2. Production Outline: Introduction to the production function A production function for auto parts Optimal input use Economies of scale Least-cost production

3. The production function Production is the process of transforming inputs into semi-finished articles (e.g., camshafts and windshields) and finished goods (e.g., sedans and passenger trucks). The production function indicates that maximum level of output the firm can produce for any combination of inputs.

4. General description of a production function Let: Q = F (M, L, K) [1] Where Q is the quantity of output produced per unit of time (measured in units, tons, bushels, square yards, etc.), M is quantity of materials used in production, L is the quantity of labor employed, and K is the quantity of capital employed in production.

5. Technical efficiency The production function indicates the maximum output that can be obtained from a given combination of inputs— that is, we assume the firm is technically efficient.

6. A production function for auto parts Consider a multi-product firm that supplies parts to major U.S. auto manufacturers. Its production function is given by Let Q = F(L, K) Where Q is the quantity of specialty parts produced per day, L is the number of workers employed per day, and K is plant size (measured in thousands of square feet).

7. This table [1] shows the quantity of output that can be obtained from various combinations of plant size and labor

8. The short run Inputs that cannot be varied in the short run are called fixed inputs. Inputs that can vary are called (not surprisingly) variable inputs The short run refers to the period of time in which one or more of the firm’s inputs is fixed—that is, cannot be varied

9. The long run The long run is the period of time sufficiently long to allow the firm to vary all inputs—e.g., plant size, number of trucks, or number of apple trees.

10. Marginal product Marginal product is the additional (or extra) output resulting from the employment of one more unit of a variable input, holding all other inputs constant. In our example, the marginal product of labor (MP L ) is the extra output of auto parts realized by employing one additional worker, holding plant size constant

11. Production of specialty parts, assuming a plant size of 10,000 square feet

12. Law of diminishing returns As units of a variable input are added (with all other inputs held constant), a point is reached where additional units will add successively decreasing increments to total output—that is, marginal product will begin to decline. Notice that, after 40 workers are employed, marginal product begins to decline

13. 500 400 300 200 100 0102030405060708090100110120130140 Total Output 20,000-square-foot plant 10,000-square-foot plant Number ofWorkers The total product of labor

14. The marginal product of labor when plant size is 10,000 square feet 5.0 4.0 3.0 2.0 1.0 0 102030405060708090100110130140 Marginal Product Number ofWorkers –1.0 –2.0 120

15. Optimal use of an input By hiring an additional unit of labor, the firm is adding to its costs—but it is also adding to its output and thus revenues.

16. Marginal revenue product of labor (MRP L ) The marginal revenue product of labor (MRP L ) is given by MRP L = (MR)(MP L ) [6.2] Where MR marginal revenue—that is, the additional (extra) revenue realized by selling one more unit. Example: If MP L is 5 units, and the firm can sell additional units for $6 each, then: MRP L = (MR)(MP L ) = (5)($6) = $30

17. Marginal cost of labor (MC L ) What additional cost does the firm incur (wages, benefits, payroll taxes, etc.) by hiring one more worker?

18.  -maximizing rule of thumb The firm should employ additional units of the variable input (labor) up to the point where MRP L = MC L 1 1 In terms of calculus, we have: MRP L = (MR)(MP L ) = (dR/dQ)(dQ/dL) and MC L = dC/dL

19. Example Example: The firm has estimated that the cost of hiring an additional worker is equal to $160 per day, that is, MC L = P L = $160. Assume the firm can sell all the parts it wants at a price of $40. Hence, MR = $40 Thus the MRP L = (MR)(MP L ) = ($40)(MP L )

21. Problem Let the production function be given by: Q = 120L – L 2 The cost function is given by C = 58 + 30L The firm can sell an unlimited amount of output at a price equal to $3.75 per unit 1.How many workers should the firm hire? 2.How many units should the firm produce?

22. Production in the long run The scale of a firm’s operation denotes the levels of all the firm’s inputs. A change in scale refers to a given percentage change in all the firm’s inputs—e.g., labor, materials, and capital. If we say “the scale of production has increased by 15 percent,” we mean the firm has increased its employment of all inputs by 15 percent.

23. Returns to scale Returns to scale measure the percentage change in output resulting from a given percentage change in inputs (or scale)

24. 3 cases 1.Constant returns to scale: 10 percent increase in all inputs results in a 10 percent increase in output. 2.Increasing returns to scale: 10 percent increase in all inputs results in a more than 10 percent increase in output. 3.Decreasing returns to scale: 10 percent increase in all inputs results in a less than 10 percent increase in output.

