Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Slide 35Slide 36Slide 37Slide 38Slide 39Slide 40Slide 41Slide 42Slide 43Slide 44Slide 45Production and Cost in the Long RunOverheadsThe long runIn the long run, there are no fixed inputs or fixed costs; all inputs and all costs are variableThe firm must decide what combination of inputs to use in producing any level of outputCost minimization assumptionFor any given level of output,the firm will choose the input combinationwith the lowest costThe cost minimization problemC(y, w1,w2, ) minx1,x2, ,xnΣni 1wixisuch that y f(x1,x2, xn)Pick y; observe w1, w2, etc;choose the least cost x’sWhy not just pick 0 for all the x’s?For any output level, there are are usually several different inputcombinations that can be usedEach combination will have a different costConsider the hay problemx1x2 TPP APP A MPP MPP TFC TVC TC AFC AVC ATC AMC MC8.0 1.0 1536.0 192.00 262.00 256.00 20.0 48.00 68.00 0.013 0.031 0.044 0.023 0.0239.0 1.0 1782.0 198.00 246.00 234.00 20.0 54.00 74.00 0.011 0.030 0.042 0.024 0.02610.0 1.0 2000.0 200.00 218.0 200.00 20.0 60.00 80.0 0.010 0.030 0.040 0.028 0.03011.0 1.0 2178.0 198.00 178.0 154.00 20.0 66.00 86.0 0.009 0.030 0.039 0.034 0.03912.0 1.0 2304.0 192.00 126.0 96.00 20.0 72.00 92.0 0.009 0.031 0.040 0.048 0.06313.0 1.0 2366.0 182.00 62.0 26.00 20.0 78.00 98.0 0.008 0.033 0.041 0.097 0.23114.0 1.0 2352.0 168.00 -14.0 -56.00 20.0 84.00 104.0 0.009 0.036 0.0444.0 2.0 1345.0 336.25 406.00 424.00 40.0 24.00 64.00 0.030 0.018 0.048 0.015 0.0145.0 2.0 1783.0 356.60 438.00 450.00 40.0 30.00 70.00 0.022 0.017 0.039 0.014 0.0136.0 2.0 2241.0 373.50 458.00 464.00 40.0 36.00 76.00 0.018 0.016 0.034 0.013 0.013 7.0 2.0 2707.0 386.71 466.00 466.00 40.0 42.00 82.00 0.015 0.016 0.030 0.013 0.0138.0 2.0 3169.0 396.13 462.00 456.00 40.0 48.00 88.00 0.013 0.015 0.028 0.013 0.0139.0 2.0 3615.0 401.67 446.00 434.00 40.0 54.00 94.00 0.011 0.015 0.026 0.013 0.01410.0 2.0 4033.0 403.30 418.0 400.00 40.0 60.00 100.0 0.010 0.015 0.025 0.014 0.01511.0 2.0 4411.0 401.00 378.0 354.00 40.0 66.00 106.0 0.009 0.015 0.024 0.016 0.01712.0 2.0 4737.0 394.75 326.0 296.00 40.0 72.00 112.0 0.008 0.015 0.024 0.018 0.02014.0 2.0 5185.0 370.36 224.0 144.00 40.0 84.00 124.0 0.008 0.016 0.024 0.027 0.04216.0 2.0 5281.0 330.06 48.0 -56.00 40.0 96.00 136.0 0.008 0.018 0.02618.0 2.0 4929.0 273.83 -176.0 -304.00 40.0 108.00 148.0 0.008There are many ways to produce2,000 bales of hay per hourWorkers Tractor-Wagons Total Cost Average Cost10 1 80 0.046.45 1.66 71.94 .035975.48 2 72.8658 0.03643.667 3 82.0015 0.0412.636 4 95.8167 0.04791.9786 5 111.872 .0559Long run total costBy minimizing total cost of production forvarious output levels with all inputs variable,the firm determines thelong run total cost of productionOutput Workers Tractor-Wagons Cost Average Cost500 3.70 1.07 43.62 0.0871,000 4.91 1.27 54.89 0.0551,500 5.78 1.47 63.99 0.0432,000 6.45 1.66 71.94 0.035972,500 7.03 1.85 79.14 0.031653,000 7.54 2.03 85.78 0.028594,000 8.42 2.37 97.90 0.024485,000 9.16 2.70 108.89 0.02177817,000 10.38 3.32 128.61 0.0183710,000 