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Single–Price Monopoly “single–price” means that it charges the same price for each unit it sells : it does not price discriminate among different buyers, or among different units bought by the same buyer two approaches first : choosing quantity pick quantity q so as to maximize profits p(q)q − C(q, w) (1) where p(q) is the (aggregate) inverse demand curve it faces — and C(q, w) is the cost function of chapter 3 (with y now called q) an alternative approach would be to have the firm – Typeset by FoilTEX – 1 choosing price pick the price P to maximize profits P Q(P ) − C(Q(P ), w) (2) where Q(P ) is the market demand curve first–order conditions Q(P ) + P Q0(P ) − Cq Q0(P ) = 0 (3) Q(P ) Q (P )P [ 0 + 1] − Cq Q0(P ) = 0 Q (P )P (4) or 0 which can be written – Typeset by FoilTEX – 2 1 −Q0(P )[M C − P (1 − )] = 0 – Typeset by FoilTEX – (5) 3 where P ≡ −Q (P ) Q(P ) 0 (6) is the (absolute value of the) market own–price elasticity of demand so at the monopoly’s optimum 1 M C = P (1 − ) (7) marginal revenue : 1 M R ≡ P (1 − ) since M R ≡ (8) d dq (p(q)q) mark–up rule : – Typeset by FoilTEX – 4 P = M C( ) −1 (9) need : > 1 – Typeset by FoilTEX – 5