3. Dr. Pages preferences over wealth (w) can be represented through the utility function u(w) = ln(w). His taxable income this year is (N+1) (in hundreds of thousands). When filling his tax returns, he finds out that he must pay 10% of his income in taxes. His cousin knows an accounting trick that would allow Dr. Pages to pay just 4% of his income in taxes. The problem is that this trick is just a form of tax fraud. A tax inspector will audit Dr Pages tax returns with probability (N+5)%. If Dr. Pages uses his cousins trick, i.e., commits tax fraud, and gets audited, he will have to pay a fine of 30% of his income in addition to the 10% he had to pay in the first place.

n=9

a) Show whether Dr. Pages will ask his cousin to let him know the accounting trick. Write the equation characterizing the maximum amount that Dr. Pages would be willing to pay his cousin to learn that trick (just write the equation, you do not need to solve it).

b) Suppose Dr. Pages cousin tells him the accounting trick for free. What would be the minimum fine in the percentage of his taxable income that would ensure that Dr. Pages does not commit tax fraud?

c) Suppose as in b) that Dr. Pages can get the tax advice from his cousin for free. Now, Dr. Pages contemplates the possibility of hiring a hitman that will kill the tax inspector in charge of his tax files. In that case, the audit probability will be zero. How much (in hundreds of tho