Economic Analysis for Business Decisions Market Power

Overview: Market Power • Competitive Equilibrium • Profit Maximization • Monopoly – Output and Price Analytics • Coordination of Multiple Plants • Pricing with Learning Effects and Network Externalities 1 Competitive 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 2 Market 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 Production: Cost C(Q) Q Distribution and Sale: Revenue R(Q) How do you maximize profit Π=R–C ? (drum roll) Pick Q such that MR = MC 3 Monopoly: Price and Output Analytics • Focus on monopoly, the simplest case of market power • Suppose we have Demand: Costs: Q = 100 - P 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. 4 Direct 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 5 MR 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 Q0(∆P) P0 P1 P1 D Q0 Q0+1 Q 6 MR, Calculus Version R = P(Q)Q MR = dR dP = P+Q dQ dQ (Compare to MR = P1 + Q0 ∆P) 7 The Monopoly Picture 120 Monopoly Solution 100 Demand 80 MR MR=MC 60 55 Competitive Solution 40 20 MC=AC c 0 0 20 40 45 60 80 c 100 120 The Mark-Up Formula MR = ⎛ 1⎞ Q dP ⎞ ⎛ ⎟⎟ = P ⎜ 1 + ⎟ = P ⎜⎜ 1 + ε P dQ ⎠ ⎝ ⎝ ⎠ dP dQ P+Q At a maximum of profits, we have MR = MC, so MC = 1⎞ ⎛ P ⎜1 + ⎟ ε ⎠ ⎝ Or, rearranging terms, 1 P − MC =− P ε ε is the price elasticity of demand 8 Example: 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 9 Multi-plant Firms Plant H: QH Cost CH(QH) Distribution and Sale: Revenue R(QH + QL) Plant L: QL Cost CL(QL) • Max profit Π = R (QH + QL) - CH(QH) - CL(QL), by • MCH(QH) = MCL(QL) = MR (QH + QL) Multi-Plant Firm: Graphical Setup Costs with Multiple Plants 8 MC L 7.5 MC H 7 6.5 Cost 6 5.5 5 4.5 4 3.5 3 0 20 40 60 80 100 120 Quantity 10 Overall MC Curve is the Horizontal Sum of Individual Plant MC Curves Costs with Multiple Plants 8 MC L 7.5 MC H 7 MC Firm 6.5 Cost 6 5.5 5 4.5 4 3.5 3 0 20 40 60 80 100 120 Quantity Pricing and Allocation of Production in a Multi-Plant Firm Costs with Multiple Plants 8 MC L 7.5 MCH 7 MCT 6.5 Cost 6 5.5 5 4.5 D 4 3.5 3 0 20 40 60 Quantity 80 100 120 MR 11 Algebra 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 12 Adjustments 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. 13 Take 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 14