The table below shows cost data for producing different amounts of oil. The market for oil produces negative externalities in the form of pollution and environmental damage.

$\backslash$table$[[$Price$,$Demand,Private Supply,Private $+$ Social Supply$],[5,49\mathrm{.}5,42,27],[13,45,45,30],[21,40\mathrm{.}5,48,33],[29,36,51,36],[37,31\mathrm{.}5,54,39]]$

How many barrels of oil will be produced by the free market?

What is the socially optimal output of oil?