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日期:2025-02-13 03:06

QUESTION 1: Excess Burden and Incidence of Taxation

a. Suppose you want to redistribute from rich to poor by taking the labor of high earners. Suppose the market for such workers is described by one of the 4 diagrams above. Which one (1, 2, 3, or 4) would provide a best-case scenario for your ability to redistribute? Which one would be the worst-case scenario? Explain your reasoning. For simplicity, you can assume you put no “(marginal) weight” on the well-being of high earners or their employers. Your answer should include the word “elasticity.”

b. Suppose you want to help low earners by giving them a labor subsidy, sort of like the Earned Income Tax Credit. Suppose the market for such workers is described by one of the 4 diagrams above. Which one would provide a best-case scenario for your ability to aid them? Which one would be the worst-case scenario? Explain your reasoning. For simplicity, you can assume you put no “(marginal) weight” on the well-being of anyone other than these workers. Your answer should include the words “elasticity” and “incidence.”

c. Provide a critique of the Earned Income Tax Credit based on your argument above. What might be a more effective way of transferring money to low earners rather than a labor subsidy?

QUESTION 2: Optimal Taxation

Consider a simple economy with 2 individuals:

1. Person A is endowed with 99 (dollars)

2. Person B is endowed with 0

The government possess a redistributive mechanism that allows it to a) take T + T2 away from Person A; and b) deliver T to Person B. In the background, you can think of this as an income tax on Person A that affects their willingness to work, but we will abstract from those details for simplicity. Assume that T cannot be negative.

a. As a function of T, what is the deadweight loss created by this mechanism? For instance, if T = 2, how much deadweight loss would be created? How do you know?

b. Imagine that you have “Utilitarian social preferences.” What is the optimal choice of T? Explain your answer.

c. Imagine that you have “Rawlsian social preferences.” What is the optimal choice of T? Explain your answer. (To get a numerical answer, you need to use of the “quadratic formula”)

d. Now suppose you are an economist, and you observe that the T = 1.5. Assume that  you has marginal social welfare weights of MSWWA and MSWWB, which of course you do not observe. However, you are willing to assume that it has “convex preferences” and set T in order to maximize their Social Welfare Function. Find MSWWA/MSWWB and explain your answer. (Hint: When T = 1.5, the slope of the Possibilities Frontier is 4.) Drawing a diagram is not necessary but can help.

e. Finally, suppose you are in the exact same situation as part d, but then you find out that in order to transfer T to Person B, Person A will lose T + 0.1T2 (rather than T + T2). If you were to recalculate the ratio of MSWWs like you did in part d, would you find a higher number or a lower number. Note, you do not need to actually do the calculation; an intuitive argument will suffice (and is in fact preferred).

QUESTION 3: Universal Basic Income

Consider the following tax scheme:

· We will tax the s% highest earners at rate t.

· Those earners will earn on average 

o I is there earnings if untaxed;

o e captures that their behavior. is elastic, so they will earn less when the tax is higher.

· We will then transfer  to all households, guaranteeing them this “Universal Basic Income.”

a. Suppose we plan to tax the top 1% of earners and their untaxed income would be I = $2,000,000. Assuming e = 1, what is the highest UBI that can be achieved, and what is the tax rate that achieves it? How does that change if e = 2? Provide economic intuition for this change. You should perform. this analysis in Excel, by simultaneously checking 0.01, 0.02, ..., 0.99 to see what they raise.

For the remainder of the problem, assume e = 1.

b. Suppose now that we will tax the top 20%, and their average untaxed income is I = 400,000. What is the highest UBI that can be achieved?

c. Repeat the analysis assuming we will tax the top 60%, and their average untaxed income is I = 200,000.

d. The larger the share of the population that we tax, the larger the UBI is that we can achieve. Explain why that is.

QUESTION 4 : Open-ended: UBI and Flat Tax

A Flat Tax (“FT”) is typically advocated by analysts who stress the importance of economic efficiency. Universal Basic Income (“UBI”) is typically advocated by analysts who stress the importance of equity. The two ideas, however, are not necessarily in opposition to each other. What is a basic structure of a tax code that both sides could probably endorse? What would the two sides agree on? What would they continue to disagree about fiercely? 





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