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Chapter 7

Chapter 7. Production, Inputs, and Cost: Building Blocks for Supply Analysis. Of course, that’s only an estimate. The actual cost will be higher. AUTO MECHANIC TO CUSTOMER. Figure 1. Historical costs for long-distance telephone transmissions. Short-Run vs. Long-Run Costs. Run

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Chapter 7

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  1. Chapter 7 Production, Inputs, and Cost: Building Blocks for Supply Analysis Of course, that’s only an estimate. The actual cost will be higher. AUTO MECHANIC TO CUSTOMER

  2. Figure 1 Historical costs for long-distance telephone transmissions

  3. Short-Run vs. Long-Run Costs • Run • Period of time • Short run • Some cost commitments – not ended • Predetermined • Plant size • Most input quantities

  4. Short-Run vs. Long-Run Costs • Long run • All cost commitments – ended • Adjustable • Plant size • Inputs

  5. Short-Run vs. Long-Run Costs • Fixed cost • Quantity of input • Doesn’t vary with output • Cost of input • Doesn’t vary with output • Variable cost • Varies with output

  6. Production, Input Choice, & Cost • Short run • Only one variable input • Total physical product (TPP) • Total amount of output • From a given quantity of input

  7. Table 1 Total physical product schedule for Al’s building company

  8. Figure 2 Total physical product with different quantities of carpenters used by Al’s firm 40 32 35 30 TPP 25 B A E F G Total Output in Garages per Year D C 20 15 10 0 1 2 3 4 5 6 7 5 Quantity of Carpenters per Year

  9. Production, Input Choice, & Cost • Average physical product (APP) • Total physical product (TPP) • Divided by quantity of input (X) • APP=TPP/X • Marginal physical product (MPP) • Increase in total output • From: one-unit increase in input • All other inputs constant

  10. Table 2 Al’s product schedules: total, average, and marginal physical product and marginal revenue product

  11. Production, Input Choice, & Cost • MPP curve • Rate of change: TPP curve • Equals slope of TPP curve • Increasing marginal returns • MPP – increases • TPP – increases • Increasing rate

  12. Production, Input Choice, & Cost • Diminishing marginal returns • MPP – decreases; positive • TPP – increases • Decreasing rate • Negative marginal returns • MPP – negative • TPP – decreases

  13. Figure 3 Al’s marginal physical product (MPP) curve 14 Increasing marginal returns Diminishing marginal returns Negative marginal returns 12 10 8 6 4 MPP in Garages per Year 2 0 -2 -4 0 1 2 3 4 5 6 7 Number of Carpenters MPP -6

  14. Production, Input Choice, & Cost • “Law” of diminishing marginal returns • Increase • Amount of one input • All other inputs amounts • Constant • Ultimately • Lower marginal returns

  15. Production, Input Choice, & Cost • Marginal revenue product (MRP) • Additional money revenue • From increased sales • From one additional unit of input • MRP=MPP ˣ Price of output

  16. Production, Input Choice, & Cost • Firm – maximize profits • Total revenue • Minus total cost • Optimal quantity of input • MRP > P of input • Use more input • MRP < P of input • Use less input • MRP = P of input • Optimal quantity of input

  17. Multiple Input Decisions • Firm • Choice: different technological options • Given: target production level • Substitute one input for another • Trade-off • Decrease use - one input • Increase use - another input • Combination of inputs - least costly • Depends on relative prices of inputs

  18. Multiple Input Decisions • Optimal quantities of inputs • MRP (input X) > MRP (input Y) • Increase spending on input X • MRP (input X) < MRP (input Y) • Increase spending on input Y • MRP (input X) = MRP (input Y) • Optimal combination of inputs • Same MRPs per dollar

  19. Multiple Input Decisions • One input - more costly • Relative to competing inputs • Substitution • Use less – more expensive input • Use more – competing inputs

  20. Cost and its Dependence on Output • Total cost (TC) • Cost of fixed inputs • Cost of variable inputs • Opportunity costs • Average cost (AC) • Total cost / Quantity produced • Marginal cost (MC) • Increase in total cost • From: one additional unit of output

  21. Cost and its Dependence on Output • Total variable cost (TVC) • Cost of variable inputs • Average variable cost (AVC) • Total variable cost / Quantity produced • Marginal variable cost (MVC) • Increase in total variable cost • From: one additional unit of output

  22. Table 3 Al’s (variable) cost schedules

  23. Cost and its Dependence on Output • TVC curve • Rise steady with output • AVC curve • U-shaped • MVC curve • U-shaped

  24. Figure 4 (a) Al’s total variable cost, average variable cost, and marginal variable cost TVC 200 180 160 Total (Variable) Cost 140 120 Total Variable Cost per Year (thousands $) 100 80 60 40 0 2 4 6 Quantity of Garages 20 8 10

  25. Figure 4 (b) Al’s total variable cost, average variable cost, and marginal variable cost 30 25 Average (Variable) Cost AVC 20 D Average Variable Cost per Garage (thousands $) C 15 10 0 2 4 6 5 Quantity of Garages 8 10

