Introduction to Technology and Cost Optimization in Industrial Organization

1. ECON 4100: Industrial Organization Technology and Costs Lecture 4

2. Introduction • Costs • Cost minimization and profit maximization • economies of size and scale • fixed, sunk, avoidable, and variable costs

3. 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?

4. 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

5. 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

6. 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)

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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 • College degrees • The latter are sunk costs: nonrecoverable if production stops • Fixed costs and sunk costs affect market structure by affecting entry

15. Next • Multi-product firm • basic structure of multiproduct firms • multiproduct economies of scale • ray average cost • economies of scope • Read Chapter 4

17. 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

18. 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