Question

2. Xuan-Thuc is a taxpayer in a country with a flat tax rate of t. Her income for the current year is $1000. Therefore, if she declares her full income she will pay $1000t in tax, leaving her with $1000 (1- t) in post-tax income. If she chooses to declare less than her full income her fraud will be discovered if and only if she is audited by the tax authority, which happens with probability p. If an audit discovers fraud, Xuan Thuc must pay tax at the penalty rate T on any undeclared income, where T > t. For example, if Xuan-Thuc declares income of $500 then with probability 1 - p she gets away with this fraud and has post-tax ncome of $ [500 (1 - t)500] and with probability p she is caught and ends up with post-tax income of $[500 (1 - t)500 (1- T) Let X denote the amount of income declared by Xuan-Thuc. Therefore, 0SX< 1000 and Xuan-Thuc can choose any value of X in this range (a) Let s1 denote the state in which Xuan-Thuc is audited and s2 the state in which she is not. Thus, s1 has probability p and s2 has p. Let xı denote Xuan-Thuc's post-tax income in state s1 and let x2 denote her post-tax income in state s2 Draw a HY diagram with 1 measured on the horizontal axis and r2 measured on the vertical axis. In your diagram indicate the probability 1 points corresponding X -0 and X-1000

Answer 1

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X ( 1000 ( 1-T ) vow the above yC) oooX

The (x) Nalua 1000-x L

F-T ん 个 lb) 1000(H)す 0to-1000 7, 1000 00) o pe budges ne 1eoo lovo (-) looo (1-t) t-