Overview: Market Power • Competitive Equilibrium • Profit Maximization • Monopoly – Output and Price Analytics • Coordination of Multiple Plants • Pricing with Learning Effects and Network Externalities 1Competitive Equilibrium • Mechanism of Competitive Equilibrium – Demand Growth • Higher prices stimulate more supply from existing firms • Emergence of profits causes entry/expansion of capacity – Demand shortfall • Lower prices cause cutbacks in in supply from existing firms • Losses (negative profits) cause exit/contraction of capacity – Processes continue until economic profits return to 0 2Market Power • Ability to raise price above costs and make sustainable profits – Economic costs and economic profits • Requires that the mechanism of competition fails to operate – Barriers to entry – Sufficient product differentiation (that cannot be copied) – Secret technology - No information on profitability – Market too small relative to efficient production scale Profit Maximization ? Pick Q such that MR = MC Production: Cost C(Q) Distribution and Sale: Revenue R(Q) Q How do you maximize profit Π = R – C(drum roll) 3Monopoly: Price and Output Analytics • Focus on monopoly, the simplest case of market power • Suppose we have Demand: Q = 100 - P Costs: MC = AC = 10 Direct Monopoly Solution Demand: Q = 100 – P implies that Revenue: R = PQ = (100 - Q) Q MC = AC = 10 implies that costs are C = 10 Q Profit: Π = R - C = (100 - Q) Q - 10 Q = (100Q - Q2)- 10Q Want to find Q (or P) that maximizes Π. 4Direct Monopoly Solution Profit: Π = (100Q - Q2) - 10Q Take derivative: d Π/dQ = (100 - 2Q) – 10 ( = MR – MC ) Profits are maximized where dΠ/dQ = 0 0 = (100 - 2Q) – 10 ( = MR – MC) Q = 45 With price P = 100 - Q = 55 5MR in Detail Approximate MR as ∆R from selling one more unit i.e., compare selling Q0 at P0 with selling Q1 = (Q0+1) at P1 [with P1 ≤ P0] MR = R1 -R0 = P1Q1 -P0Q0 = P1(Q1 -Q0) + Q0(P1 -P0) = P1 + Q0 ∆P MR in Pictures P Q D Q0 Q0+1 P0 P1 Q0(∆P) P1 6MR, Calculus Version R = Q Q P ( ) dR dPMR = = P+QdQ dQ (Compare to MR = P1 + Q0 ∆P) 7The Monopoly Picture 0 20 40 60 80 100 120 0 20 40 60 80 100 120 Demand MR c c MR=MC 55 45 MC=AC Monopoly Solution Competitive Solution ⎞⎟⎠ 1 ε+⎛⎜⎝ = ⎞ ⎟⎟⎠ ⎞⎟⎠ 1 ε+ 1 ε + − ⎛⎜⎝ ⎛⎜⎜⎝ = = = Or, rearranging terms, − += The Mark-Up Formula dPMR P Q P 1 Q dP P 1dQ P dQ At a maximum of profits, we have MR = MC, so MC P 1 P MC ε is the price elasticity of demand P 8Example: Supermarkets and Convenience Stores • Supermarkets: ε ≈ −10 (P-MC)/P = .1, 10% markup • Small convenience stores: ε ≈ −5 (P-MC)/P = .2, 20% markup • Which do you expect to show higher profits? Example: Drug pricing • Elasticity estimates often are near -1.0 • If elasticity is -1.1, then (P –MC)/P = .9; 90% markup • e.g. Tagamet monopoly, elasticity is -1.7 (P-MC)/P = .58; 58% markup 9Multi-plant Firms • Π = H + QL H(QH L(QL), by H(QH) = MCL(QL) = MR (QH + QL) Plant H: Cost CH(QH) Distribution and Sale: Revenue R(QH + QL) QH Plant L: Cost CL(QL) QL Max profit R (Q ) - C ) - C•MCMulti-Plant Firm: Graphical Setup 3 4 5 6 7 8 0 100 120 MC H MC L Costs with Multiple Plants 3.5 4.5 5.5 6.5 7.5 20 40 60 80 Quantity Cost 10Overall MC Curve is the Horizontal Sum of Individual Plant MC Curves 3 4 5 6 7 8 0 100 120 MC H MC L MCCosts with Multiple Plants 3.5 4.5 5.5 6.5 7.5 20 40 60 80 Quantity Cost Firm Pricing and Allocation of Production in a Multi-Plant Firm i l3 4 5 6 7 8 0 MCH MCL MCT D MR Costs w th Multiple P ants 3.5 4.5 5.5 6.5 7.5 20 40 60 80 100 120 Quantity Cost 11Algebra of Constructing MC Curve Plant “H”: MCH = 5 + Q/10 Plant “L”: MCL = 4 + Q/20 • Up to Q=20, all production is at “L” and the cost curve is equal to the single plant supply curve (since MCL(20) = MCH(0) = 5 ) • Above Q=20, some production occurs at “H” Algebra of Overall MC • To sum horizontally, must solve for Q to add QH= -50 + 10 MC QL= -80 + 20 MC • So for QT< 20 QT= QL= -80 + 20 MC or MC = 4 + QT /20 • And for QT > 20, QT = QL +QH QT= -130 + 30 MC or MC = 13/3 + QT/30 12Adjustments to Current MR and MC • When current production has future implications, the overall profit-maximizing output is typically not given by (current period) MC0 = MR0 • Learning: Additional production Q0 gives MR0 plus lower future costs C1. • Network Externalities: Additional production Q0 gives MR0 plus larger future revenue R1. • Produce more and lower price. How much depends on size of learning/network effects. 13Take Away Points • Nearly any firm has some degree of market power • MR = MC; MR = MC; MR = MC (say 100 times) • MR = MC has a number of implications – The mark-up formula summarizes optimal pricing – With multiplant firms, MR = MCH = MCL