You are currently viewing Linear Tax Brackets and Subsidies with Costs to Achieve Absolutely Fair Social Redistribution

Linear Tax Brackets and Subsidies with Costs to Achieve Absolutely Fair Social Redistribution

  •   Yip, Matthew Siu Ting

There is no doubt that people with high incomes redistribute the money to low-income and no-income people through taxation so that everyone can meet their living needs. However, the redistribution mechanism should be absolutely fair to avoid changing the income ranking of each person after redistribution. For example, A earns $10 per month, B earns $3 per month, and C earns $2 per month. During the redistribution, A needs to pay $2 in tax to support C’s living expenses. This is unfair because C’s income after receiving the subsidy is higher than B’s. This unfair situation may cause some people to deliberately reduce or falsify their personal income in order to obtain funding, thereby refusing funding. It may also cause those who do not receive funding to feel unfair and oppose those who distribute and receive funding. In order to avoid the above situation, linear taxation and cost subsidy rules can also be implemented.

$ represents net chargeable income, $ represents monthly tax (a negative number represents the monthly subsidy), and  represents the subsidy available when income is 0. The amount is determined by the current price to ensure Sufficient to maintain living needs;  is the theoretical tax rate when income tends to positive infinity, which is a positive number less than 1, ensuring that the income ranking of each person remains unchanged after redistribution. For example, Ben, Amy and Eva have monthly incomes of $55,000, $32,000 and $10,000 respectively, and enjoy tax allowance of $5,000, $2,000 and $0 respectively, that is, their net chargeable income is $50,000, $30,000 and $10,000. If m=0.2 and c=-6000 (taking Hong Kong prices in 2025 as an example, $6000 per month is enough for one person to rent a house and maintain basic living. This amount can eliminate the need to set up public housing and subsidized housing, and greatly avoid biased subsidies; Increased funding for those with children), then y=0.2x-6000.

People Calculation Tax amount (subsidy amount) ($)
Ben 0.2(50000)-6000=4000 4000
Amy 0.2(30000)-6000=0 0
Eva 0.2(10000)-6000=-4000 (4000)

After wealth redistribution, Ben, Amy and Eva’s actual monthly incomes are $51,000, $32,000 and $14,000 respectively.

For inflation (or deflation), the value of c can be changed only according to inflation (or deflation). Using the above example, if the annual inflation rate is 2%, the linear function for next year should be changed to y=0.2x-6000(1+2%), that is, y=0.2x-6120. Assuming that Ben, Amy and Eva’s monthly income all increase by 2%, the monthly income of Ben, Amy and Eva will be $56,100, $32,640 and $10,200 respectively. Assuming that each person’s tax-free allowance increases by 2%, they will enjoy tax allowance of $5,100, $2,040 and $0 respectively. Their net chargeable income will be $51,000, $30,600 and $10,200 respectively.

People Calculation Tax amount (subsidy amount) ($)
Ben 0.2(51000)-6120=5100 4080
Amy 0.2(30600)-6120=0 0
Eva 0.2(10200)-6120=-3060 (4080)

After wealth redistribution, Ben, Amy and Eva’s actual monthly incomes are $52,020, $32,640 and $14,280 respectively.

Since (52020-51000)/51000×100%=2%, (32640-32000)/32000×100%=2% and (14280-14000)/14000×100%=2%, which means that after wealth redistribution, each person’s annual income growth rate is still 2%.

The above linear law can keep the income ranking of each person unchanged after redistribution, and can prevent people from deliberately reducing their personal income. However, if there is no cost in obtaining the subsidy, some people will still falsify their personal income in order to obtain the subsidy (because accurate income verification is more difficult for some part-time workers). Therefore, except for those who are old, disabled, or in other reasonable situations, the rest of the people who receive subsidies need to pay a price proportional to the amount of subsidies. The most direct way is to divide the amount of subsidies by the statutory minimum hourly wage and stipulate that the recipients need to pay a price proportional to the amount of subsidies. Hours of service. For example, if Tom declares himself unemployed, according to the formula, Tom can receive $6,000 in subsidies per month in the first year. When the statutory minimum hourly wage is $50, Tom should perform 6,000÷50=120 hours of compulsory service per month (in the next year, he can receive $6,120 per month in subsidies, and the statutory minimum hourly wage is $51, Tom should perform 6120÷51=120 hours of compulsory service each month, so the number of hours has not changed; because the additional subsidies for children are not included in the calculation of compulsory service hours), so as to avoid Tom from benefiting from falsely reporting income and exempting him from the necessary of evaluation of asset, saving the cost required for the evaluation. Finally, the calculated amount of funding is only the maximum amount that can be obtained in theory, whether the recipient takes it is a personal decision. For example, Eva can decide not to take funding, or only take less funding in order to avoid or reduce compulsory services.

Remark: The figure below shows the example of the relationship between the actual taxable income and the tax rate. The tax rate is y/x=(mx+c)/x=m+c/x. The higher the income, the lower the tax rate. As income increases, the tax rate increases more slowly, and the asymptote is y=m.

Linear Tax Brackets and Subsidies with Costs to Achieve Absolutely Fair Social Redistribution