1. Production and Cost in the Long Run Overheads

2. The long run In the long run, there are no fixed inputs or fixed costs; all inputs and all costs are variable The firm must decide what combination of inputs to use in producing any level of output

3. Cost minimization assumption For any given level of output, the firm will choose the input combination with the lowest cost

4. The cost minimization problem Pick y; observe w 1, w 2, etc; choose the least cost x’s Why not just pick 0 for all the x’s?

5. For any output level, there are are usually several different input combinations that can be used Each combination will have a different cost

6. Consider the hay problem x 1 x 2 TPPAPP A MPPMPPTFCTVCTCAFCAVCATCAMCMC 8.01.01536.0192.00 262.00 256.00 20.0 48.00 68.00 0.0130.0310.0440.0230.023 9.01.01782.0198.00 246.00 234.00 20.0 54.00 74.00 0.0110.0300.0420.0240.026 10.01.02000.0200.00 218.0 200.00 20.0 60.00 80.0 0.0100.0300.0400.0280.030 11.01.02178.0198.00 178.0 154.00 20.0 66.00 86.0 0.0090.0300.0390.0340.039 12.01.02304.0192.00 126.0 96.00 20.0 72.00 92.0 0.0090.0310.0400.0480.063 13.01.02366.0182.00 62.0 26.00 20.0 78.00 98.0 0.0080.0330.0410.0970.231 14.01.02352.0168.00 -14.0 -56.00 20.0 84.00 104.0 0.0090.0360.044 4.02.01345.0336.25 406.00 424.00 40.0 24.00 64.00 0.0300.0180.0480.0150.014 5.02.01783.0356.60 438.00 450.00 40.0 30.00 70.00 0.0220.0170.0390.0140.013 6.02.0 2241.0 373.50 458.00 464.00 40.0 36.00 76.00 0.0180.016 0.034 0.0130.013 7.02.02707.0386.71 466.00 466.00 40.0 42.00 82.00 0.0150.0160.0300.0130.013 8.02.03169.0396.13 462.00 456.00 40.0 48.00 88.00 0.0130.0150.0280.0130.013 9.02.03615.0401.67 446.00 434.00 40.0 54.00 94.00 0.0110.0150.0260.0130.014 10.02.04033.0403.30 418.0 400.00 40.0 60.00 100.0 0.0100.0150.0250.0140.015 11.02.04411.0401.00 378.0 354.00 40.0 66.00 106.0 0.0090.0150.0240.0160.017 12.02.04737.0394.75 326.0 296.00 40.0 72.00 112.0 0.0080.0150.0240.0180.020 14.02.05185.0370.36 224.0 144.00 40.0 84.00 124.0 0.0080.0160.0240.0270.042 16.02.05281.0330.06 48.0 -56.00 40.0 96.00 136.0 0.0080.0180.026 18.02.04929.0273.83 -176.0 -304.00 40.0 108.00 148.0 0.008

7. There are many ways to produce 2,000 bales of hay per hour WorkersTractor-WagonsTotal CostAverage Cost 101800.04 6.451.6671.94.03597 5.48272.86580.0364 3.667382.00150.041 2.636495.81670.0479 1.97865111.872.0559

8. Long run total cost By minimizing total cost of production for various output levels with all inputs variable, the firm determines the long run total cost of production

9. OutputWorkersTractor-WagonsCost Average Cost 5003.701.0743.62 0.087 1,0004.911.2754.89 0.055 1,5005.781.4763.99 0.043 2,0006.451.6671.94 0.03597 2,5007.031.8579.14 0.03165 3,0007.542.0385.78 0.02859 4,0008.422.3797.90 0.02448 5,0009.162.70108.89 0.0217781 7,00010.383.32128.61 0.01837 10,00011.854.17154.54 0.0154543 20,00015.306.67225.13 0.0112564 30,00017.778.85283.60 0.00945317 50,00021.5112.73383.71 0.00767416 75,00025.1317.11493.00 0.00657338 100,00028.1821.22593.50 0.00593498 150,00033.4829.17784.20 0.00522799 200,00038.4137.36977.58 0.00488791 244,00042.9945.521168.26 0.00478795 245,00043.1045.721173.06 0.00478798 250,00043.6746.771197.51 0.00479003 275,00046.8652.801337.08 0.00486212 290,00049.3957.691450.07 0.00500025 300,00052.1363.141575.65 0.00525218 301,00052.6464.171599.25 0.00531311

10. Long run average cost of production LRATC

11. Examples y = 2000 y = 100000

12. Graphically we can plot LRATC (LAC) as Long Run Average Cost 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 050000100000150000200000250000300000 Output - y Cost LAC

13. Long run costs are less than or equal to short run costs for any given output level Why? If we are free to vary all inputs in the long run, we can match any short run least cost combination

14. Consider the following data where the short run costs hold wagons fixed at the long run least cost level OutputLACAC - 1000AC - 5000AC - 50000 5000.08723330.08809 1,0000.054880.05488 1,5000.04266270.04296 2,0000.03597130.038930.03929 2,5000.031650.03351 3,0000.028590.02959 3,5000.026290.02678 4,0000.024480.02467 4,5000.0230030.02305 5,0000.02177830.021778 6,0000.01984390.020018 7,0000.018370.019202 10,0000.01545430.027668 20,0000.01125640.0149885 30,0000.009453170.0107744 40,0000.008392010.00872874 50,0000.007674160.00767416 52,5000.007528350.00757569

15. Consider long and short run average cost when wagons are at the 50,000 bale minimum cost Long And Short Run Average Cost 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0100002000030000400005000060000 Output - y Cost LAC AC - 50000

