讲义成本曲线ppt课件.ppt

Chapter Twenty-OneCost CurvesStructureuTypes of cost curvesuFixed, variable and total cost functionsuAverage fixed, average variable and average cost functionsuMarginal cost functionsuMarginal and variable cost functionsuMarginal and average cost functionsuShort run and long run cost curvesTypes of Cost CurvesuA total cost curve 〔 〔总总本本钱钱曲曲线线〕 〕is the graph of a firm’s total cost function.uA variable cost curve 〔 〔可可变变本本钱钱曲曲线线〕 〕is the graph of a firm’s variable cost function.uAn average total cost curve 〔 〔平均本平均本钱钱曲曲线线〕 〕is the graph of a firm’s average total cost function.Types of Cost CurvesuAn average variable cost curve 〔 〔平均平均可可变变本本钱钱曲曲线线〕 〕is the graph of a firm’s average variable cost function.uAn average fixed cost curve 〔 〔平均固平均固定本定本钱钱曲曲线线〕 〕is the graph of a firm’s average fixed cost function.uA marginal cost curve 〔 〔边边沿本沿本钱钱曲曲线线〕 〕is the graph of a firm’s marginal cost function.Types of Cost CurvesuHow are these cost curves related to each other?uHow are a firm’s long-run and short-run cost curves related?Fixed, Variable & Total Cost FunctionsuF is the total cost to a firm of its short-run fixed inputs 〔 〔固定投入固定投入〕 〕. F, the firm’s fixed cost, does not vary with the firm’s output level.ucv(y) is the total cost to a firm of its variable inputs 〔 〔可可变变投入投入〕 〕when producing y output units. cv(y) is the firm’s variable cost function.ucv(y) depends upon the levels of the fixed inputs.Fixed, Variable & Total Cost Functionsuc(y) is the total cost of all inputs, fixed and variable, when producing y output units. c(y) is the firm’s total cost function;y$Fy$cv(y)y$Fcv(y)y$Fcv(y)c(y)FAv. Fixed, Av. Variable & Av. Total Cost CurvesuThe firm’s total cost function isFor y > 0, the firm’s average total cost function isAv. Fixed, Av. Variable & Av. Total Cost CurvesuWhat does an average fixed cost curve look like?uAFC(y) is a rectangular hyperbola so its graph looks like ...$/output unitAFC(y)y0AFC(y) ® 0 as y ® ¥Av. Fixed, Av. Variable & Av. Total Cost CurvesuIn a short-run with a fixed amount of at least one input, the Law of Diminishing (Marginal) Returns must apply, causing the firm’s average variable cost of production to increase eventually.$/output unitAVC(y)y0$/output unitAFC(y)AVC(y)y0Av. Fixed, Av. Variable & Av. Total Cost CurvesuAnd ATC(y) = AFC(y) + AVC(y)$/output unitAFC(y)AVC(y)ATC(y)y0ATC(y) = AFC(y) + AVC(y)$/output unitAFC(y)AVC(y)ATC(y)y0AFC(y) = ATC(y) - AVC(y)AFC$/output unitAFC(y)AVC(y)ATC(y)y0Since AFC(y) ® 0 as y ® ¥,ATC(y) ® AVC(y) as y ® ¥.AFC$/output unitAFC(y)AVC(y)ATC(y)y0Since AFC(y) ® 0 as y ® ¥,ATC(y) ® AVC(y) as y ® ¥.And since short-run AVC(y) musteventually increase, ATC(y) must eventually increase in a short-run.Marginal Cost FunctionuMarginal cost is the rate-of-change of variable production cost as the output level changes. That is,Marginal Cost FunctionuThe firm’s total cost function isand the fixed cost F does not change with the output level y, souMC is the slope of both the variable cost and the total cost functions.Marginal and Variable Cost FunctionsuSince MC(y) is the derivative of cv(y), cv(y) must be the integral of MC(y). That is,Marginal and Variable Cost FunctionsMC(y)y0Area is the variablecost of making y’ units$/output unitMarginal & Average Cost FunctionsuHow is marginal cost related to average variable cost?Marginal & Average Cost FunctionsSinceMarginal & Average Cost FunctionsSinceTherefore,asMarginal & Average Cost FunctionsSinceTherefore,asas$/output unityAVC(y)MC(y)$/output unityAVC(y)MC(y)$/output unityAVC(y)MC(y)$/output unityAVC(y)MC(y)$/output unityAVC(y)MC(y)The short-run MC curve intersectsthe short-run AVC curve frombelow at the AVC curve’s minimum.Marginal & Average Cost FunctionsSimilarly, sinceMarginal & Average Cost FunctionsSimilarly, sinceTherefore,asMarginal & Average Cost FunctionsSimilarly, sinceTherefore,asas$/output unityMC(y)ATC(y)asMarginal & Average Cost FunctionsuThe short-run MC curve intersects the short-run AVC curve from below at the AVC curve’s minimum.uAnd, similarly, the short-run MC curve intersects the short-run ATC curve from below at the ATC curve’s minimum.