Market Structures and Concentration: Measuring, Defining, and Analyzing

1. Chapter 2 Technology, Costs and Market Structure Industrial Organization: Chapter 2

2. Introduction • Industries have very different structures • numbers and size distributions of firms • ready-to-eat breakfast cereals: high concentration • newspapers: low concentration • How best to measure market structure • summary measure • concentration curve is possible • preference is for a single number • concentration ratio or Herfindahl-Hirschman index Industrial Organization: Chapter 2

3. Measure of concentration • Compare two different measures of concentration: Firm Rank Market Share Squared Market (%) Share 1 25 25 625 2 25 25 625 3 25 25 625 4 5 5 25 5 5 25 6 5 25 7 5 25 8 5 25 Concentration Index CR4 = 80 H = 2,000 Industrial Organization: Chapter 2

4. Firm Rank Market Share Squared Market (%) Share • Concentration index is affected by, e.g. merger 1 25 Assume that firms 4 and 5 decide to merge 25 Market shares change 625 2 25 25 625 3 25 25 625 4 5 5 } } } 25 100 10 5 5 25 6 5 The Concentration Index changes 25 7 5 25 8 5 25 Concentration Index CR4 = 80 85 H = 2,000 2,050 Industrial Organization: Chapter 2

5. What is a market? • No clear consensus • the market for automobiles • should we include light trucks; pick-ups SUVs? • the market for soft drinks • what are the competitors for Coca Cola and Pepsi? • With whom do McDonalds and Burger King compete? • Presumably define a market by closeness in substitutability of the commodities involved • how close is close? • how homogeneous do commodities have to be? • Does wood compete with plastic? Rayon with wool? Industrial Organization: Chapter 2

6. Market definition (cont.) • Definition is important • without consistency concept of a market is meaningless • need indication of competitiveness of a market: affected by definition • public policy: decisions on mergers can turn on market definition • Staples/Office Depot merger rejected on market definition • Coca Cola expansion turned on market definition • Standard approach has some consistency • based upon industrial data • substitutability is production not consumption (ease of data collection) Industrial Organization: Chapter 2

7. Market definition (cont.) • Government statistical sources • FedStats • Naics • The measure of concentration varies across countries • Use of production-based statistics has limitations: • can put in different industries products that are in the same market • The international dimension is important • Boeing/McDonnell-Douglas merger • relevant market for automobiles, oil, hairdressing Industrial Organization: Chapter 2

8. Market definition (cont.) • Geography is important • barrier to entry if the product is expensive to transport • but customers can move • what is the relevant market for a beach resort or ski-slope? • Vertical relations between firms are important • most firms make intermediate rather than final goods • firm has to make a series of make-or-buy choices • upstream and downstream production • measures of concentration may assign firms at different stages to the same industry • do vertical relations affect underlying structure? Industrial Organization: Chapter 2

9. Market definition (cont.) • Firms at different stages may also be assigned to different industries • bottlers of soft drinks: low concentration • suppliers of sift drinks: high concentration • the bottling sector is probably not competitive. • In sum: market definition poses real problems • existing methods represent a reasonable compromise Industrial Organization: Chapter 2

10. The Neoclassical View of the Firm • Concentrate upon a neoclassical view of the firm • the firm transforms inputs into outputs Inputs Outputs The Firm • There is an alternative approach (Coase) • What happens inside firms? • How are firms structured? What determines size? • How are individuals organized/motivated? Industrial Organization: Chapter 2

11. The Single-Product Firm • Profit-maximizing firm must solve a related problem • minimize the cost of producing a given level of output • combines two features of the firm • production function: how inputs are transformed into output Assume that there are n inputs at levels x1 for the first, x2 for the second,…, xn for the nth. The production function, assuming a single output, is written: Q = F(x1, x2, x3,…,xn) • cost function: relationship between output choice and production costs. Derived by finding input combination that minimizes cost n  wixi Minimize subject to F(x1, x2, x3,…,xn) = Q1 xi i=1 Industrial Organization: Chapter 2