25. Sources of increasing returns 1.Specialization of plant and equipment Example:Large scale production in furniture manufacturing allows for application of specialized equipment in metal fabrication, painting, upholstery, and materials handling. 2.Economies of increased dimensions Example: Doubling the circumference of pipeline results in a fourfold increase in cross sectional area, and hence more than doubling of capacity, measured in gallons per day. 3.Economies of massed reserves. Example: A factory with one stamping machine needs to have spare 100 parts in inventory to be prepared for breakdown—does a factory with 20 machines need to have 2,000 spare parts on hand?

26. Economies of increased dimensions r h

27. Effect of a 1 inch change in vessel radius Surface Area and Volume PIr (in.)h (in.)S.A. (sq. in.)V (cu. in.) 3.14166104146.9021130.973 3.14167104838.0531539.380 Change in S.A (%)Change in V. (%) 16.666736.111

28. Intermodal Freight Containers The shift from the 20 foot to the 40 foot freight container has made shipping goods more economical See linklink

29. Fixed and Sunk Costs Fixed costs (FC) are elements of cost that do not vary with the level of output. Examples: Interest payments on bonded indebtedness, fire insurance premiums, salaries and benefits of managerial staff. Sunk costs are costs already incurred and hence non-recoverable. Examples: Research & development costs, advertising costs, cost of specialized equipment.

30. Definitions Variable cost (VC) is the sum of the firm’s expenditure for variable inputs such as hourly employees, raw materials or semi-finished articles, or utilities. Average total cost (SAC) is total cost divided by the quantity of output. Average variable cost (AVC) is variable cost divided by the quantity of output. Marginal cost (SMC) is the addition to total cost attributable to the last unit produced

31. Firm’s Costs in the Short Run

32. 3,000 060 Output (Thousands of Units) Total Cost (Thousands of Dollars) 555045403530252015105 2,000 1,000 Cost function

34. 64 060 Output (Thousands of Units) Cost/Unit (Thousands of Dollars) 44 48 52 56 555045403530252015105 SMC SAC 60

35. Relationship between Average and Marginal  When average cost is falling, marginal cost lies everywhere below average cost.  When average cost is rising, marginal cost lies everywhere above average cost.  When average cost is at its minimum, marginal cost cost is equal to average cost. If your most recent (marginal) grades are higher than your GPA at the start of the term, your GPA will rise

36. What explains rising (short-run) marginal cost? If labor is the only variable input then marginal cost can be expressed by: [7.1] Recall that the marginal product of labor will begin to fall at some point due to the law of diminishing returns.

37. Behavior of Average Fixed Cost As output increases, fixed cost can be spread more thinly

38. Production costs is the long run In the long run there are no fixed inputs; hence all costs are “variable.” The long run average cost curve shows the minimum average cost achievable at each level of output in the long run—that is, when all inputs are variable.

39. Constant Returns to Scale $5 0 Output (Thousands of Units) Long-Run Average Cost 4 21614410872 SAC 1 (9,000-square- foot plant) - SAC 2 (18,000-square foot plant) ( SAC 3 27,000-square- foot plant) SMC 1 SMC 2 SMC 3 LAC = LMC

40. The U-Shaped Long Run Average Cost Function Increasing returns Decreasing returns

41. Notice on the previous slide that up to a scale of Q MIN, the firm experiences decreasing (long run) unit cost. Economies of scale are exhausted at the point

42. Minimum Efficient Scale (Q MES ) Q MES is the minimum scale of operation at which long unit production costs can be minimized.

43. LAC Demand Q MES is large relative to he “size of the market.” Q Cost per unit 0 10002000 To produce on an efficient scale, you must supply 50% of the product demanded at a price equal to minimum unit cost

44. How large do you have to be to minimize unit costs? 1  Not very large (as a percent of U.S. consumption) : Bricks, flour milling, machine tools, cement, glass containers, cigarettes, shoes, bread baking.  Fairly large (as a percent of U.S. consumption): Synthetic fibers, passenger cars, household refrigerators and freezers, commercial aircraft.  Very large (as a percent of U.S. consumption): Turbine generators, diesel engines, electric motors, mainframe computers. 1 F.M. Scherer and D. Ross. Industrial Market Structure and Performance, 3 rd edition, 1990, pp. 115-116.

47. Local telephone service, electricity distribution, and cable TV distribution are well represented by this cost function.