Calculate price and quantity

Question No. 1 :
a) Quote some real-life practices of price discrimination (1st degree, 2nd degree, 3rd degree), Two-part Pricing and Tie-in Sale.
b) We studied the concept of “pareto efficiency” and learned that a competitive environment ensures “pareto efficient” allocation of resources, and we also learned that sometimes monopolies that are regulated by government also ensures efficient resource allocation. Will a monopoly ever provide a “pareto efficient” level of output on its own? Discuss and support your arguments with graph in terms of consumer surplus, producer surplus, dead weight loss and social welfare (Ref. price Discrimination).
c) Suppose that a monopolist faces two markets with inverse demand functions given by: p1 = 100-q1
p2 = 50-q2/2
Also assume constant MC = $20 per unit, i) calculate price and quantity combination in each market, ii) Also calculate price and quantity combination if same price is charged in each market, iii) compare both polices (i), (ii) in terms of consumer/producer surplus and social welfare, and comment which factor led the monopolist to adopt policy (i) and which policy (i) or (ii) is beneficial for society.

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