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Chapter 7

Chapter 7. The Cost of Production. Topics to be Discussed. Measuring Cost: Cost in the Short Run Cost in the Long Run Long-Run Versus Short-Run Cost Curves. Introduction. The production technology measures the relationship between input and output.

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Chapter 7

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  1. Chapter 7 The Cost of Production

  2. Topics to be Discussed • Measuring Cost: • Cost in the Short Run • Cost in the Long Run • Long-Run Versus Short-Run Cost Curves Chapter 7

  3. Introduction • The production technology measures the relationship between input and output. • Production technology, together with prices of factor inputs, determine the firm’s cost of production • The optimal, cost minimizing, level of inputs can be determined. • A firm’s costs depend on the rate of output and will change over time. • The characteristics of the firm’s production technology can affect costs in the long run and short run. Chapter 7

  4. Measuring Cost: Which Costs Matter? Economic Cost vs Accounting Cost • Accountants tend to take a retrospective view of firms costs, where as economists tend to take a forward-looking view • Accounting Cost • Actual expenses plus depreciation charges for capital equipment • Economic Cost • Cost to a firm of utilizing economic resources in production, including opportunity cost • Accountants and economists often treat depreciation differently as well Chapter 7

  5. Economic Costs • Economic costs distinguish between costs the firm can control and those it cannot • Concept of opportunity cost plays an important role • Opportunity cost • Cost associated with opportunities that are foregone when a firm’s resources are not put to their highest-value use. • An Example • A firm owns its own building and pays no rent for office space. The building could have been rented instead. • Foregone rent is the opportunity cost of using the building for production and should be included in economic costs of doing business Chapter 7

  6. Sunk Cost • Although opportunity costs are hidden and should be taken into account, sunk costs should not • Sunk Cost • Expenditure that has been made and cannot be recovered • Should not influence a firm’s future economic decisions. • Firm buys a piece of equipment that cannot be converted to another use • Expenditure on the equipment is a sunk cost • Has no alternative use so cost cannot be recovered – opportunity cost is zero Chapter 7

  7. Prospective Sunk Cost: An Example • Firm is considering moving its headquarters to a new city • Last year it paid $500,000 for an option to buy a building in the city. • The cost of the building is $5 million or a total of $5.5 million (5 million + 500,000). • The firm finds another building for $5.25 million. Which building should the firm buy? • The first building should be purchased. • The $500,000 is a sunk cost and should not be considered in the decision to buy • What should be considered is • Spending an additional $5,250,000 or • Spending an additional $5,000,000 Chapter 7

  8. Fixed Costs and Variable Costs • Some costs vary with output, while some remain the same no matter amount of output • Total cost can be divided into: • Fixed Cost • Does not vary with the level of output • Variable Cost • Cost that varies as output varies Chapter 7

  9. Fixed and Variable Costs • Total output is a function of variable inputs and fixed inputs. • Therefore, the total cost of production equals the fixed cost (the cost of the fixed inputs) plus the variable cost (the cost of the variable inputs), or… Chapter 7

  10. Short run versus long run • Which costs are variable and which are fixed depends on the time horizon • Short time horizon – most costs are fixed • Long time horizon – many costs become variable Chapter 7

  11. Fixed Cost Versus Sunk Cost • Fixed cost and sunk cost are often confused • Fixed Cost • Cost paid by a firm that is in business regardless of the level of output • Sunk Cost • Cost that have been incurred and cannot be recovered Chapter 7

  12. Marginal and Average Cost • Must also distinguish between • Average Cost • Marginal Cost • After definition of costs is complete, one can consider the analysis between short-run and long-run costs Chapter 7

  13. Measuring Costs • Marginal Cost (MC): • The cost of expanding output by one unit. • Fixed cost have no impact on marginal cost, so it can be written as: Chapter 7

  14. Measuring Costs • Average Total Cost (ATC) • Cost per unit of output • Also equals average fixed cost (AFC) plus average variable cost (AVC). Chapter 7

  15. A Firm’s Short Run Costs Chapter 7

  16. Determinants of Short-run Costs • The rate at which these costs increase depends on the nature of the production process • The extent to which production involves diminishing returns to variable factors • Diminishing returns to labor • When marginal product of labor is decreasing • If marginal product of labor decreases significantly as more labor is hired • Costs of production increase rapidly • Greater and greater expenditures must be made to produce more output Chapter 7

  17. Determinants of Short-run Costs – An Example • Assume the wage rate (w) is fixed relative to the number of workers hired. • Variable costs is the per unit cost of extra labor times the amount of extra labor: wL Chapter 7

  18. Determinants of Short-run Costs – An Example • Remembering that • And rearranging • We can conclude: The last equation states that when there is only one variable input, the MC is equal to the price of input divided by its marginal product Chapter 7

