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Topic cost

  1. 1. Topic on Production and Cost Functions and Their Estimation
  2. 2. Production function <ul><li>A table, graph, or equation showing the maximum output rate of the product that can be achieved from any specified set of usage rates of inputs </li></ul>
  3. 3. Production function Thomas Machine Company
  4. 4. Production function Thomas Machine Company
  5. 5. Production function Thomas Machine Company
  6. 6. Law of diminishing marginal returns <ul><li>If equal increments of an input are added to a production process, and the quantities of other inputs are held constant, eventually the marginal product of the input will diminish </li></ul><ul><li>Note: 1) This is an empirical generalization. </li></ul><ul><li> 2) Technology remains fixed. </li></ul><ul><li> 3) The quantity of at least one input is </li></ul><ul><li>held fixed. </li></ul>
  7. 7. Marginal revenue product <ul><li>The amount that an additional unit of the variable input adds to the firm’s total revenue </li></ul><ul><li>MRP Y =  TR/  Y </li></ul>
  8. 8. Marginal expenditure <ul><li>The amount that an additional unit of the variable input adds to the firm’s total costs. </li></ul>ME Y =  TC /  Y
  9. 9. Optimal level of input use <ul><li>MRP Y = ME Y </li></ul>
  10. 10. Production functions with two variable inputs
  11. 11. Q = f (labor, machine Tools)
  12. 12. Isoquant <ul><li>A curve showing all possible (efficient) combinations of inputs that are capable of producing a certain quantity of output </li></ul><ul><li>Iso quant </li></ul><ul><li> </li></ul><ul><li>same quantity </li></ul>
  13. 13. Labor Capital 0 K 2 100 200 300 K 1 L 2 L 1
  14. 14. Marginal rate of technical substitution <ul><li>Shows the rate at which one input can be substituted for another input, if output remains constant. (Slope of the isoquant.) </li></ul><ul><li> </li></ul><ul><li>Given Q = f(X 1, X 2 ) </li></ul><ul><li>MRTS = -  X 2 /  X 1 </li></ul><ul><li> = -MP 1 / MP 2 </li></ul>
  15. 15. Isocost curves <ul><li>Various combinations of inputs that a firm can buy with the same level of expenditure </li></ul><ul><li>P L L + P K K = M </li></ul><ul><li>where M is a given money outlay. </li></ul>
  16. 16. Labor Capital 0 M/P K M/P L Slope = -P K /P L
  17. 17. Maximization of output for given cost Labor Capital 0 100 200 300 R
  18. 18. MP L /P L = MP K /P K Labor Capital 0 100 200 300 R
  19. 19. Optimal Lot Size <ul><li>To consider the size of inventory </li></ul><ul><li>Find the relationship between size of lot and total annual cost. </li></ul>
  20. 20. What Toyota Taught the World? <ul><li>Lower the cost per setup </li></ul><ul><li>Reduce the optimal lot size </li></ul><ul><li>Just-in-time production system </li></ul>
  21. 21. Returns to scale <ul><li>If the firm increases the amount of all inputs by the same proportion: </li></ul><ul><li>Increasing returns means that output increases by a larger proportion </li></ul><ul><li>Decreasing returns means that output increases by a smaller proportion </li></ul><ul><li>Constant returns means that output increases by the same proportion </li></ul>
  22. 22. Output elasticity <ul><li>The percentage change in output resulting from 1 percent increase in all inputs. </li></ul><ul><li>  > 1 ==> increasing returns </li></ul><ul><li> < 1 ==> decreasing returns </li></ul><ul><li> = 1 ==> constant returns </li></ul>
  23. 23. Example: Xerox <ul><li>Sending out teams of engineers and technicians to visit other firms to obtain information concerning best-practice methods and procedures. </li></ul><ul><li>Competitive Benchmarking </li></ul>
  24. 24. Measurement of Production Functions <ul><li>Three types of statistical analysis </li></ul><ul><li>Time series data </li></ul><ul><li>Cross section data </li></ul><ul><li>Technical information </li></ul>
  25. 25. The Analysis of Costs
  26. 26. Opportunity costs <ul><li>The value of the other products that the resources used in production could have produced at their next best alternative </li></ul>
  27. 27. Historical costs <ul><li>The amount the firm actually paid for a particular input </li></ul>
  28. 28. Explicit vs. implicit costs <ul><li>Explicit costs include the ordinary items that an accountant would include as the firms expenses </li></ul><ul><li>Implicit costs include opportunity costs of resources owned and used by the firm’s owner </li></ul>
  29. 29. Short run <ul><li>A period of time so short that the firm cannot alter the quantity of some of its inputs </li></ul><ul><li>Typically plant and equipment are fixed inputs in the short run </li></ul><ul><li>Fixed inputs determine the scale of the firm’s operation </li></ul>
  30. 30. Three concepts of total costs <ul><li>Total fixed costs = FC </li></ul><ul><li>Total variable costs = VC </li></ul><ul><li>Total costs = FC + VC </li></ul>
  31. 31. Fixed, variable, and total costs Media Corp.
  32. 32. Fixed, Variable, and Total Costs -- Media Corp.
  33. 33. Average and marginal costs Media Corp.
  34. 34. Average and marginal costs Media Corp.
  35. 35. Long-run cost functions <ul><li>Often considered to be the firm’s planning horizon </li></ul><ul><li>Describes alternative scales of operation when all inputs are variable </li></ul>Quantity of output Average cost
  36. 36. Long-run average cost function <ul><li>Shows the minimum cost per unit of producing each output level when any scale of operation is available </li></ul>Quantity of output Average cost SR average cost functions LR average cost
  37. 37. Key steps: Cost estimation process <ul><li>Definition of costs </li></ul><ul><li>Correction for price level changes </li></ul><ul><li>Relating cost to output </li></ul><ul><li>Matching time periods </li></ul><ul><li>Controlling product, technology, and plant </li></ul><ul><li>Length of period and sample size </li></ul>
  38. 38. Minimum efficient scale The smallest output at which long-run average cost is a minimum. Quantity of output Average cost Q mes
  39. 39. The survivor technique <ul><li>Classify the firms in an industry by size and compute the percentage of industry output coming from each size class at various times </li></ul><ul><li>If the share of one class diminishes over time, it is assumed to be inefficient </li></ul><ul><li>These firms are then operating below minimum efficient scale </li></ul>
  40. 40. Economies of scope <ul><li>Exist when the cost of producing two (or more) products jointly is less than the cost of producing each one alone. </li></ul><ul><li>S = C(Q 1 ) + C(Q 2 ) - C(Q 1 + Q 2 ) </li></ul><ul><li>C(Q 1 + Q 2 ) </li></ul>
  41. 41. Break-even analysis Quantity of output Dollars Total Revenue Total Cost Loss Profit