Consider a monopolist who faces two types of consumers, named Type A and Type B respectively.

The market inverse demand curve of Type A is:

pA=2QA

The market inverse demand curve of Type B is:

pB=4QB

The monopolist can distinguish between them but can only charge a simple per-unit price to each type, i.e. it can engage in third-price discrimination.

The cost function of the monopoly is:

C(Q)=Q

whose marginal cost is:

MC(Q)=1

** Part a (5 marks)

Find the profit-maximizing levels of output supplied to Type A and B, denoted by QA and QB respectively.

** Part b (5 marks)

Find the optimal prices the price-discriminating monopolists are charging to Type A and Type B consumers.

** Part c (5 marks)

Find the optimal profit of the price-discriminating monopolist in terms of qA,PA,qB,PB (no need to evaluate the final answer).