Chapter 6-the-theory-of-cost

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Chapter 6-the-theory-of-cost

  1. 1. Written by: Edmund Quek CHAPTER 6 THE THEORY OF COST LECTURE OUTLINE 1 INTRODUCTION 2 SHORT-RUN THEORY OF COST 2.1 2.2 2.3 2.4 2.5 2.6 Distinction between fixed cost and variable cost Total cost Marginal cost Average cost Relationship between marginal cost and average cost Optimum capacity 3 LONG-RUN THEORY OF COST 3.1 3.2 3.3 Cost minimisation in the long run Long-run average cost Productive efficiency References John Sloman, Economics William A. McEachern, Economics Richard G. Lipsey and K. Alec Chrystal, Positive Economics G. F. Stanlake and Susan Grant, Introductory Economics Michael Parkin, Economics David Begg, Stanley Fischer and Rudiger Dornbusch, Economics © 2011 Economics Cafe All rights reserved. Page 1
  2. 2. Written by: Edmund Quek 1 INTRODUCTION Explicit costs are costs that involve monetary payments such as the costs of materials and labour. Accounting costs include only explicit costs. Implicit costs are costs that do not involve monetary payments such as the costs of the owner’s labour and financial capital. Economic costs include both explicit costs and implicit costs. Economists are concerned with economic profit and hence economic costs. An increase in output will require an increase in the quantity of factor inputs which will lead to an increase in costs. The theory of cost is the study of how the cost of production changes as the output level changes. This chapter gives an exposition of the theory of cost. 2 SHORT-RUN THEORY OF COST 2.1 Distinction between fixed costs and variable costs Fixed costs are costs that do not vary with the output level as they are associated with fixed factor inputs. In other words, an increase in the output level will not lead to an increase in fixed costs. Fixed costs will still be incurred even if the firm shuts down production. Examples of fixed costs are interest payments on loans for the purchase of capital goods (factories and machinery), insurance premiums and rent. Variable costs are costs that vary directly with the output level as they are associated with variable factor inputs. In other words, an increase in the output level will lead to an increase in variable costs since more variable factor inputs are needed to produce more output. Variable costs will not be incurred if the firm shuts down production. Examples of variable costs are the costs of materials and direct labour (labour provided by factory workers). 2.2 Total cost Total cost (TC) is the cost of all the factor inputs needed to produce an amount of output. In the short run, total cost is the sum of total fixed cost (TFC) and total variable cost (TVC) and is positively related to the output level. © 2011 Economics Cafe All rights reserved. Page 2
  3. 3. Written by: Edmund Quek TC Curve In the above diagram, since fixed costs do not vary with the output level, the TFC curve is horizontal. However, since more variable factor inputs are needed to produce more output, the TVC curve is upward-sloping. Since TC is the sum of TFC and TVC, the TC curve is geometrically similar to the TVC curve, except that the former is higher than the latter by TFC at each output level. From the first unit of output to Q0, the firm is experiencing increasing marginal returns. In other words, each additional unit of the variable factor input is adding more to total output than the previous additional unit. Therefore, each additional unit of output requires fewer units of the variable factor input to produce and this makes the TC and the TVC curves rise at a decreasing rate (i.e. the slopes of the TC and the TVC curves are decreasing). After Q0, the firm is experiencing diminishing marginal returns. In other words, each additional unit of the variable factor is adding less to total output than the previous additional unit. Therefore, each additional unit of output requires more units of the variable factor input to produce and this causes the TC and the TVC curves to rise at an increasing rate (i.e. the slopes of the TC and the TVC curves are increasing). 2.3 Marginal cost Marginal cost (MC) is the additional cost resulting from producing one more unit of output. Mathematically, TC TVC MC  -------- or ---------Q Q © 2011 Economics Cafe All rights reserved. Page 3
  4. 4. Written by: Edmund Quek Therefore, marginal cost is the slope of the TC or the TVC curve. MC Curve In the above diagram, from the first unit of output to Q0, the firm is experiencing increasing marginal returns. The slope of the TC curve is decreasing and hence the MC curve is falling. At Q0, the slope of the TC curve is the smallest and hence the MC curve is at its minimum. After Q0, the firm is experiencing diminishing marginal returns. The slope of the TC curve is increasing and hence the MC curve is rising. 2.4 Average cost Average cost (AC) is the cost per unit of output. Mathematically, TC AC  ------Q Therefore, average cost is the slope of the line from the origin to the TC curve. © 2011 Economics Cafe All rights reserved. Page 4
  5. 5. Written by: Edmund Quek AC Curve In the above diagram, from the first unit of output to Q2, since the slope of the line from the origin to the TC curve is decreasing, the AC curve is falling. At Q2, the slope of the line from the origin to the TC curve is smallest and hence the AC curve is at its minimum. After Q2, since the slope of the line from the origin to the TC curve is increasing, the AC curve is rising. Average variable cost (AVC) is the variable cost per unit of output. Mathematically, TVC AVC  -------Q Therefore, average variable cost is the slope of the line from the origin to the TVC curve. © 2011 Economics Cafe All rights reserved. Page 5
