# Answers to Ques 4,5,6,7 - P0Q0S0 Price P1D0 Quantity Q1S1...

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S0 S1 Quantity D0 Q0 Q1 Price P1 P0 4. (ADG) Raghuveer, a risk neutral taxpayer (i) has a pre-tax income of USD 50,000; (ii) owes income tax to the government at a flat 20% rate; (iii) can choose to either report his income truthfully or report zero income and evade the tax; (iv) must pay a penalty equal to 200% of evaded taxes (+ evaded taxes) if he is investigated by a tax inspector; and (v) believes that there are 20% dutiful tax inspectors who always investigate cases assigned to them and 80% lazy tax inspectors who investigate only 10% of cases assigned to them. There are 2 types of risk neutral tax investigators: dutiful ones (all named Fernanda) who always investigate cases assigned to them and lazy tax investigators (all named Ronnie) who weigh their monetary rewards against the opportunity cost of time spent investigating. (ii) Investigators receive a reward of 20% of any extra tax or penalty their investigation help the government recover (e.g. \$15,000 in Raghuveer's case); (iii) if lazy, assesses the opportunity cost of time and effort spent investigating at \$4,000 per taxpayer; (iv) believe that 60% of taxpayers evade taxes. a. What is Raghuveer's expected payoff if he is assigned to Ronnie? What is his overall expected payoff from evading taxes ( he is always investigated if assigned to Fernanda )? b. What is the Ronnie's expected payoff if Raghuveer is assigned to him and he investigates? c. Model the taxpayer-investigator interaction as a sequential moves game by drawing the game tree. a) Tax owed to the government by Raghuveer = \$10,000 Probability that Raghuveer pays tax = 0.4 Probability of evading tax = 0.6 Probability that Ronnie investigates if the case is assigned to him = 0.1 Probability that Ronnie does not investigate if the case is assigned to him = 0.9 Case 1 : Raghuveer pays tax Raghuveer would need to pay \$10,000 as the tax. No other payout required. Case 2: Raghuveer evades tax Case 2a: Ronnie investigates the case Raghuveer would need to pay \$30,000 as penalty. Case 2b: Ronnie does not investigate the case Raghuveer would not need to pay any taxes

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Case 2c: Fernanda Investigates the case Raghuveer would need to pay \$30,000 as penalty Raghuveer’s Expected payout can be calculated as expected value from the below figure. Expected Value = 0.4*10000 + 0.6*0.8*(0.1*30000 + 0.9*0)+0.6*0.2*30000 = 4000+1440+3600 = \$9040 b) Raghuveer is assigned to Ronnie and he investigates Case 1 Ronnie doesn’t get any commission and also incurs opportunity cost of \$4000. Thus, he doesn’t get anything. Case 2
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## This note was uploaded on 12/27/2010 for the course MKTNG 123 taught by Professor Jha during the Spring '10 term at Symbiosis International University.

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Answers to Ques 4,5,6,7 - P0Q0S0 Price P1D0 Quantity Q1S1...

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