First, the socially optimal quantity of paper is found by setting MC
p + MC
e = p or
![](data:image/png;base64, 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)
. Rearranging yields Q = 30. The competitive equilibrium is found by setting MC
p = p or 10 + Q = 100 - Q. Rearranging yields Q = 45. The deadweight loss of those additional units equals (45 - 30) ∗ (70-40)/2 = 225. Under monopoly, the firm sets
![](data:image/png;base64, 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)
. The monopoly produces the socially optimal quantity, and therefore has no deadweight loss. Social welfare is greater under monopoly.