Workers in the country of Newtopia currently pay no income taxes. However, a new government was recently elected, and they have decided to introduce a personal income tax to finance a large purchase of futiliguns. Futiliguns are completely useless: the people of Newtopia do not currently consume them, and they will get no utility from knowing the government owns many of them. Thus it is safe to assume that this policy change will not affect the prices of consumption goods in Newtopia, and that the only change in Newtopian workers’ utility will be the direct result of the income tax. Five different options for the income tax have been proposed. They are:

1. A flat tax. Under this tax, every worker would be required to pay a tax equal to 10% of their labour earnings. All of the tax revenue will be spent on futiliguns.

2. A flat tax with redistribution. Under this tax, each worker would be required to pay a tax equal to 20% of their labour earnings. Only half of the tax revenue would be spent on futiliguns. The other half would be returned to the citizens of Newtopia as a lump sum transfer. Each citizen, including those who do not work, would receive an equal transfer. That is, if there are N citizens of Newtopia and the total tax revenue under this option is R dollars, then each Newtopian would receive a payment in the amount C = R/(2N) dollars from the government.

3. A progressive tax. Under this tax, every worker would be required to pay a tax equal to 5% of their first D dollars of labour earnings, plus 15% of any labour earnings in excess of D dollars. All of the tax revenue will be spent on futiliguns.

4. A regressive tax. Under this tax, every worker would be required to pay a tax equal to 15% of their first D dollars of labour earnings, plus 5% of any labour earnings in excess of D dollars. All of the tax revenue will be spent on futiliguns.

5. A bizzaro tax. Under this tax, every worker would be required to pay a tax equal to 100% of their labour earnings for the first H hours that they work. Any hours of work in excess of H hours would not be taxed. Each person who works at least H hours would be given a lump sum transfer of B dollars. The remainder of the tax revenue will be spent on futiliguns.

Your assignment is as follows. Use the leisure-consumption choice model to analyze how each of the five proposed taxes will affect labour supply. Assume that workers’ only source of income is their labour earnings (plus the lump sum transfers defined in options 2 and 5). For each of the proposed taxes, do the following:

a. Draw the worker’s budget constraint before and after the tax is introduced. Clearly identify the slope of each segment of the budget constraint, and label each point where the slope changes.

b. Identify the labour supply response to each of the taxes. To do this, answer the following questions. Explain your answer to each one in the context of the leisure-consumption choice model.

I. Is it possible that people who worked a positive number of hours before the income tax choose to increase their hours of work in response to the tax? If yes, does the tax make them better off, worse off, leave them indifferent, or is the effect on their utility uncertain?

II. Is it possible that people who worked a positive number of hours before the income tax choose to decrease their hours of work in response to the tax? If yes, does the tax make them better off, worse off, leave them indifferent, or is the effect on their utility uncertain?

III. Is it possible that people who worked a positive number of hours before the income tax choose to exit from the labour force (stop working) in response to the tax? If yes, does the tax make them better off, worse off, leave them indifferent, or is the effect on their utility uncertain?

IV. Is it possible that people that worked zero hours before the income tax choose to enter the labour force (start working) in response to the tax? If yes, does the tax make them better off, worse off, leave them indifferent, or is the effect on their utility uncertain?

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