12. The production function can be illustrated as a set of isoquants, one for each level of output Now assume that input 1 becomes cheaper • Review input choice: one output and two inputs Cost of producing output Q1 is minimized by finding the point where an isocost line is tangent to the Q1 isoquant This makes the isocost lines less steep x2 The input choice is x11 of input 1 and x12 of input 2 Production cost can be illustrated as a set of isocost lines, with slope w1/w2. The lower the isocost line, the lower the cost. The cost-minimizing input combination changes The new cost- minimizing point x12 x22 More of input 1 is used and less of input 2 Q2 Q1 Q0 x11 x21 x1 Industrial Organization: Chapter 2

13. This analysis has interesting implications • different input mix across • time: as capital becomes relatively cheaper • space: difference in factor costs across countries • Analysis gives formal definition of the cost function • denoted C(Q): total cost of producing output Q • average cost = AC(Q) = C(Q)/Q • marginal cost: • additional cost of producing one more unit of output. • Slope of the total cost function • formally: MC(Q) = dC(Q)/d(Q) Industrial Organization: Chapter 2

14. Cost curves: an illustration Typical average and marginal cost curves $/unit Relationship between AC and MC MC If MC < AC then AC is falling AC If MC > AC then AC is rising MC = AC at the minimum of the AC curve Quantity Industrial Organization: Chapter 2

15. Economies of scale • Definition: average costs fall with an increase in output • Represented by the scale economy index AC(Q) S = MC(Q) • S > 1: economies of scale • S < 1: diseconomies of scale • S is the inverse of the elasticity of cost with respect to output dC(Q) dQ dC(Q) C(Q) MC(Q) 1 hC = = = = C(Q) Q dQ Q AC(Q) S Industrial Organization: Chapter 2

16. An example • Take a simple example Output Total Cost Average Cost Marginal Cost Scale Economy ($) ($) ($) Index 5 725 } 145 140.5 91 140.5/91 = 1.54 6 816 136 Average cost is taken as the mean of 145 and 136 11 1331 } 121 122.5 157 122.5/157 = 0.78 12 1488 124 Average cost is taken as the mean of 121 and 124 816 - 725 Check the relationship to the elasticity of the cost curve Percentage increase in cost of increasing output from 5 to 6 = 11.8% (816+725)/2 6-5 Percentage increase in output = 18.2% (6+5)/2 hC = 11.8/18.2 = 0.65 and 1/ hC = 1/0.65 = 1.54 Industrial Organization: Chapter 2

17. Minimum efficient scale: • output at which economies of scale are first exhausted $/unit With average cost curve AC1 minimum efficient scale is MES1 AC1 With average cost curve AC2 minimum efficient scale is MES2 AC2 MES1 Quantity MES2 Industrial Organization: Chapter 2

18. Natural monopoly • If the extent of the market is less than MES then the market is a natural monopoly: S > 1 in such a market. • But a natural monopoly can exist even if S < 1. Economies of scale • Sources of economies of scale • “the 60% rule”: capacity related to volume while cost is related to surface area • product specialization and the division of labor • “economies of mass reserves”: economize on inventory, maintenance, repair • indivisibilities Industrial Organization: Chapter 2

19. Indivisibilities VC $ • Some inputs can be employed only in indivisible units • transport routes • major items of capital equipment • Three implications: • cost is “lumpy” or fixed at F1 • maximum rated capacity Q1 • average fixed cost F1/Q falls with output up to rated capacity F1 FC Quantity Q1 $ ATC • Other inputs vary with output: variable costs • Average total costs exhibit economies of scale over some range AVC AFC Quantity Q1 Industrial Organization: Chapter 2

20. If projected output is greater than current capacity install higher-rated capacity equipment or add additional capacity • It may be cheaper to have spare capacity than operate up to capacity If projected output is greater than Q* it is cheaper to install higher capacity even though there is spare capacity $/unit AC1 AC2 Consistent with evidence on excess capacity: see Federal Statistics Q* Q1 Q2 Quantity Industrial Organization: Chapter 2

21. Fixed costs, indivisibilities and sunk costs • Indivisibilities make scale of entry an important strategic decision: • enter large with large-scale indivisibilities: heavy overhead • enter small with smaller-scale cheaper equipment: low overhead • Some indivisible inputs can be redeployed • aircraft • Other indivisibilities are highly specialized with little value in other uses • market research expenditures • rail track between two destinations • The latter are sunk costs: nonrecoverable if production stops • Fixed costs and sunk costs affect market structure by affecting entry Industrial Organization: Chapter 2

