Suppose electricians come in two types: competent and incompetent. Both types of electricians can get certified, but for the incompetent types certification takes extra time and effort. Competent ones...

Suppose electricians come in two types: competent and incompetent. Both types of electricians can get certified, but for the incompetent types certification takes extra time and effort. Competent ones have to spend C months preparing for the certification exam; incompetent ones take twice as long. Certified electricians can earn 100 (thousand dollars) each year working on building sites for licensed contractors. Uncertified electricians can earn only 25 (thousand dollars) each year in freelance work; licensed contractors won’t hire them. Each type of electrician gets a payoff equal to
  where S is the salary measured in thousands of dollars and M is the number of months spent getting certified. What is the range of values of C for which a competent electrician will choose to signal with this device but an incompetent one will not?