# Demand and Elasticity

**Pages:**3 (902 words)

**Published:**January 12, 2013

Linear demand curve: Q = a – bP Elasticity: E d = (ΔQ/ΔP)/(P/Q) = -b(P/Q)E d = -1 in the middle of demand curve (up is more elastic) Total revenue and Elasticity:Elastic: Ed < -1↑P→↓R (↑P by 15%→↓Q by 20%)

Inelastic: 0 > Ed > -1↑P→↑R (↑P by 15%→↓Q by 3%)

Unit elastic: Ed = -1R remains the same (↑P by 15%→↓Q by 15%) MR: positive expansion effect (P(Q) – sell of additional units) + price reduction effect (reduces revenues because of lower price (ΔP/ΔQ)/Q) 1. Monopoly – maximizes profit by setting MC = MR

Monopolist’s Markup = price-cost margin = Lerner index: (P-MC)/P = -1/ Ed (the less elastic demand, the greater the markup over marginal cost) 2. Price Discrimination

Perfect price discrimination – the firm sets the price to each individual consumer equal to his willingness to payMR=P(Q)=demand (without the price reduction effect), no consumer surplus,find profit from graph Two-part Tariffs – a fixed fee (= consumer surplus) + a separate per-unit price for each unit they buy (P = MC) 2 groups of customers – with discrimination: inverse demand function for individual demands → MR → MR=MC * without discrimination: sum of not-inverse demand functions = one option for aggregate demand. Other option is the “rich” people demand function. Compare profits to find Qagg. * max fixed payment F (enabling discrimination) = ∆ π; max d added to MC1 = ∆π/q1 (with discrimination) Quantity-dependent pricing – one price for first X units and a cheaper price for units above quantity X. profit function = π = Pa*Qa+Pb(Qb-Qa)-2Qb Qb includes Qa, so the additional units sold are Qb-Qa. Example: P=20-Q. Firm offers a quantity discount. Setting a price for Qa (Pa) and a price for additional units Qb-Qa (Pb). Pa=20-Qa Pb=20-Qb. Π=(20-Qa)Qa + (20-Qb)(Qb-Qa) -2Qb = 18Qb-Qa^2 – Qb^2 +QaQb derive π’a=-2Qa+Qb π’b=18-2Qb+Qa compare to 0. 2Qa=Qb. Plug into second function: 18-2(2Qa)+Qa=0. So Qa=6 Qb=12 3. Cost and Production...

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