Question #49327

a. Assume that workers whose incomes are less about $40 per day currently pay no
income taxes. However, workers with incomes over this amount pay an income tax
of 20%. Draw the budget line facing workers on a wage rate of $20 per hour.
b. Suppose a new government program guarantees each worker the equivalent of
$10 per day, whether or not he or she earns any income. On a separate diagram
draw the new budget line facing the workers under this new program and discuss
the likely effects of this program on desired hours of work?
c. Now suppose the government reduces the tax rate on workers earning more than
$40 per day to 10%. Draw the new budget line facing workers on a wage rate of
$20 per hour. Outline the likely effects of this change on desired hours of work.

Expert's answer

a) We understand that as long as income is less than $40 per day, one earns $20 per hour with no tax. This means one can work only two hours of untaxed work(2 hrs. x $20/hr = $40) before hitting the level at which there is an income tax. If the worker works more than two hours, she pays 20% of her wages, or $4/hr. as a tax. So, if you work more than two hours a day, you are instead making $16/hr. instead of the original $20. We can represent this on a graph that shows daily income on the y-axis, and hours worked per day on the x-axis. As we begin to plot our points, we can see that someone who works 1 hour would make $20. Someone who works 2 hours would make $40. Up until x=2 our line has a slope of 20, which comes from the hourly pay. But then, at all points where x>2, or situations in which more than two hours are worked, we instead see a line with a slope of 16, which comes from the after-tax income for everyone earning over $40.

b) In this case, no matter what the worker does, the government is going to give him or her $10. The tax, however, remains at income above $40, it just takes less hours of work to reach that point, because you begin with the $10 the government has already given you. So, one can only work 1.5 hours at the full rate of $20 per hour before hitting an income of $40. beyond x=1.5 hours of work, after-tax income is back to the $16/hr rate. In part B as opposed to part A, it takes 30 minutes of work less to earn $40; so if $40 per day is a liveable income, this new guaranteed $10 per day is likely to inspire people to work fewer hours, because a slightly higher portion of their hours are at a reduced income than before.

c) In this situation, the switch occurs at the same time, because the worker is still guaranteed $10, and she still starts out making $20 per hour. In this case, because the tax is lower, the worker still earns $18 per hour as opposed to $16, meaning the line continues from x=1.5 at a slope of 18.

b) In this case, no matter what the worker does, the government is going to give him or her $10. The tax, however, remains at income above $40, it just takes less hours of work to reach that point, because you begin with the $10 the government has already given you. So, one can only work 1.5 hours at the full rate of $20 per hour before hitting an income of $40. beyond x=1.5 hours of work, after-tax income is back to the $16/hr rate. In part B as opposed to part A, it takes 30 minutes of work less to earn $40; so if $40 per day is a liveable income, this new guaranteed $10 per day is likely to inspire people to work fewer hours, because a slightly higher portion of their hours are at a reduced income than before.

c) In this situation, the switch occurs at the same time, because the worker is still guaranteed $10, and she still starts out making $20 per hour. In this case, because the tax is lower, the worker still earns $18 per hour as opposed to $16, meaning the line continues from x=1.5 at a slope of 18.

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