constraint called? {d} Please compute the derivative of the social welfare frmction above with respect to 1:. Remember that you now do need to consider the effect of a change in the tax rate on the choices. If you complete the relevant substitutions and simplify, what do each of the items in what you are left with represent? How many derivatives {and thus elasticities} does this term contain? (e) To determine the welfare impact of a change in the income tax rate, is it necessary to use data to estimate all of these derivatives? Why! why not? Who came up with this result? If] How might you use data to estimate this behavioral response so that you can advise government on the distortions introduced by the income tax? {3} Notwithstanding this result, why might it still be useful to consider the impact of the government's tax instruments on the degree of evasion? Question 4 {21] points) Recall our discussion of optimal deductibility in class. (a) Please summarize in two sentences or less the main theoretical insight in the paper, in particular its relation to the Feldstein {1999) result. {b} What is the main caveat of the theoretical result in the paper {i.e., what would have to be true in order for the theoretical result to be invalid)? [c] In two sentences or less, please explain how launching is used in the paper to identify the deduction elasticity. What is done to address concerns that deductions might have changed over time for reasons other than the policy change? {d} Roughly what proportion of taxable income is accounted for by deductions? For ev ery one per cent decrease in taxable income, by what percentage do deductions increase? As a result, how many times larger is the proportional increase in deductions than the pro portional decrease in gross income? {d} Using your knowledge of the key driver of optimal tax design that you have learnt in this course, in two sentences or less, what implications does this result have for optimal tax