  6. 6. Written by: Edmund Quek AVC Curve In the above diagram, from the first unit of output to Q1, since the slope of the line from the origin to the TVC curve is decreasing, the AVC curve is falling. At Q1, the slope of line from the origin to the TVC curve is smallest and hence the AVC curve is at its minimum. After Q1, since the slope of the line from the origin to the TVC curve is increasing, the AVC curve is rising. Average fixed cost (AFC) is the fixed cost per unit of output. Mathematically, TFC AFC  -------Q Therefore, average fixed cost is the slope of the line from the origin to the TFC curve. © 2011 Economics Cafe All rights reserved. Page 6
  7. 7. Written by: Edmund Quek AFC Curve In the above diagram, from the first unit of output, since the slope of the line from the origin to the TFC curve is decreasing, the AFC curve is falling. 2.5 Relationship between marginal cost and average cost In the above diagram, from the first unit of output to Q0, the MC curve is falling, and is rising thereafter. From the first unit of output to Q1, the MC curve is lower than the AC and the AVC curves and hence the AC and the AVC curves are falling. After Q1, the MC curve is higher than the AVC curve and hence the AVC curve is rising. After Q2, the MC curve is higher than the AC curve and hence the AC curve is rising. Therefore, the MC curve cuts the AVC and the AC curves at the minimum points. © 2011 Economics Cafe All rights reserved. Page 7
  8. 8. Written by: Edmund Quek Since AC is the sum of AVC and AFC, the vertical distance between the AVC and the AC curves is equal to AFC. Since the AFC curve is falling, the vertical distance between the AVC and the AC curves narrows as the output level increases. 2.6 Optimum capacity If a firm produces the output level that corresponds to the lowest point on the average cost curve, it is producing at optimum capacity. In the above diagram, if the firm produces Q0, it is producing at optimum capacity. If the firm produces an output level lower than Q0, such as Q1, it is producing under capacity or with excess capacity. If the firm produces an output level higher than Q0, such as Q2, it is producing over capacity. © 2011 Economics Cafe All rights reserved. Page 8
  9. 9. Written by: Edmund Quek 3 LONG-RUN THEORY OF COST 3.1 Cost minimisation in the long run Since there are no fixed factor inputs in the long run, a firm will choose the quantity of fixed factor inputs that achieves the lowest average cost of producing any output level. Suppose that a firm can choose among three quantities of fixed factor inputs: small quantity, medium quantity and large quantity. In the above diagram, the average cost curves that correspond to the three quantities of fixed factor inputs are AC0, AC1 and AC2, where AC0 corresponds to the small quantity, AC1 corresponds the medium quantity and AC2 corresponds to the large quantity. If the firm wants to produce Q0, average cost will be lowest if it produces on AC0 and hence it will choose the small quantity of fixed factor inputs. If the firm wants to produce Q1, average cost will be lowest if it produces on AC1 and hence it will choose the medium quantity of fixed factor inputs. If the firm wants to produce Q2, average cost will be lowest if it produces on AC2 and hence it will choose the large quantity of fixed factor inputs. 3.2 Long-run average cost The long-run average cost (LRAC) curve shows the lowest average cost of producing each output level when all the factor inputs used in the production process are variable in the long run. Each point on the LRAC curve is a point of tangency to the AC curve with the lowest average cost of producing the corresponding output level. In section 3.1, we assume that a firm can choose among three quantities of fixed factor inputs. For an output level below Q’, the lowest-average-cost quantity of fixed factor inputs is the small quantity of fixed factor inputs that corresponds to AC0. For an output © 2011 Economics Cafe All rights reserved. Page 9
  10. 10. Written by: Edmund Quek level between Q’ and Q”, the lowest-average-cost quantity of fixed factor inputs is the medium quantity of fixed factor inputs that corresponds to AC1. For an output level above Q”, the lowest-average-cost quantity of fixed factor inputs is the large quantity of fixed factor inputs that corresponds to AC2. Therefore, the LRAC curve is the bold curve in the below diagram. However, if we assume that a firm can choose among an infinite number of quantities of fixed factor inputs, we will get a U-shaped LRAC curve. LRAC curve © 2011 Economics Cafe All rights reserved. Page 10
  11. 11. Written by: Edmund Quek 3.3 Productive efficiency From a firm’s perspective, it is productively efficient when it produces on its LRAC curve and this occurs when it is x-efficient and uses the least-cost combination of factor inputs to produce any amount of output. As we discussed earlier, the least-cost condition is met when the last dollar of each factor input employed produces the same additional output. If a firm employs two factor inputs, labour (L) and capital (K), the least-cost condition can be expressed mathematically as MPL/PL = MPK/PK, where MP denotes marginal product and P denotes price. A firm is x-efficient when it is not lax in cost control. In other words, it is not overstaffed, it does not lack the incentive to use the most efficient production technology, etc. Since the least-cost condition will be met, in the long run, if not in the short run, whether a firm is productively efficient depends on whether it is x-efficient. In other words, if a firm is x-efficient, it will also be productively efficient. The converse is also true. From society’s perspective, a firm is productively efficient when it produces on the lowest point on its LRAC curve. © 2011 Economics Cafe All rights reserved. Page 11

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