A regressive tax system imposes a higher effective tax rate on lower-income earners compared to higher-income earners. By placing a disproportionate financial burden on those with less disposable income, such a system reduces the net income of the poor relative to the wealthy, thereby widening the income gap.

The marginal tax rate of 40% applies to the incremental income of Rs2,000, resulting in an additional tax of Rs800. If the initial tax was Rs4,000 (40% of 10,000), the new total is Rs4,800. The source answer is mathematically consistent with this calculation.

Progressive taxation is designed to reduce income inequality by taxing higher earners at a higher percentage rate than lower earners. By redistributing wealth from the affluent to fund public services or social safety nets, it helps narrow the gap between different income groups in the economy.

Vertical equity is a principle of fairness in taxation which suggests that individuals with a greater ability to pay should contribute more to the public treasury. This is the theoretical justification for progressive tax systems, where tax rates rise with income levels, ensuring that the tax burden is distributed in a way that reflects the varying economic capacities of taxpayers.

Vertical equity requires that those with a greater ability to pay should contribute more. The average tax rate is the standard measure for this assessment because it reflects the actual proportion of total income paid as tax, providing a clearer picture of the tax burden distribution across different income levels than marginal rates.

A regressive tax is characterized by a situation where the average tax rate decreases as the taxpayer's income increases. This means that lower-income individuals pay a higher percentage of their income in taxes compared to higher-income individuals, placing a disproportionate burden on the poor.

A regressive tax is characterized by a structure where the effective tax rate falls as the taxpayer's income rises. This means that lower-income individuals pay a higher percentage of their total income toward the tax compared to higher-income individuals, which is the opposite of a progressive tax system.

Horizontal equity in taxation requires that individuals who are in similar economic circumstances or have the same ability to pay should be treated equally by the tax system. This means they should face the same tax burden, ensuring fairness by preventing arbitrary differences in tax treatment for people with identical income levels or financial capacities.

Regressive taxes take a larger percentage of income from low-income earners than from high-income earners. By placing a heavier relative burden on the poor, regressive taxation reduces the disposable income of those at the bottom of the economic ladder, thereby widening the gap between the rich and the poor.

An effective tax system balances multiple objectives: it must be simple to administer to reduce compliance costs, it should generate sufficient revenue efficiently, and it must minimize deadweight losses or economic distortions that discourage productive activity. A system that successfully integrates these features is considered optimal for economic stability.