Question

Assume that workers whose incomes are less than \(\$ 10,000\) currently pay no federal income taxes. Suppose a new government program guarantees each worker \(\$ 5000,\) whether or not he or she earns any in come. For all earned income up to \(\$ 10,000\), the worker must pay a 50 -percent tax. Draw the budget line facing the worker under this new program. How is the program likely to affect the labor supply curve of workers?

Short answer

The budget line under this new program will start at a minimum of \$5,000 on the y-axis, have a slope of 0.5 for incomes up to \$10,000 and then a slope of 1 for incomes beyond \$10,000. The labour supply curve is likely to shift to the left due to disincentives from a high tax rate until their income reaches \$10,000, where it is likely to return back to normal as the additional income over \$10,000 won't be taxed.

Step-by-step solution

Understanding the Tax System

Firstly, it is important to understand that any income up to \$10,000 by the worker will be taxed at 50%. This means, if a worker earns \$10,000, they will have to pay \$5,000 in taxes. However, the government guarantees each worker \$5,000, whether they earn any income or not. So in essence, every worker will have at least \$5,000 in hand.

Plot the Budget Line

Now, plot the budget line. Assuming the total possible income of the worker on the x-axis and the remaining income after tax on the y-axis, the budget line for the workers will be a two-part line. For any income up to \$10,000, the line would have a slope of 0.5 (indicating 50% taxation) starting at the \$5,000 mark on both axes. Beyond \$10,000, the line would be straight, with the slope 1, as no further tax is assessed on incomes over this threshold.

Understand the effects on labour supply curve

The labour supply curve plots the relation between wages and the quantity of labour supplied. It can be assumed that the labour supply would decrease at a high tax rate of 50%, at least until \$10,000. This is because a higher portion of the extra wages earned (through working more) would be taken as tax, reducing the incentive to work. So, the labour supply curve would likely shift to the left for wages up to \$10,000 due to the decrease in quantity supplied, caused by the disincentive from a high tax rate. After the income crosses \$10,000, since there would be no further taxation, the labour supply would go back to normal, assuming other factors remain constant.

Key concepts

Federal Income Tax

The federal income tax is a levy by the government on the earnings of individuals and entities. It's a progressive tax system in the United States, meaning that the tax rate increases as the taxable amount of an individual's income rises. In our scenario, workers earning up to \(\$10,000\) pay a tax rate of 50%. This approach essentially sets up a two-tiered tax bracket for workers under the new government program: no income results in a guaranteed \(\$5,000\), and income up to \(\$10,000\) is taxed at 50%, leaving them with half of their earned income.

A key feature of the federal income tax system is its ability to influence individual behavior. Changes to tax rates and tax credits can act as either incentives or disincentives for certain actions. In the context of the exercise, the imposition of a 50% tax on earned income represents a disincentive for workers to supply additional labor, as their take-home pay above a certain threshold is significantly reduced.

Labor Supply Curve

The labor supply curve illustrates the relationship between the wage rate and the quantity of labor that workers are willing to supply. It typically slopes upwards, representing that as wages increase, workers are incentivized to work more because they can earn more.

In the given exercise, plotting the labor supply curve involves understanding the impact of the tax and subsidy scheme provided by the government. Before the introduction of the new program, the supply curve would have likely shown a steady increase in labor supplied as wages rose. However, with a 50% tax rate on earnings up to \(\$10,000\), the inclination to supply more labor diminishes, as additional earnings are significantly reduced by taxes. Therefore, the supply curve after the implementation of the tax would be steeper below \(\$10,000\), indicating less labor supplied at each wage rate within this range compared to before the tax was implemented.

Taxation and Labor Supply

The relationship between taxation and labor supply is complex and multifaceted, heavily influenced by the structure of the tax system. Increased taxation on labor income, such as in our example, generally leads to what economists call a 'substitution effect' and an 'income effect'.

• The substitution effect occurs when higher taxes on wages make leisure relatively cheaper, thereby encouraging workers to substitute labor for leisure.
• The income effect occurs when higher taxes reduce disposable income, potentially compelling workers to work more to maintain their lifestyle.

However, when the tax is as high as 50%, the substitution effect often outweighs the income effect, leading to a decrease in the labor supply. With the guarantee of \(\$5,000\) irrespective of work done, individuals might choose not to work at all until earnings surpass this threshold. This would likely shift the labor supply curve to the left, suggesting that at every wage rate up to \(\$10,000\), the quantity of labor supplied would decrease.