Explain why the profit maximizing price and quantity for a price-setting firm (in a market where it can only set one price) will result in an outcome that can be considered Pareto inefficient

Consider an inverse demand function given by: P = A - Q

Monopoly:

P = A -Q

TR = (A-Q)*Q

TR'(Q) = MR = A - 2Q

MC = c

Equating MR to MC, we get:

A - 2Q = c, or

Qm = (A-c)/2

Pm = (A+c)/2

Perfect Competition:

Equilibrium requires equating price to marginal cost, i.e.

A - Q = c, or

Qc = A- c

Hence, we can see that under monopoly the price charged is higher while quantity produced is lower than under perfect competition. Hence, price and quantity for a price-setting firm will result in an outcome that can be considered Pareto inefficient.