futuresearch.ai | Report ncrX

1
What percentage of Chinese households can afford the cheapest BYD electric vehicle?
$45.6 %$

$I_{single} \sim LN (10.74, 0.63), I_{non-single} \sim LN (10.46, 0.63)$

What is the distribution of disposable income in China?

Key Parameter	Value	Source
Mean disposable income in China in the first quarter of 2024 in Yuan $(μ_{1/4 2024})$		1
Median disposable income in China in the first quarter of 2024 in Yuan $(m_{1/4 2024})$		1
Share of the population under 18 $(S_{children})$	$20 % (50% CI: [18, 22])$	2 3
The share of single households as of 2018 $(S_{single 2018})$	$17 % (50% CI: [16, 18])$	4

We estimate overall mean disposable income in China to be around 45k CNY and median disposable income to be around 36.5k CNY.

Mean income in the first quarter of 2024 was 11539 and median income was 9,462. In previous years, annual income was a bit less than four times the income for the first quarter[5]. We therefore multiply the given value with 4 and deduct a small percentage.

Annual income $\approx$ quarterly income $\times$ 4.

This yields a median $m \approx 36500$ and a mean $μ \approx 45000$ .

Single-person households likely earn more than non-single households on a per-capita basis.

Per capita income differences are due to

children not contributing to household income
higher income required to afford higher per-person costs of living in a single household

For simplicity, we ignore differences in social status between single and non-single households, and only take per-capita income differences due to the number of children into account.

We estimate that the mean per capita income is 56250 CNY for single-person households and 42361 CNY for non-single households.

Single households

Around 20% of the Chinese population are younger than 18[2][3]. We assume that all of these live in non-single households and don't contribute to household income.

The average per capita income is given as

I_{per capita} = I_{adults} \times S_{adults} + 0 \times S_{children} .

Solving for $I_{adults}$ , we get

I_{adults} = \frac{I _{per capita}}{S _{adults}}

This implies an average income per adult of 56250 CNY. For simplicity, we assume that this directly corresponds to the average income for a single-person household.

Non-single household

There are around 480M households in China. In 2018, 17% of them were single households. Since this number has risen steadily, we assume that it has increased to 19% in 2024.

The average per capita disposable income is the average of the single-household income and the non-single-household income weighted by the relative proportions:

I_{per capita} = I_{single} \times S_{single} + I_{not single} S_{not single}

Solving for $I_{not single}$ we get

I_{not single} = \frac{I _{per capita} - I _{single} \times S _{single}}{S _{not single}}

This implies a per-capita household income of non-single households of 42361 CNY.

We can model the distribution of disposable income in China as a log-normal distribution and infer the parameters based on the mean and median of the income distribution. We assume that for both single and non-single households, the median is 82% of the mean, as is the case for the overall per capita distribution[1].

This yields

I_{single} \sim log-normal (10.74, 0.63)

I_{non-single} \sim log-normal (10.46, 0.63)

A random variable $X$ is log-normally distributed if $lo g (X)$ is normally distributed.

This implies that:

X \sim Log-Normal (μ, σ),

where $μ$ is the mean of the natural logarithm of $X$ and $σ$ is the standard deviation of the natural logarithm of $X$ .

The median of $X$ is given as

m = exp (μ_{l o g}) .

This is because for the normally distributed $lo g X$ the mean equals the median and applying a monotone transformation doesn't change the order of percentiles. We therefore have

μ_{l o g single} = lo g (m_{single}) = lo g (0.82 * 56250) = 10.73911.

μ_{l o g non-single} = lo g (m_{non-single}) = lo g (0.82 * 42361) = 10.45553.

The mean of the log-normal distribution is given as

μ = exp (μ_{l o g} + \frac{σ ^{2}}{2}) .

Solving for $σ$ , we get

σ_{l o g} = 2 \times (lo g μ - μ_{l o g}) .

Plugging in the known values for $μ$ and $μ_{l o g}$ , we obtain

σ_{l o g single} = 2 \times (lo g 56250 - 10.73911) = 0.6300021

σ_{l o g non-single} = 2 \times (lo g 42361.11 - 10.45553) = 0.6300095

Supporting Evidence

[1]
Mean household income in the first quarter of 2024 in China was 11539 CNY. The median was 9,462 CNY, 82% of the mean
www.stats.gov.cn/english/PressRelease/202404/t20240424_1948702.html
[2]
16.61% of the Chinese population were 14 and younger, 7.49% were between 15 and 19, and 3.37% of the population were older than 75
en.wikipedia.org/wiki/Demographics_of_China#Structure_of_the_population
[3]
National Bureau of Statistics of People's Republic of China on Major Figures of the 2010 Population Census
www.stats.gov.cn/english/NewsEvents/201104/t20110428_26449.html
[4]
The percentage of single households was around 17% in 2018 and has been increasing over the last years.
www.researchgate.net/publication/360831990_Does_living_alone_increase_the_consumption_of_social_resources
[5]
In 2023, the median of the nationwide per capita disposable income was 33,036 yuan, an increase of 5.3 percent, and the median was 84.2 percent of the average.
www.stats.gov.cn/english/PressRelease/202402/t20240201_1947120.html

1
What percentage of Chinese households can afford the cheapest BYD electric vehicle?
$45.6 %$