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?