This assignment is motivated by the research described in “Tax… ?This assignment is motivated by the research described in “Tax Farming Redux: Experimental Evidence on Performance Pay for Tax Collectors,” by Khan, Khwaja, and Olken (2014). During this assignment, you will walk through a simple model to motivate the approach taken in this research, ?nd described in detail during lecture.?ncentives for Tax Collectors?Consider a citizen who owes t *?in taxes to the government. The gov- ernment, who does not know t *, ?ends a tax collector. ?he tax collector observes the true t *?and then makes a report t ? 0. ?he collector may either report truthfully t = t * ?r lie and report t < t *. ?f the tax collector lies, the taxpayer must pay a cost of f (t * - t ) and the collector must pay a cost of g(t * - t ) where? ? (x) =?(x) = 1?2 + ax21?2 + ?2 ? These costs represent the potential risk of lying or hiding assets. Finally, the taxpayer may pay a bribe b to the collector in exchange for lying. Payouts are therefore:?? citizen = -t - f (t * - t ) - bU collector ? -g(t * - t ) + b?????1) Total payment can be expressed as H = U citizen truth + U collector truth. What is the the total payout if the collector reports truthfully t = t *?(a) t - b(b) t or t *(c) a + ?d) (a + ? * (-t *)? ??(2) What is the total payout if the collector chooses to lie and reportt < t *?(a) t or t *(b) -t - (a + ?(t * - t )(c) -t - (t * -t?2 - (a + ?(t * - t )(d) -t - 2(t? - t )2 + (a - ?(t * - t )?3) What condition on a and ?must be met for telling ?he ?ruth ?o always be more profitable than lying?(a) a = ?b) a > ?(c) a + ?= 1 (d) a + ?= 0?4) Suppose the condition in question 3 is not satisfied. What choice oft would maximize total payout? (a) Any t * ? t2?(b) t * – ?-a-??(c) -???a-?d) t + 1 – a – ?(5) Suppose the condition in question 3 is satisfied. True or false: The tax collector has no incentive to lie.(a) True(b) False?6) Suppose the taxpayer pays a bribe so that the collector receives her utility from telling the truth plus a share ? of the surplus from lying. that is, b is set so that:?collector lie = U collector truth + ?(?lie? ?truth)??Which of the following expressions would you need to ?olve to determine the level of the bribe? ?You do not need to solve for b, only select the expression that you would use to solve for b.)2?(a) b = t * – ?-a-?2?(b) b-?t?-t?-?(t?-t?2?=?+? ??????a??)(t??????t????2?(c) g(t * – t + b)? f (t * – t – b)2?(d)??t *??????t????2?=?t?????a??)(t??????t????2??? Now suppose the government introduces performance pay for tax collec- tors. Collectors are payed a fraction r of the total tax revenue they report. Their payout is now:? collector ? rt – g(t * – t ) + b?(7) Now what is the total payoff if the tax collector reports truthfully? (a) -t * + r(b) -t? – r(c) -t? + rt?(d) -t? – rt??8) Now what is the total payoff if the tax collector lies? (a) -t * + rt *(b) -rt – (a + ?(t * – t )(c) -t + rt – (t * – t )2 – (a + ?(t * – t )(d) rt – 2(t? – t )2 + (a – ?(t * – t )?9) Now what condition must be satisfied for truth-telling ?o always be preferred over lying?(a) a + ?+ r = 1(b) a + ?+ r = 1(c) a + ?= r(d) a + ?= r + 1?10) What is the optimal level of t in this case? (a) Any rt * ? t2?(b) t * – ?-a-?r2?(c) rt * – ?-a-?r(d) 1 – a – ?- r?11) For a given choice of t , does the bribe size per bribe (conditional on some bribe being paid) increase or decrease when incentive pay is introduced? (a) Increase (b) Decrease (c) No change(d) Could increase or decrease; it depends ??(12) Suppose the condition in question 3 is not met. ?hat does this model predict will happen to revenue when the government intro- duces incentive pay? (You can assume that on average, overall pay to tax collectors remains the same, and that we do not have to worry about pay to the tax collector in computing government ?evenue. For example, the government could take a fixed amount out of the collector’s salary to offset the additional performance earnings.) (a) Increase (b) Decrease (c) No change(d) Could increase or decrease; it depends?13) Suppose again the condition in question 3 is not met. What does this model predict will happen to the total amount of bribes collected? (a) Increase(b) Decrease(c) No change(d) Could increase or decrease; it dependsBusinessEconomicsMacroeconomicsECON 101
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