Final answer:
A carbon tax leads to welfare gain by reducing pollution and improving societal health, while a payroll tax can cause welfare loss by discouraging employment and productivity. The carbon tax corrects a market inefficiency, whereas the payroll tax can create market distortions.
Step-by-step explanation:
The statement "A carbon tax and a payroll tax both generate tax revenue but the former creates a welfare gain and the latter creates a welfare loss" can be explored by comparing the economic effects of both taxes.
A carbon tax is designed to reduce negative externalities, such as pollution, by making it more expensive to release carbon emissions. This tax can lead to a welfare gain as it incentivizes reducing pollution, which benefits society by improving public health and mitigating climate change. In economic diagrams, this can be seen as a shift in the supply curve, reflecting the higher cost of pollution to the producers. The area representing the welfare gain is typically shown between the supply curves before and after the tax imposed, up to the amount of reduced emissions.
Conversely, a payroll tax, which is a proportional tax on wages, tends not to address a specific externality and is instead used to fund programs such as Social Security and Medicare. It reduces the take-home pay of employees and increases the labor costs for employers, which can lead to a welfare loss since it discourages employment and productivity. In economic diagrams, the welfare loss is demonstrated by a wedge between the labor supply and demand curves, indicative of the payroll tax's impact on reducing the equilibrium level of employment.
The disparity in outcomes between a carbon tax and a payroll tax arises from the former targeting a negative externality and thus correcting a market inefficiency, whereas the latter does not target an externality and its impact on labor markets can cause distortions leading to lower overall welfare.