3 - Should I go pro? Suppose you are considering becoming a professional athlete. Whilst a pro athlete can expect to make a lot of money when they're young, they may struggle to find gainful employment later in life. If you decide against going pro, you can expect a much steadier income, though perhaps not quite as lucrative at 21. Which will you choose? Let's set this up formally. Suppose that you live for two periods, t =1,2. If you go pro, in t=1, you will earn 1 p , which is more than what you would earn in t=1 if you do not go pro, 1 np. In other words, 1 p >1 np . However, in period t=2, as a pro you will earn zero: 2 p =0. By contrast, 2 np >0. Being a pro athlete makes you a prominent public figure. In period t=1, you have to pay security guards a fixed amount S to keep you safe from the mob of fans who stalk your every move on social media. Once your professional career is over, you are quickly forgotten, so you don't have to spend anything on security