goods and services. For example, when a house of 1 bedroom and 1 bathroom (say about 600 sq. ft) is quite spacious for one or two occupants. But people would normally prefer a bigger house, with more bedrooms and bathrooms. In hedonic pricing analyses, these two variables (or floor areas) are almost always positive with very slow rate of decline. It is argued that people take houses as investment and not just consumable goods, so the more the better!
Interestingly, unlike the example of over-eating, almost all these hedonic pricing analyses on housing provisions do not starts from the origin. That is they start from ONE bedroom + ONE bathroom (or minimal floor area) and above, rather than starting from ZERO bedroom and ZERO bathroom (or zero floor area). But in fact the most critical change must be the FIRST few sq. ft. or from 0 to 1 bathroom if the Law of Diminishing Marginal Utility is true.
The reasons why the researchers do not take into account the ‘zeros’ are clear: because the ‘zero’ situations are hardly in existence. As there are building regulations that govern the minimum provisions in houses, such as the minimum floor area, minimum number of bathrooms, minimum number of windows, etc. The architects or the developers would also design the most profitable houses with the market preferred provisions. In other words, so far there have been NO empirical critical tests on the Law of Diminishing Marginal Utility of Housing Provisions, until our recent paper (Leung & Yiu, 2019).
One of the possible sources of data for testing the change of market prices from zero to one in the number of bedrooms and bathrooms (near-zero floor area) and number of windows is from the informal housing markets where the houses do not comply with the building regulations. Yet, the most common type of informal housing is slum which normally does not have rental or price data available. The subdivided units (SDUs) in Hong Kong, however, is an unique type of informal housing that the cubicles are subdivided from a formal housing unit. This hybrid mode of housing (informal subdivisions from a formal housing flat) enables us to conduct the first empirical study on the Law of Diminishing Marginal Utility on housing provisions.
What is a SDU?
SDU (subdivided units) generally refers to the subdivision of a formal housing flat into two or more individual units for accommodation. Due to the constraints of the building layout, some of the SDUs may or may not have windows or bathrooms, etc. Figure 2 shows a typical floor plan of a Chinese Tenement in Hong Kong, with one of the flats being subdivided into 4 subunits (Apartments 1,2,3,4).
The typical size of a flat in a Chinese Tenement in Hong Kong is about 450 sq. ft. A subdivision into 4 independent subunits plus a corridor results in an average of about 100 sq. ft. per each subunit. Figure 3 compares the average per person living area in the US, New Zealand (NZ), Singapore, Hong Kong (formal housing) and SDU, the per person floor area of SDU is just about 50 sq. ft. in comparison with 160 sq. ft. in the formal housing markets and 800 sq. ft. in the US or NZ.
By means of a hedonic pricing model (Model 1), the effects of floor area (AREA), the provision of the first 2 windows (WIN4_12), and the first bathroom (TOILET), etc. on the rental difference of the 71 extremely small-sized SDUs are investigated.
The diminishing marginal utility of windows, for example, is vividly revealed as shown in Figure 4. When the first 2 windows require on average 34.4% higher in rent, ceteris paribus, the next 2 windows require only 8.9% more and the next 2 require another 6.2% more.
The result is logically tenable as a housing unit without a window can be stuffy and moist, especially in a city with hot and wet climate. There have been several studies confirming the poor indoor air quality in SDUs without windows, and thus causing a higher occurrence of asthma and other indoor-air-quality-related illnesses (Cheung, Jim & Siu, 2019). If you would like to know also the price (rent) of the 1st bathroom, you are welcome to read the full paper at Leung & Yiu (2019) or watch the youtube video at https://youtu.be/yxmULwjQFio (The Most Unaffordable Informal Housing in the Most Unaffordable City — An empirical study on its rent determinants).
We have just finished another paper discussing on the size elasticity (floor area effect) of SDU by comparing the size effect between the units in the informal and the formal housing markets. Let’s discuss it in details in another Medium post.
Cheung, P.K., Jim, C.Y. & Siu, C.T. (2019) Air quality impacts of open-plan cooking in tiny substandard homes in Hong Kong, Air Quality, Atmosphere & Health, 12, 865–878. https://doi.org/10.1007/s11869-019-00705-9
Leung, K.M. & Yiu, C.Y. (2019) Rent determinants of sub-divided units in Hong Kong, Journal of Housing and the Built Environment, 34(19). DOI: 10.1007/s10901–018–9607–4