16. Consider long and short run average cost when wagons are at the 5,000 bale minimum cost Long and Short Run Average Cost 0.021 0.023 0.025 0.027 34003800420046005000 Output - y Cost LAC AC - 5000

17. Consider long and short run average cost when wagons are at the 1,000 bale minimum cost Long and Short Run Average Cost 0.03 0.04 0.05 0.06 0.07 0.08 0.09 4006008001000120014001600180020002200 Output - y Cost AC - 1000 LAC

18. Because non-integer values for wagons are not typically feasible, we might consider alternative wagon levels instead 0.02 0.03 0.04 0.05 0.06 0.07 50015002500350045005500 Output - y Cost AC 2 Wagons

19. Consider 1, 2 and 3 wagons 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 500150025003500450055006500 Output - y Cost LAC AC 1 Wagon AC 2 Wagons AC 3 Wagons

20. Consider 1, 2, 3 and 5 wagons LAC AC 1 Wagon AC 2 Wagons AC 5 Wagons 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 50055001050015500205002550030500 Output - y Cost AC 3 Wagons

21. Now add 10 wagons LAC AC 1 Wagon AC 2 Wagons AC 5 Wagons 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 50055001050015500205002550030500 Output - y Cost AC 3 Wagons AC 10 Wagons

22. Output per period $ Long-run average cost ATC 1 ATC 2 ATC 3 The long run average total cost curve (LRATC) is an envelope curve that touches all the short run average total cost curves (SRATC) from below.

23. Another Example 0 50 100 150 200 250 300 350 400 05101520253035

24. Plant size and economies of scale Economists often refer to the collection of fixed inputs at a firm’s disposal as its plant Restaurant Corn farmer Dentist building fixtures kitchen items land machinery breeding stock office drill

25. Choosing the optimal plant size For different output levels, different plants are appropriate Short Run Average Cost 0.03 0.04 0.05 0.06 0.07 0.08 0.09 50075010001250150017502000 Output - y Cost AC 1 Wagon AC 2 Wagons

26. Consider plant sizes of 1, 2 and 3 wagons Short Run Average Cost 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 50015002500350045005500 Output - y Cost AC 1 Wagon AC 2 Wagons AC 3 Wagons

27. We can add 5, 6 and 7 wagons Short Run Average Cost 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 50055001050015500 Output - y Cost AC 1 Wagon AC 2 Wagons AC 3 Wagons AC 5 Wagons AC 6 WagonsAC 7 Wagons

28. AC 1 Wagon AC 2 Wagons AC 5 Wagons AC 7 Wagons AC 10 Wagons AC 15 Wagons Or 1, 2, 3, 5, 7, 10 and 15 wagons Short Run Average Cost 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 50080001550023000305003800045500 Output - y Cost AC 3 Wagons

29. AC 2 Wagons AC 3 Wagons AC 10 Wagons AC 15 Wagons AC 20 Wagons And all the way up to 40 wagons 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 50010500205003050040500505006050070500 Output - y Cost AC 1 Wagon AC 7 Wagons AC 40 Wagons AC 5 Wagons

30. 7 Wagons 10 Wagons 20 Wagons Long and Short Run Average Costs 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 04000080000120000160000200000 Output - y Cost 5 Wagons 15 Wagons 40 Wagons LAC 40 wagons is only efficient at over 200,000 bales

31. Economies of size and the shape of LRATC We measure the relationship between average cost and output by the elasticity of scale (size)

32. If AC > MC, then the cost curve is downward sloping and  S > 1 If MC > AC, then the cost curve is upward sloping and  S < 1

33. MC Long Run Average & Marginal Cost Curves 0 10 20 30 40 50 60 70 80 010203040 LRAC AC > MC   S > 1 y LRAC is downward sloping

34. MC Long Run Average & Marginal Cost Curves 0 10 20 30 40 50 60 70 80 010203040 LRAC AC < MC   S < 1 y LRAC is upward sloping

35. Economies of scale (size) When average cost is falling as output rises, we say the firm experiences economies of scale or increasing returns to size When long run total cost rises proportionately less than output, production is characterized by economies of scale and the LRATC curve slopes downward

36. MC Long Run Average & Marginal Cost Curves 0 10 20 30 40 50 60 70 80 010203040 LRAC AC > MC   S > 1 y Economies of Size/Scale

37. Why do economies of scale occur? Gains from specialization More efficient use of lumpy inputs blast furnace combine X-ray machine receptionist

38. Diseconomies of scale (size) When average cost rises as output rises, we say the firm experiences diseconomies of scale or decreasing returns to size When long run total cost rises more than in proportion to output, production is characterized by diseconomies of scale and the LRATC curve slopes upward

39. MC Long Run Average & Marginal Cost Curves 0 10 20 30 40 50 60 70 80 010203040 LRAC AC > MC   S > 1 y Diseconomies of Size

40. Why do diseconomies of scale occur? Changes in the quality of inputs Supervision and motivation problems Externalities or congestion in production

41. Constant returns to scale (size) When average cost does not change as output rises, we say the firm experiences constant returns to size or scale When both output and long run total cost rise by the same proportion, production is characterized by constant returns to scale and the LRATC is flat

42. Why do constant returns to scale occur? Duplication of processes Fixed production proportions and replication Economies and diseconomies balance out

43. General shape of the LRAC curve 0 4 8 12 16 20 24 28 32 36 40 051015202530 Output - y Cost LRAC

44. The End

45. LAC AC 1 Wagon AC 2 Wagons AC 5 Wagons 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 50055001050015500205002550030500 Output - y Cost AC 3 Wagons AC 10 Wagons