Instead of a lump-sum tax we had in the textbook model, suppose the government imposes a proportional

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Question:

Instead of a lump-sum tax we had in the textbook model, suppose the government imposes a proportional income tax at a rate t on the consumer’s wage income. That is, for a given market wage rate w, the effective wage rate the consumer faces would be w(1 − t). The rest of the model structure is the same as what you saw in class as well as in the textbook (except Question 3).

1. [5] Write down the consumer’s budget constraint under this tax policy.

2. [5] Describe the consumer’s budget constraint in a diagram. Label properly, and explain the key difference(s) in this case compared to the lump-sum tax case, if any.

3. Consider the consumption bundle where the consumer consumes h units of leisure on the budget constraint (at the upper right corner of the diagram you drew above). (a) [5] This point may or may not be the optimal consumption bundle depending on the consumer’s preferences. Under what assumption/condition is this point not likely to be optimal? Explain.

(b) [5] Suppose the assumption you gave above is satisfied. Then, explain why this may not be the optimal by comparing the MRSl,c at that point and w. How does this consumer adjusts her consumption bundle? Explain in detail.

4. [30] Suppose the government reduces the tax rate from t0 to t1. (In the following, draw a separate diagram for each question. Do not clam everything into one diagram.) (a) Describe how this policy change affects the consumer’s budget constraint in the diagram. Label properly, and explain the key difference(s) in this case compared to the tax policy change we discussed in class, if any.

(b) Describe how you measure the substitution effect under this tax policy, if any.

(d) How can you conclude whether this tax policy increases or decreases the consumer’s labour supply? Discuss. (e) Suppose the consumer’s labour supply curve is given by the upward sloping line as we saw in class. Describe and explain how this tax policy change affects the consumer’s labour supply curve. Be consistent with your analysis in (d).