Jim McKelvey, the co-founder of the mobile payments firm Square, plans to match 100 computer programmers with 100 companies in the next month in St. Louis through an effort called LaunchCode. McKelvey, who started Square in St. Louis and has been involved in promoting the area as a technology hub, said programmers will earn $15 an hour “until they get fired or get hired” for a permanent position. Each will work next to an experienced employee in a system known as pair programming. McKelvey knew that employers perceived there to be a shortage of programmers and began calling companies about LaunchCode after an entrepreneur told him that many of his friends had programming skills but couldn’t find jobs. So far, 78 firms have said yes — they range from startups to giants like MasterCard and Express Scripts — and none has said no.