Monica's solution was to politely tell Phoebe that her music didn't fit with the classy-theme of the restaurant. Phoebe agreed, but then arrived the next night singing the same songs, just in a fancy dress (she even buys a top hat and spectacles to appear fancy). This leads Monica to directly tell Phoebe that it's the songs that don't go with the theme, which sparks a fight among friends. Phoebe criticizes Monica's small portions and over-garlicky dishes and Monica continues to criticize Phoebe's singing ability. However, since Monica does not own the sidewalk in front of her restaurant, Phoebe has the property rights and begins singing targeted songs to drive away customers, singing "the food here at Javu, will kill you."
Now let's take a Coasian approach and see what would've happened if Coase had written this episode. Monica would've noticed that Phoebe's singing was driving away n customers a day. At an average cost per meal per customer of c dollars, Monica would value Phoebe not singing at n*c dollars per night. Phoebe on the other hand, was probably making a (relatively) large amount of money singing for this wealthy crowd compared to her normal singing at Central Perk coffee house. Thus, her value of singing outside Javu is the difference between what she makes outside Javu and what she would have made outside Central Perk, let's call it j and assume that j < n*c (which it most likely is if Phoebe's accusations of over-priced meals are accurate). Thus, Coase would suggest that Monica pay Phoebe somewhere between j and n*c dollars to not sing outside the restaurant.
However, there is a reason Coase is not the writer for Friends because if Monica went to Phoebe and paid her to not play her music, Phoebe would probably react much worse than the way she reacted initially. While Phoebe and Monica made up in the episode, they may not have made up in Coase's version of it (and you can't put a price on the lost friendship). Coase may work for independent business agreements; however, when it comes to friends, money might not be the answer. Friends don't need money to settle arguments, because when it hasn't been your day, your week, your month, or even your year - they'll be there for you.
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