Why monopoly is a market failure diagrams

Question 1

Allocative efficiency diagram

Answer 1

No market failure

allocative efficiency occurs at MC=AR (where the CoP for one more output is the price consumers are willing to pay)

However given the chance firms wont want allocative efficiency they will want profit maximisation

Question 2

Profit maximisation diagram

Answer 2

If the monopoly decides to profit maximise the price consumers pay increases to RpM, reducing the consumer surplus.
There is also large increases in the producer surplus.
However this also causes a welfare loss, the reduction in consumer and producer surplus, which is why monopolies usually cause a market failure.