  19. Example: • Suppose that MPL = 3 and wage rate = $30 per hour • Thus, i. The extra labor needed to obtain an extra unit of output is ∆L/∆q = 1/MPL = 1/3 This implies that 1 hour of L will increase output by 3 units so that 1 unit of output will require 1/3 additional hour of L ii. The marginal cost of producing that unit of output is $10 which is equal MC = w/MPL = 30 / 3 = $10 Chapter 7

  20. TC Cost ($ per year) 400 VC 300 200 100 FC 50 Output 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Cost Curves for a Firm Total cost is the vertical sum of FC and VC. Variable cost increases with production and the rate varies with increasing & decreasing returns. Fixed cost does not vary with output Chapter 7

  21. MC ATC AVC AFC Cost Curves Chapter 7

  22. Cost Curves • When MC is below AVC, AVC is falling • When MC is above AVC, AVC is rising • When MC is below ATC, ATC is falling • When MC is above ATC, ATC is rising • Therefore, MC crosses AVC and ATC at the minimums • The Average – Marginal relationship Chapter 7

  23. The line drawn from the origin to the variable cost curve: Its slope equals AVC The slope of a point on VC or TC equals MC Therefore, MC = AVC at 7 units of output (point A) TC P 400 VC 300 200 A 100 FC 1 2 3 4 5 6 7 8 9 10 11 12 13 Output Cost Curves for a Firm Chapter 7

  24. Cost in the Long Run • In the long run a firm can change all of its inputs • In making cost minimizing choices, must look at the cost of using capital and labor in production decisions • Refer example in Pindyick (on Delta) Chapter 7

  25. Cost in the Long Run • The Isocost Line • A line showing all combinations of L & K that can be purchased for the same cost • Total cost of production is sum of firm’s labor cost, wL and its capital cost rK C = wL + rK • For each different level of cost, the equation shows another isocost line • Rewriting C as an equation for a straight line: • K = C/r - (w/r)L Chapter 7

  26. Cost in the Long Run • Slope of the isocost: • -w/r = is the ratio of the wage rate to rental cost of capital. • This shows the rate at which capital can be substituted for labor with no change in cost. Chapter 7

  27. Optimal Combination of inputs • how to minimize cost for a given level of output by combining isocosts with isoquants • We choose the output we wish to produce and then determine how to do that at minimum cost • Isoquant is the quantity we wish to produce • Isocost is the combination of K and L that gives a set cost Chapter 7

  28. Capital per year K2 A K1 Q1 K3 C0 C1 C2 Labor per year L3 L2 L1 Producing a Given Output at Minimum Cost Q1is an isoquant for output Q1. There are three isocost lines, of which 2 are possible choices in which to produce Q1 Isocost C2 shows quantity Q1 can be produced with combination K2L2or K3L3. However, both of these are higher cost combinations than K1L1. Chapter 7

  29. Input Substitution When an Input Price Change • If the price of labor changes, then the slope of the isocost line change, w/r • It now takes a new quantity of labor and capital to produce the output • If price of labor increases relative to price of capital - capital is substituted for labor as capital are relatively cheaper Chapter 7

  30. B K2 A K1 Q1 C2 C1 L1 L2 Input Substitution When an Input Price Change Capital per year If the price of labor rises, the isocost curve becomes steeper due to the change in the slope -(w/L). The new combination of K and L is used to produce Q1. Combination B is used in place of combination A = more of capital and less of labor Labor per year Chapter 7

  31. Cost in the Long Run • How does the isocost line relate to the firm’s production process? Chapter 7

  32. MPL/w – is the additional output that results from spending an additional dollar for labor. • Suppose wage rate is $10 and adding a worker to the production process will increase output by 20 units. The additional output per dollar spent on additional worker will be 20/10= 2 units of output per dollar • Similarly for MPK/r – is the additional output that results from spending additional dollar for capital • Suppose rental = $2 and adding a worker to the production process will increase output by 20 units. The additional output per dollar spent on additional worker will be 20/2 = 10 units of output per dollar. Chapter 7

  33. Cost in the Long Run • Cost minimization with Varying Output Levels • For each level of output, there is an isocost curve showing minimum cost for that output level • A firm’s expansion path shows the minimum cost combinations of labor and capital at each level of output. • Slope equals K/L Chapter 7

  34. Capital per year $3000 150 Expansion Path $2000 100 C 75 B 50 300 Units A 25 200 Units Labor per year 100 150 200 300 A Firm’s Expansion Path The expansion path illustrates the least-cost combinations of labor and capital that can be used to produce each level of output in the long-run. 50 Chapter 7

  35. Long-Run Versus Short-Run Cost Curves • In the short run some costs are fixed • In the long run firm can change anything including plant size • Can produce at a lower average cost in long run than in short run • Capital and labor are both flexible • We can show this by holding capital fixed in the short run and flexible in long run Chapter 7