  26. Figure 4 (c) Al’s total variable cost, average variable cost, and marginal variable cost MVC 50 45 40 Marginal (Variable) Cost 35 30 Marginal Variable Cost per Added Garage (thousands $) 25 20 15 10 0 2 4 6 Quantity of Garages 5 8 10

  27. Cost and its Dependence on Output • Total fixed cost (TFC) • Doesn’t vary with output • TFC curve – straight horizontal line • Average fixed cost (AFC) • Total fixed cost / quantity produced • AFC curve – decreases with output • Marginal fixed costs (MFC) • Are always = 0

  28. Table 4 Al’s fixed costs

  29. Figure 5 (a) Fixed costs: total and average TFC 14 12 10 Total Fixed Cost per Year (thousands $) 8 6 4 7 9 1 3 5 0 2 4 6 2 Output 8 10

  30. Figure 5 (b) Fixed costs: total and average 14 12 10 Average Fixed Cost per Year (thousands $) 8 TFC 6 4 7 9 1 3 5 0 2 4 6 2 Output 8 10

  31. Cost and its Dependence on Output • Total cost • TC = TFC + TVC • Average cost • AC = AFC + AVC • Marginal cost • MC = MFC + MVC = 0 + MVC = MVC

  32. Cost and its Dependence on Output • AC curve • U-shaped • Downward-sloping segment • Increasing MPP • Spread fixed costs • Upward-sloping segment • Rise in administrative costs

  33. Cost and its Dependence on Output • Average (marginal & total) cost curve • Depend - firm’s planning horizon • Long run average (& total) cost curve • Different than short run • Long run – Choose plant size • Short-run AC curve • Most economical • Long run AC curve • Lowest possible short-run AC • Each quantity of output

  34. Figure 6 Short-run and long-run average cost curves B S L U V $0.40 G T W 0.35 Average Cost per Pound of Chicken 40 0 Output in Pounds of Chicken 100

  35. Economies of Scale • Economies of scale • Increasing returns to scale • All input quantities - increase by X% • TC – increase by X% • Quantity of output - rises > X% • Decreasing long run AC curves

  36. Economies of Scale • Constant returns to scale • Horizontal long run AC curve • All input quantities - increase by X% • TC – increase by X% • Quantity of output - rises by X% • Decreasing returns to scale • Rising long run AC curve • All input quantities - increase by X% • TC – increase by X% • Quantity of output - rises < X%

  37. Figure 7 Three possible shapes: long-run average cost curve Increasing returns to scale Constant returns to scale Decreasing returns to scale AC Long-Run Average Cost Long-Run Average Cost Long-Run Average Cost AC AC Quantity of Output Quantity of Output Quantity of Output (b) (c) (a)

  38. Economies of Scale • Different concepts • Returns to scale • All inputs vary proportionately • Diminishing marginal returns • One input varies • All other inputs - constant • Production function - diminishing returns • Returns to scale • Diminishing • Constant • Increasing

  39. Economies of Scale • Analytical cost curves • Cost curves • Same period of time • Different points • Alternative possibilities • Historical costs diagram • Evolution of costs over time

  40. Figure 8 Declining historical cost curve with the analytical average cost curve also declining in each year $100 A 1942 Analytical Cost Curve 75 Cost per Unit 50 2007 Analytical Cost Curve 25 B 0 Historical Cost Curve Quantity of Output

  41. Figure 9 Declining historical cost curve with u-shaped analytical cost curves in each year 1942 Analytical Cost Curve $100 75 Cost per Unit 50 Historical Cost Curve 2007 Analytical Cost Curve B 25 A 0 Quantity of Output

  42. Production indifference curves • Production indifference curve • Isoquant • All different quantities of two inputs • Just sufficient • Given quantity of output • Characteristics • Higher curves - larger outputs • Negative slope • Curve inward toward origin

  43. Figure 10 A production indifference map 600 A B D C E 260,000 bushels 240,000 bushels 220,000 bushels Quantity of Land in Acres 400 200 7 3 5 0 Quantity of Labor in Years 10

  44. Production indifference curves • Budget line • Equally costly input combinations • Given • Budget • Input prices • Straight line • Budget lines • Same slope • Parallel

  45. Figure 11 A budget line J 360 Quantity of Land in Acres K 40 0 Number of Workers

  46. Production indifference curves • Minimize production cost • Given level of output • Tangency point • Budget line • Indifference curve (given level of output)

  47. Figure 12 Cost minimization J 450 A 270 $360,000 $270,000 360 T $450,000 Quantity of Land in Acres 225 240,000 bushels B K 40 15 30 0 Number of Workers 50

  48. Production indifference curves • Expansion path - locus • Cost-minimizing input combinations • All relevant output levels • Tangency points • Production indifference curves • Budget lines • Yields (for each point on expansion path) • Output • Total cost • Cost curves

  49. Figure 13 The firm’s expansion path B’ E J B $270,000 S’ T S Quantity of Land in Acres 220,000 bushels 300,000 bushels 240,000 bushels E K B 15 0 Number of Workers B’ 10

  50. Figure 14 Optimal input choice at a different set of input prices W 300 180 E Quantity of Land in Acres 240 240,000 bushels V 60 45 0 Quantity of Labor in Years 75

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