How did Easy Living use mistaken identity and coincidence?

In the screwball comedy Easy Living (1937), directed by Mitchell Leisen, the plot relies on a series of coincidences and misunderstandings that propel the narrative.1

The story is set in motion by a stroke of serendipity: an office worker, played by Jean Arthur, becomes the accidental owner of an expensive fur coat that is discarded by a wealthy banking tycoon, portrayed by Edward Arnold. This initial event leads to a cascade of misapprehensions regarding her status and lifestyle.1

The element of mistaken identity centers on her involvement with a bumbling waiter, played by Ray Milland. While she interacts with him, she remains unaware that he is actually the banking tycoon’s son, who is living a modest life away from his father’s influence. These layers of deception and chance encounters are fundamental to the film's comedic structure.1