22. Multi-Product Firms • Many firms make multiple products • Ford, General Motors, 3M etc. • What do we mean by costs and output in these cases? • How do we define average costs for these firms? • total cost for a two-product firm is C(Q1, Q2) • marginal cost for product 1 is MC1 = C(Q1,Q2)/Q1 • but average cost cannot be defined fully generally • need a more restricted definition: ray average cost Industrial Organization: Chapter 2

23. Ray average cost • Assume that a firm makes two products, 1 and 2 with the quantities Q1 and Q2 produced in a constant ratio of 2:1. • Then total output Q can be defined implicitly from the equations Q1 = 2Q/3 and Q2 = Q/3 • More generally: assume that the two products are produced in the ratio 1/2 (with 1 + 2 = 1). • Then total output is defined implicitly from the equations Q1 = 1Q and Q2 = 2Q • Ray average cost is then defined as: C(1Q, 2Q) RAC(Q) = Q Industrial Organization: Chapter 2

24. An example of ray average costs • Assume that the cost function is: • Marginal costs for each product are: C(Q1, Q2) = 10 + 25Q1 + 30Q2 - 3Q1Q2/2 3Q2 C(Q1,Q2) MC1 = = 25 - 2 Q1 3Q1 C(Q1,Q2) MC2 = = 30 - 2 Q2 Industrial Organization: Chapter 2

25. C(Q1, Q2) = 10 + 25Q1 + 30Q2 - 3Q1Q2/2 • Ray average costs: assume 1 = 2 = 0.5 Q1 = 0.5Q; Q2 = 0.5Q C(0.5Q, 0.5Q) RAC(Q) = Q 10 + 25Q/2+ 30Q/2 - 3Q2/8 10 55 3Q - + = = Q 2 8 Q Now assume 1 = 0.75; 2 = 0.25 C(0.75Q, 0.25Q) RAC(Q) = Q 10 + 75Q/4+ 30Q/4 - 9Q2/32 10 105 9Q - + = = Q 4 32 Q Industrial Organization: Chapter 2

26. Economies of scale and multiple products • Definition of economies of scale with a single product C(Q) AC(Q) S = = MC(Q) Q.MC(Q) • Definition of economies of scale with multiple products C(Q1,Q2,…,Qn) S = MC1Q1 + MC2Q2 + … + MCnQn • This is by analogy to the single product case • relies on the implicit assumption that output proportions are fixed • so we are looking at ray average costs in using this definition Industrial Organization: Chapter 2

27. The example once again C(Q1, Q2) = 10 + 25Q1 + 30Q2 - 3Q1Q2/2 MC1 = 25 - 3Q2/2 ; MC2 = 30 - 3Q1/2 Substitute into the definition of S: C(Q1,Q2,…,Qn) S = MC1Q1 + MC2Q2 + … + MCnQn 10 + 25Q1 + 30Q2 - 3Q1Q2/2 = 25Q1 - 3Q1Q2/2 + 30Q2 - 3Q1Q2/2 It should be obvious in this case that S > 1 This cost function exhibits global economies of scale Industrial Organization: Chapter 2

28. Economies of Scope • Formal definition C(Q1, 0) + C(0 ,Q2) - C(Q1, Q2) SC = C(Q1, Q2) • The critical value in this case is SC = 0 • SC < 0 : no economies of scope; SC > 0 : economies of scope. • Take the example: 10 + 25Q1 + 10 + 30Q2 - (10 + 25Q1 + 30Q2 - 3Q1Q2/2) > 0 SC = 10 + 25Q1 + 30Q2 - 3Q1Q2/2 Industrial Organization: Chapter 2

29. Economies of Scope (cont.) • Sources of economies of scope • shared inputs • same equipment for various products • shared advertising creating a brand name • marketing and R&D expenditures that are generic • cost complementarities • producing one good reduces the cost of producing another • oil and natural gas • oil and benzene • computer software and computer support • retailing and product promotion Industrial Organization: Chapter 2

30. Flexible Manufacturing • Extreme version of economies of scope • Changing the face of manufacturing • “Production units capable of producing a range of discrete products with a minimum of manual intervention” • Benetton • Custom Shoe • Levi’s • Mitsubishi • Production units can be switched easily with little if any cost penalty • requires close contact between design and manufacturing Industrial Organization: Chapter 2