  36. E C Long-Run ExpansionPath A K2 Short-Run ExpansionPath P K1 Q2 Q1 L1 L2 L3 B D F The Inflexibility of Short-Run Production Capital per year Capital is fixed at K1 To produce q1, min cost at K1,L1 If increase output to Q2, min cost is K1 and L3 in short run In LR, can change capital and min costs falls to K2 and L2 Labor per year Chapter 7

  37. Long-Run Versus Short-Run Cost Curves • The Inflexibility of Short-Run Production • Long-Run Average Cost • - economies if scale and diseconomies of scale • 3. The Relationship between LR and SR cost Chapter 7

  38. Long-Run Average Cost • Long-Run Average Cost (LAC) • Able to change the amount of capital – allows the firm to reduce costs • To see how costs vary as the firm moves along its expansion path in the LR – look at AC and MC • In SR, the shapes of AC and MC determined by diminishing marginal returns • Most important determinant of the shape of the LR AC and MC curves is relationship between scale of the firm’s operation and inputs required to min cost Chapter 7

  39. Long-Run Versus Short-Run Cost Curves Example: 1. If firm’s production exhibits Constant Returns to Scale • Doubling of inputs leads to a doubling of output • AC cost is constant at all levels of output (because input prices remain unchanged as output increase) E.g. For Q = 100, LRAC = 1000/100 = $10 per unit For Q = 200, LRAC = 2000/200 = $10 per unit * Constant AC means constant MC, so LRAC and LMC is horizontal line Chapter 7

  40. 2. If Increasing Returns to Scale • If input is doubled, output will more than double • AC decreases at all levels of output. 3. Decreasing Returns to Scale • If input is doubled, output will less than double • AC increases at all levels of output Chapter 7

  41. Long-Run Versus Short-Run Cost Curves • In the long-run: • Firms experience increasing and decreasing returns to scale and therefore long-run average cost is “U” shaped. • Long-run marginal cost curve measures the change in long-run total costs as output is increased by 1 unit • 2 curves intersect where LRAC achieves its minimum Chapter 7

  42. LMC LAC A Long-Run Average and Marginal Cost • Long-run marginal cost leads long-run average cost: • 1. If LMC < LAC, LAC will fall • 2. If LMC > LAC, LAC will rise • 3. Therefore, LMC = LAC at the minimum of LAC • 4. In special case where LAC if constant, LAC and LMC are equal Cost ($ per unit of output Output Chapter 7

  43. Economies and Diseconomies of Scale Economies of scale (firm able to double output for less then twice the cost) • As output increases, firm’s AC of producing is likely to decline to a point • On a larger scale, workers can better specialize • Scale can provide flexibility to vary the combination of inputs used – managers can organize production more effectively • Firm may be able to get inputs at lower cost if can get quantity discounts. Lower prices might lead to different input mix Chapter 7

  44. Diseconomies of scale (doubling output requires more than twice the cost) • At some point, AC will begin to increase • Factory space and machinery may make it more difficult for workers to do their job efficiently • Managing a larger firm may become more complex and inefficient as the number of tasks increase • Bulk discounts can no longer be utilized. Limited availability of inputs may cause price to rise Chapter 7

  45. U-shaped LAC shows economies of scale for relatively low output levels and diseconomies of scale for higher levels Comparison between Increasing Returns to Scale and Economies of Scale • Increasing Returns to Scale • Output more than doubles when the quantities of all inputs are doubled • Economies of Scale • Doubling of output requires less than a doubling of cost Chapter 7

  46. Cost-Output Elasticity • Economies of scale are measured in terms of cost-output elasticity, EC • EC is the percentage change in the cost of production resulting from a 1-percent increase in output Ec = (∆C/C )/ (∆q/q) Chapter 7

  47. If cost-output elasticity, EC is equal to 1, MC = AC • Costs increase proportionately with output • Neither economies nor diseconomies of scale • EC < 1 when MC < AC • Economies of scale • Both MC and AC are declining • EC > 1 when MC > AC • Diseconomies of scale • Both MC and AC are rising Chapter 7

  48. The Relationship between Long-Run and Short-Run Cost Curves • We will use short and long-run cost to determine the optimal plant size • We can show the short run average costs for 3 different plant sizes (SAC1, SAC2 and SAC3) • This decision is important because once built, the firm may not be able to change plant size for a while Chapter 7

  49. Long-Run Cost with Economiesand Diseconomies of Scale Chapter 7

  50. Long-Run Cost withConstant Returns to Scale • The optimal plant size will depend on the anticipated output • If expect to produce q0, then should build smallest plant: AC = $8 • If produce more, like q1, AC rises • If expect to produce q2, middle plant is least cost • If expect to produce q3, largest plant is best Chapter 7

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