Wednesday, 9 August 2023

The income and substitution effects of a tax cut

Benjamin Franklin once famously wrote that "in this world nothing can be said to be certain, except death and taxes". Taxes may be certain, but the tax rate is not. Tax rates vary widely across the world, and have varied widely over time for each country. Economists are concerned about tax rates because, among other things, they affect the incentives to work.

However, it isn't just any tax rate that affects work incentives. We need to take into account all of the changes that affect a worker's income, as a result of working more. Working more results in more income tax payable, but might also reduce a worker's entitlement to government transfers (social security benefits, student allowances), or reduce their entitlement to subsidies (for example, subsidised housing or healthcare) or rebates (for example childcare rebates). All of those changes need to be taken into account.

The effective marginal tax rate (EMTR) is the amount of the next dollar of earnings that a person loses to taxes, to decreases in entitlements to government transfers, and to decreases in subsidies and rebates. It is the EMTR that best captures the incentive effects of the tax and transfer system. When a worker faces a high EMTR, there is a disincentive to work more. When the EMTR is lower, there is more incentive to work.

To see why, consider what happens if the EMTR decreases. For example, if the government offers an income tax cut, this will decrease the EMTR. The after-tax-and-transfers reward for working increases, making work more attractive. The opportunity cost of leisure time (measured as the after-tax-and-transfers wage) increases, making leisure time less attractive. The worker decides to work more. This is an example of the substitution effect. The relative price of working compared with leisure has increased, encouraging a shift to more work and less leisure.

However, there is also an income effect. The higher wage increases the worker's income, and they use that income to consume more normal goods. Leisure time is a normal good, so the worker wants to consume more of it (and work less). Notice that the income effect works in the opposite direction to the substitution effect here. They offset each other.

This leads to an interesting implication of a tax cut. For some workers, especially those on low wages, the substitution effect (work more) is larger than the income effect (work less). In general, a tax cut encourages those on low wages to work more. However, for other workers, especially those on high wages, the substitution effect (work more) is smaller than the income effect (work less). In general, a tax cut encourages those on high wages to work less. Why might the high wage workers work less? Those workers may realise that they can continue to earn the same amount as before, while working fewer hours. This allows them to continue to spend the same amount as before, and have more leisure at the same time. In fact, some workers may be able to both earn and spend more, and have more leisure time.

The income and substitution effects of a tax cut do not necessarily lead all workers to work more. Some workers will respond by working less. In fact, if we look at work and leisure time over the long run (as in this post), we see workers both earning more income, and spending more time on leisure (and working fewer hours). Changes in tax rates change the incentive to work, but they don't necessarily affect all workers in the same way.

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