31. Flexible Manufacturing (cont.) • Take a simple model based on a spatial analogue. • There is some characteristic that distinguishes different varieties of a product • sweetness or sugar content • color • texture • This can be measured and represented as a line • Individual products can be located on this line in terms of the quantity of the characteristic that they possess • One product is chosen by the firm as its base product • All other products are variants on the base product Industrial Organization: Chapter 2

32. Flexible Manufacturing (cont.) • An illustration: soft drinks that vary in sugar content (Diet) (LX) (Super) 0 0.5 1 Low High Each product is located on the line in terms of the amount of the characteristic it has This is the characteristics line Industrial Organization: Chapter 2

33. The example (cont.) (Diet) (LX) (Super) • Assume that the process is centered on LX as base product. 0 0.5 1 Low High A switching cost s is incurred in changing the process to either of the other products. There are additional marginal costs of making Diet or Super - from adding or removing sugar. These are r per unit of “distance” between LX and the other product. There are shared costs F: design, packaging, equipment. Industrial Organization: Chapter 2

34. The example (cont.) • In the absence of shared costs there would be specialized firms. • Shared costs introduce economies of scope. m S Total costs are: C(zj, qj) = F + (m - 1)s + [(c + rzj - z1)qj] j=1 If production is 100 units of each product: one product per firm with three firms C3 = 3F + 300c one firm with all three products C1 = F + 2s + 300c + 100r C1 < C3 if 2s + 100r < 2F  F > 50r + s This implies a constraint on set-up costs, switching costs and marginal costs for multi-product production to be preferred. Industrial Organization: Chapter 2

35. Economies of scale and scope • Economies of scale and scope affect market structure but cannot be looked at in isolation. • They must be considered relative to market size. • Should see concentration decline as market size increases • For example, entry to the medical profession is going to be more extensive in Chicago than in Oxford, Miss Industrial Organization: Chapter 2 2-37

36. Network Externalities • Market structure is also affected by the presence of network externalities • willingness to pay by a consumer increases as the number of current consumers increase • telephones, fax, Internet, Windows software • utility from consumption increases when there are more current consumers • These markets are likely to contain a small number of firms • even if there are limited economies of scale and scope Industrial Organization: Chapter 2

37. The Role of Policy • Government can directly affect market structure • by limiting entry • taxi medallions in Boston and New York • airline regulation • through the patent system • by protecting competition e.g. through the Robinson-Patman Act Industrial Organization: Chapter 2

38. Market Performance • Market structure is often a guide to market performance • But this is not a perfect measure • can have near competitive prices even with “few” firms • Measure market performance using the Lerner Index P-MC LI = P Industrial Organization: Chapter 2

39. Market Performance (cont.) • Perfect competition: LI = 0 since P = MC • Monopoly: LI = 1/h – inverse of elasticity of demand • With more than one but not “many” firms, the Lerner Index is more complicated: need to average. • suppose the goods are homogeneous so all firms sell at the same price P-SsiMCi LI = P Industrial Organization: Chapter 2

40. Industrial Organization: Chapter 2

41. MC´A MC´B Assume two identical firms each with costs AC1 If they are to produce a given output at lowest cost, they must operate at the same marginal cost $/unit MC Why? Assume firm A is operating at MCA and firm B is operating at MCB MCA AC1 Transferring one unit of output from A to B lowers total cost MCB If the two firms operate at the same marginal cost they must produce identical outputs Suppose not: firm A has output QA and firm B has output QB QB QA Quantity Transferring one unit of output from A to B lowers total cost Industrial Organization: Chapter 2

42. Q1 2Q1 Q2 2Q2 It follows that AC2 represents the lowest possible average cost if output is produced by two firms: AC2 is obtained by adding AC1 to itself horizontally AC1 is average cost if output is produced by one firm. Now assume that output is produced by two firms. If total output is 2Q1 then we know that each firm has to produce Q1 and average cost is AC1 $/unit This market is a natural monopoly up to output QM even though this is greater than MES Q*: it is less costly for output to be produced by one rather than two firms: subadditivity If total output is 2Q2 then we know that each firm has to produce Q2 and average cost is AC2 If total output is 2Q* then we know that each firm has to produce Q* and average cost is AC* AC1 AC2 AC1 AC2 AC* Q* QM 2Q* Quantity Industrial Organization: Chapter 2

43. Illustration of ray average costs Industrial Organization: Chapter 2