1. The Determination of Costs Howard Davies

2. Objectives n To examine the relationship between inputs and outputs n To identify the most important determinants of cost per unit –economies of capacity utilization –economies of scale –economies of scope –learning effects n To identify the difficulties involved in the empirical estimation of these effects n To explain the unusual features of costs in the information sector

3. The Relationship Between Inputs and Outputs n The fundamental relationship is that between inputs and outputs - expressed as the production function n This can be examined at a number of levels –the economy as a whole –the industry –the firm n A number of different mathematical forms can be used to model the relationship –Cobb-Douglas: Q = aK a L b –translog production function

4. The Cobb-Douglas Example n Q = aK a L b : Where K= capital; L = Labour n As each individual input (K,L) is increased, output increases, but at a decreasing rate - the principle of diminishing returns - one of the most fundamental economic ideas n A production function identifies many different techniques within the same technology

5. The Cobb-Douglas Example n Q = aK a L b : Where K= capital; L = Labour n If (a+b) > 1; economies of scale n If (a+b) < 1; diseconomies of scale n If (a+b) = 1; constant returns to scale

6. How to Find the Cost Minimizing Way to Produce Each Level of Output? n As a mathematical problem, for level of output Q* minimiseTC=(w)(L)+(r)(K) subject to Q*=aK a L b As a graphical approach, see the book p.133 As a verbal explanation –the ratio of the wage rate to the cost of capital should be equal to the ratio of the marginal productivity of labour to the marginal productivity of capital: WHY? –because otherwise $1 could be moved from spending on one input to another and increase output without increasing cost

7. From Production Functions to Cost Curves n Short run - some inputs are fixed. (K). The firm is restricted to a fixed set of plant and equipment –capacity utilisation decisions n Long run - both inputs are variable. (K,L). The firm can choose the set of plant and equipment it wants –investment decisions

8. From Production Functions to Cost Curves n Short run cost curves each short run curve shows costs for a specific set of plant and equipment AFC declines Average variable cost rises after some point AC is U-shaped n Long run cost curves the firm can choose from all of the known sets of plant and equipment the shape of the curve depends upon economies or diseconomies of scale

9. Economies and diseconomies of scale n The source of scale economies –in manufacturing, engineering relationships –indivisibilities –specialization and division of labour –stochastic economies n The source of diseconomies –managerial diseconomies –control loss –transactional problems

10. Empirical evidence? n Statistical approach –production function or cost function n Engineering approach n Survivor technique n BUT THEY ALL EMBODY PROBLEMS

11. Statistical approach n Collect data on size and cost, or on inputs and outputs and fit a production or cost function –but are the observed firms on their cost curve? They may be above it –how can firms at high cost/inefficient sizes survive? If they cannot where do we get the data from? –Is the curve fitted a good fit? n Observed firms may be X-inefficient, so a ‘data envelope’ approach may be required

12. The fundamental problem n What we need to know is: n WHAT COST WOULD BE IF FIRMS WERE PRODUCING OUTPUT USING THE BEST SET OF PLANT AND EQUIPMENT FOR THE PURPOSE, USING THE CURRENT TECHNOLOGY AND AT CURRENT FACTOR PRICES, AND IF THEY ARE 100% EFFICIENT n But we cannot observe that by looking at real firms

13. Engineering approach n Ask consulting engineers to design facilities of different sizes and calculate cost –advantage is that it does involve estimating cost for current technology and best practice –disadvantage is that this approach takes no account of the MANAGERIAL factors which might cause scale economies

14. The engineering approach gives this kind of result n$n$ Q MES

15. Survivor technique n Divide the industry into groups of firms by size –e.g. small, medium, large n Observe the market share of the different groups over time –if large firms gain share - scale economies –small firms - diseconomies –medium - U-shaped curve

16. Can market forces be relied upon to select out the lowest cost firms over time? n Firms might have different objectives, different products, different environments, different strategies n But used in a recent study of the US beer industry (Elzinga 1990)

17. Economies of Scope and Learning Effects n Economies of scope –the production of two or more products together is more efficient than producing them separately n Learning Effects –costs fall as cumulative output to date increases

18. Economies of scope n May arise from the existence of resources which can be shared by different products n Physical facilities or perhaps ‘core competences’ - but the latter might not be real

19. Multi-product Firms n Multi-product firms complicate the idea of scale economies –ray economies - if costs fall as more is produced of the same output mix –product-specific economies - if costs fall as output of a single product increases

20. Learning effects n Important in World War 2 - the same plants, same rate of output but lower costs over time n Most important for complex products and processes where humans can learn n A possible source of ‘first-mover’ advantages - important in business strategy n Boston Consulting Group made the experience curve and learning effects the centre of their approach in the 1970s

21. Costs in the information sectors n Products like software, CDs have unusual cost structures n Most costs are fixed and also SUNK –they cannot be even partially recovered –‘first copy’ costs and marketing costs n Average variable and marginal cost is almost zero n No natural limits to scale

22. Implications of this cost structure n High sunk costs may be an entry barrier because the cost of exit is low n Industries where consumers respond strongly to spending on sunk costs - advertising, R&D - tend to be more concentrated n Competition may force price right down to zero

23. Other ‘cost drivers’ n Location n Timing n Company policy - what type of product n Government policy - taxes, subsidies, health and safety n Vertical integration n Institutional factors - trade unions, the legal system, corruption etc