Short answers, pulled from the story.
John Maynard Keynes published The General Theory of Employment Interest and Money in 1936. This work described a situation where nominal wages display downward rigidity as workers resist pay cuts.
In France and the UK during the late 1990s, 19% of prices changed every month on average. This implies that an average price spell lasts about 5.3 months before changing again.
John B. Taylor published a paper in 1980 describing firms that change prices every nth period. Guillermo Calvo followed with a model in 1983 where price changes follow a Poisson process.
N. Gregory Mankiw and Ricardo Reis added a feature allowing firms to replan with a fixed probability each quarter. They assumed 25% of randomly chosen firms could plan trajectories based on current information while others rely on outdated data from last period contracts.
Charles I. Jones wrote about sticky inflation in his 2013 textbook Macroeconomics. He explained how firms set prices slowly in response to monetary policy changes causing gradual rate adjustments.