An Apple OrchardAnother short detourMmmm, Uncle John’s!But getting down to business…Production DataMarginal Product of LaborFeatures of MPLMoving to Costs: 2 basic typesThe Costs for Apple ProductionCalculating averagesCalculating MCPutting it all together in a table…Putting it all together in a graph…Basic features of the pictureOptimal decision at $9/bushelRecapHappy Ending…An Apple Orchard Steven J. Haider EC201 Spring 2012Another short detour  We just covered a lot of ground  To review, we’ll use actual data about apple orchards in in Michigan  Data was obtained in 1995 by two MSU professors, Carl Liedholm and Byron Brown  Some of the numbers are simplified/changed to make the example work for our class—but it is broadly accurate  One can think of the data as coming from…. EC201-apples-p2Mmmm, Uncle John’s! EC201-apples-p3But getting down to business…  We’ve been analyzing basic firm-level data to understand optimal firm behavior  The analyses are connected—and use just a couple of basic inputs  We are going to use data for apple production to see how the various pieces fit together  The raw data are in black The calculations we will be making are in blue  Our simplified view of apple production  An orchard exists and is fixed  The orchard owner hires only one additional input, labor, to produce apples  The orchard is small: there is a going price for apples and a going price for apple pickers which the orchard cannot affect EC201-apples-p4Production Data  How does the firm translate inputs into outputs?  The one variable input: labor  The output: apples  The fixed input: the orchard  This table is the Production Function or the Production Schedule Labor (worker days) Apples (bushels) 0 0 100 4,000 200 16,000 300 27,000 400 32,000 531 34,000 656 35,000 799 36,000 960 37,000 1,165 38,000 1,411 39,000 5,500 45,000 EC201-apples-p5Marginal Product of Labor  How does additional labor translate into additional output?  MPL=∆Q / ∆L  Usually we the change in labor is 1—but not here EC201-apples-p6 Labor (worker days) Apples (bushels) MP of Labor (bush. / w. day) 0 0 100 4,000 40.0 200 16,000 120.0 300 27,000 110.0 400 32,000 50.0 531 34,000 15.3 656 35,000 8.0 799 36,000 7.0 960 37,000 6.2 1,165 38,000 4.9 1,411 39,000 4.1 5,500 45,000 1.5Features of MPL  We usually think there is diminishing MPL  Starts to diminish from 200 to 300 in this data  Why diminishing? The additional workers must pick apples from further trees or from higher parts of trees Why increase at first? Perhaps they can cooperate somehow  Why is diminishing MPL important?  The additional workers are picking fewer… implying that the costs of additional apples are increasing EC201-apples-p7 Labor (worker days) Apples (bushels) MP of Labor (bush. / w. day) 0 0 100 4,000 40.0 200 16,000 120.0 300 27,000 110.0 400 32,000 50.0 531 34,000 15.3 656 35,000 8.0 799 36,000 7.0 960 37,000 6.2 1,165 38,000 4.9 1,411 39,000 4.1 5,500 45,000 1.5Moving to Costs: 2 basic types  Fixed costs  Costs that are….fixed Suppose that the fixed costs are $140,000  Think of this as the rental price of an orchard or the opportunity cost of the capital to buy the orchard for a year and the basic upkeep  Variable costs  Costs that….vary  The only thing we have varying is labor Suppose labor is $56/worker day EC201-apples-p8The Costs for Apple Production * Since variable costs were given in worker/day terms ($56/worker day), we had to multiply that cost by the labor column EC201-apples-p9 Labor (worker days) Apples (bushels) Fixed Costs Variable Costs * Total Costs 0 0 $140,000 0 $140,000 100 4,000 $140,000 $5,600 $145,600 200 16,000 $140,000 $11,200 $151,200 300 27,000 $140,000 $16,800 $156,800 400 32,000 $140,000 $22,400 $162,400 531 34,000 $140,000 $29,736 $169,736 656 35,000 $140,000 $36,736 $176,736 799 36,000 $140,000 $44,744 $184,744 960 37,000 $140,000 $53,760 $193,760 1,165 38,000 $140,000 $65,240 $205,240 1,411 39,000 $140,000 $79,016 $219,016 5,500 45,000 $140,000 $308,000 $448,000Calculating averages  Average costs per apple is going to be useful  AFC = FC / Q  AVC = VC / Q  ATC = TC / Q EC201-apples-p10 Apples (bushels) Fixed Costs Variable Costs Total Costs AFC AVC ATC 0 $140,000 0 $140,000 $0 $0 $0 4,000 $140,000 $5,600 $145,600 $35.00 $1.40 $36.40 16,000 $140,000 $11,200 $151,200 $8.75 $0.70 $9.45 27,000 $140,000 $16,800 $156,800 $5.19 $0.62 $5.81 32,000 $140,000 $22,400 $162,400 $4.38 $0.70 $5.08 34,000 $140,000 $29,736 $169,736 $4.12 $0.87 $4.99 35,000 $140,000 $36,736 $176,736 $4.00 $1.05 $5.05 36,000 $140,000 $44,744 $184,744 $3.89 $1.24 $5.13 37,000 $140,000 $53,760 $193,760 $3.78 $1.45 $5.24 38,000 $140,000 $65,240 $205,240 $3.68 $1.72 $5.40 39,000 $140,000 $79,016 $219,016 $3.59 $2.03 $5.62 45,000 $140,000 $308,000 $448,000 $ 3.11 $6.84 $9.96Calculating MC  Two ways to calculate MC  MC = ∆TC / ∆ Q  MC = ∆VC / ∆ Q EC201-apples-p11 Apples (bushels) Fixed Costs Variable Costs Total Costs MC* 0 $140,000 0 $140,000 4,000 $140,000 $5,600 $145,600 $1.40 16,000 $140,000 $11,200 $151,200 $0.47 27,000 $140,000 $16,800 $156,800 $0.51 32,000 $140,000 $22,400 $162,400 $1.12 34,000 $140,000 $29,736 $169,736 $3.67 35,000 $140,000 $36,736 $176,736 $7.00 36,000 $140,000 $44,744 $184,744 $8.01 37,000 $140,000 $53,760 $193,760 $9.02 38,000 $140,000 $65,240 $205,240 $11.48 39,000 $140,000 $79,016 $219,016 $13.78 45,000 $140,000 $308,000 $448,000 $38.16Putting it all together in a table… EC201-apples-p12 Apples (bushels) Fixed Costs Variable Costs AFC AVC ATC MC 0 $140,000 0 $0 $0 $0 4,000 $140,000 $5,600 $35.00 $1.40 $36.40 $1.40 16,000 $140,000 $11,200 $8.75 $0.70 $9.45 $0.47 27,000 $140,000 $16,800 $5.19 $0.62 $5.81 $0.51 32,000 $140,000 $22,400 $4.38 $0.70 $5.08 $1.12 34,000 $140,000 $29,736 $4.12 $0.87 $4.99 $3.67 35,000 $140,000 $36,736