A monopolist faces two different n1arkets (assume no resale between markets). The quantities sold in markets 1 and 2 are denoted Y1 andY2 (where tot al output y = Y1 + y2). In market 1, demand is given by D1(p1) = 60 - Pl and marginal revenue is M R1(y1) = 60 - 2y1. In market 2, demand

is given by D2(p2) = 50 - P2 and marginal revenue is MR2(y2) = 100 - 4y2. F o r a n y quantity of total output (y1 + y2), the monopolist's cost function is given by c(y1 + y2) = (y1 + y2)2, and marginal cost is MC(y1 +y2) = 2(y1 +y2). Please show your work for all parts.

For the following parts (a), (b), (c), suppose that the monopolist can third-degree price discriminate.

(a)Find the inverse de1nand functions p₁(yi) and p₂(y₂) and an expression for the monopolist 's total profit 1r (y1, Y2).

(b)Find the optimal prices (Pi, p2) and the quantities (Yi, y2) that the monopolist chooses for the two markets.

(c)Given your results from part (b), which of the two markets is more elastic in this case?

(d)Now suppose instead that the monopolist can first -degree (perfectly) price discriminate. Would the deadweight loss under 1s t-degree price discrimination ( D W L ₁ ) be larger or smaller thanthat in the case of 3^rd-degree price discrimination (D W L ₃ )? Explain.