11.85 4.17 154.54 0.015454320,000 15.30 6.67 225.13 0.011256430,000 17.77 8.85 283.60 0.0094531750,000 21.51 12.73 383.71 0.0076741675,000 25.13 17.11 493.00 0.00657338100,000 28.18 21.22 593.50 0.00593498150,000 33.48 29.17 784.20 0.00522799200,000 38.41 37.36 977.58 0.00488791244,000 42.99 45.52 1168.26 0.00478795245,000 43.10 45.72 1173.06 0.00478798250,000 43.67 46.77 1197.51 0.00479003275,000 46.86 52.80 1337.08 0.00486212290,000 49.39 57.69 1450.07 0.00500025300,000 52.13 63.14 1575.65 0.00525218301,000 52.64 64.17 1599.25 0.00531311Long run average cost of productionLRATCLRATC LRAC LRTCyC(y, w)yExamplesLRATC LRTCy71.942,000 0.03597LRATC LRTCy593.5100,000 0.005935y = 2000y = 100000Graphically we can plot LRATC (LAC)asLong Run Average Cost00.010.020.030.040.050.060.070.080.090 50000 100000 150000 200000 250000 300000Output - yCostLACLong run costs are less than or equalto short run costs for any given output levelWhy?If we are free to vary all inputs in the long run, we can match any short run least cost combinationConsider the following data where the short run costs hold wagons fixed at the long run least cost level Output LAC AC - 1000 AC - 5000 AC - 50000500 0.0872333 0.088091,000 0.05488 0.054881,500 0.0426627 0.042962,000 0.0359713 0.03893 0.039292,500 0.03165 0.033513,000 0.02859 0.029593,500 0.02629 0.026784,000 0.02448 0.024674,500 0.023003 0.023055,000 0.0217783 0.0217786,000 0.0198439 0.0200187,000 0.01837 0.01920210,000 0.0154543 0.02766820,000 0.0112564 0.014988530,000 0.00945317 0.010774440,000 0.00839201 0.0087287450,000 0.00767416 0.0076741652,500 0.00752835 0.00757569Consider long and short run average cost whenwagons are at the 50,000 bale minimum costLong And Short Run Average Cost00.010.020.030.040.050.060.070.080.090 10000 20000 30000 40000 50000 60000Output - yCostLACAC - 50000Consider long and short run average cost whenwagons are at the 5,000 bale minimum costLong and Short Run Average Cost0.0210.0230.0250.0273400 3800 4200 4600 5000Output - yCostLACAC - 5000Consider long and short run average cost whenwagons are at the 1,000 bale minimum costLong and Short Run Average Cost0.030.040.050.060.070.080.09400 600 800 1000 1200 1400 1600 1800 2000 2200Output - yCostAC - 1000LACLACBecause non-integer values for wagons are not typicallyfeasible, we might consider alternative wagon levels instead0.020.030.040.050.060.07500 1500 2500 3500 4500 5500Output - yCostAC 2 WagonsConsider 1, 2 and 3 wagons00.010.020.030.040.050.060.070.080.09500 1500 2500 3500 4500 5500 6500Output - yCostLACAC 1 WagonAC 2 WagonsAC 3 WagonsConsider 1, 2, 3 and 5 wagonsLACAC 1 WagonAC 2 WagonsAC 5 Wagons00.010.020.030.040.050.060.070.080.09500 5500 10500 15500 20500 25500 30500Output - yCostAC 3 WagonsNow add 10 wagonsLACAC 1 WagonAC 2 WagonsAC 5 Wagons00.010.020.030.040.050.060.070.080.09500 5500 10500 15500 20500 25500 30500Output - yCostAC 3 WagonsAC 10 WagonsOutput per period$Long-runaverage costATC1ATC2ATC3The long run average total cost curve (LRATC) is an envelope curve that touches
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