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, and described in detail during lecture.

Incentives for Tax Collectors

Consider a citizen who owes in taxes to the government. The gov- ernment, who does not know , sends a tax collector. The tax collector observes the true and then makes a report 0. The collector may either report truthfully = or lie and report < . If the tax collector lies, the taxpayer must pay a cost of f ( ) and the collector must pay a cost of g( ) where

f (x) =

g(x) =

1x2 + x

2

1x2 + x

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:

U citizen = f ( ) b

U collector = g( ) + 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 = ?

(a) b

(b) or

(c) +

(d) ( + ) ( )

1

(2) What is the total payout if the collector chooses to lie and report

< ?

(a) or

(b) ( + )( )

(c) ( )2 ( + )( )

(d) 2( )2 + ( )( )

(3) What condition on and must be met for telling the truth to always be more profitable than lying?

(a) =

(b) >

(c) + 1 (d) + 0

(4) Suppose the condition in question 3 is not satisfied. What choice of

would maximize total payout? (a) Any >

2

(b) 1

2

(c) (d) + 1

(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:

Ucollector lie = U collector truth + (lie truth)

Which of the following expressions would you need to solve 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 = 1

2

(b) b()1

()2=0+ (+)()()2

(c) g( + b)= f ( b)

2

(d)( )1()2=(+)()()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:

U collector = r g( ) + b

(7) Now what is the total payoff if the tax collector reports truthfully? (a) + r

(b) r

(c) + r

(d) r

(8) Now what is the total payoff if the tax collector lies? (a) + r

(b) r ( + )( )

(c) + r ( )2 ( + )( )

(d) r 2( )2 + ( )( )

(9) Now what condition must be satisfied for truth-telling to always be preferred over lying?

(a) + + r 1

(b) + + r = 1

(c) + r

(d) + r + 1

(10) What is the optimal level of in this case? (a) Any r >

2

(b) 1r

2

(c) r 1r(d) 1 r

(11) For a given choice of , 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. What 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 revenue. 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 depends