$/output unityAVC(y)MC(y)ATC(y)Short-Run & Long-Run Total Cost CurvesuA firm has a different short-run total cost curve for each possible short-run circumstance.uSuppose the firm can be in one of just three short-runs;x2 = x2¢ or x2 = x2¢¢ x2¢ < x2¢¢ < x2¢¢¢.or x2 = x2¢¢¢.y0F¢ = w2x2¢F¢cs(y;x2¢)$yF¢0F¢ = w2x2¢F¢¢F¢¢ = w2x2¢¢cs(y;x2¢)cs(y;x2¢¢)$yF¢0F¢ = w2x2¢F¢¢ = w2x2¢¢A larger amount of the fixedinput increases the firm’sfixed cost.cs(y;x2¢)cs(y;x2¢¢)$F¢¢yF¢0F¢ = w2x2¢F¢¢ = w2x2¢¢A larger amount of the fixedinput increases the firm’sfixed cost. Why does a larger amount of the fixed input reduce the slope of the firm’s total cost curve?cs(y;x2¢)cs(y;x2¢¢)$F¢¢MP1 is the marginal physical productivityof the variable input 1, so one extra unit ofinput 1 gives MP1 extra output units.Therefore, the extra amount of input 1needed for 1 extra output unit isShort-Run & Long-Run Total Cost Curves units of input 1.MP1 is the marginal physical productivityof the variable input 1, so one extra unit ofinput 1 gives MP1 extra output units.Therefore, the extra amount of input 1needed for 1 extra output unit isShort-Run & Long-Run Total Cost Curves units of input 1.Each unit of input 1 costs w1, so the firm’sextra cost from producing one extra unitof output isShort-Run & Long-Run Total Cost Curvesis the slope of the firm’s total cost curve.Short-Run & Long-Run Total Cost Curvesis the slope of the firm’s total cost curve.If input 2 is a complement to input 1 thenMP1 is higher for higher x2.Hence, MC is lower for higher x2.That is, a short-run total cost curve startshigher and has a lower slope if x2 is larger.yF¢0F¢ = w2x2¢F¢¢ = w2x2¢¢F¢¢¢F¢¢¢ = w2x2¢¢¢cs(y;x2¢¢¢)cs(y;x2¢)cs(y;x2¢¢)$F¢¢Short-Run & Long-Run Total Cost CurvesuThe firm has three short-run total cost curves.uIn the long-run the firm is free to choose amongst these three since it is free to select x2 equal to any of x2¢, x2¢¢, or x2¢¢¢.uHow does the firm make this choice?yF¢0F¢¢¢y¢y¢¢For 0 £ y £ y¢, choose x2 = x2¢.cs(y;x2¢¢¢)cs(y;x2¢)cs(y;x2¢¢)$F¢¢yF¢0F¢¢¢y¢y¢¢For 0 £ y £ y¢, choose x2 = x2¢.For y¢ £ y £ y¢¢, choose x2 = x2¢¢.cs(y;x2¢¢¢)cs(y;x2¢)cs(y;x2¢¢)$F¢¢yF¢0F¢¢¢cs(y;x2¢¢¢)y¢y¢¢For 0 £ y £ y¢, choose x2 = x2¢.For y¢ £ y £ y¢¢, choose x2 = x2¢¢.For y¢¢ < y, choose x2 = x2¢¢¢.cs(y;x2¢)cs(y;x2¢¢)$F¢¢yF¢0cs(y;x2¢)cs(y;x2¢¢)F¢¢¢cs(y;x2¢¢¢)y¢y¢¢For 0 £ y £ y¢, choose x2 = x2¢.For y¢ £ y £ y¢¢, choose x2 = x2¢¢.For y¢¢ < y, choose x2 = x2¢¢¢.c(y), thefirm’s long-run totalcost curve.$F¢¢Short-Run & Long-Run Total Cost CurvesuThe firm’s long-run total cost curve consists of the lowest parts of the short-run total cost curves. The long-run total cost curve is the lower envelope of the short-run total cost curves.Short-Run & Long-Run Total Cost CurvesuIf input 2 is available in continuous amounts then there is an infinity of short-run total cost curves but the long-run total cost curve is still the lower envelope of all of the short-run total cost curves.$yF¢0F¢¢¢cs(y;x2¢)cs(y;x2¢¢)cs(y;x2¢¢¢)c(y)F¢¢Short-Run & Long-Run Average Total Cost CurvesuFor any output level y, the long-run total cost curve always gives the lowest possible total production cost.uTherefore, the long-run av. total cost curve must always give the lowest possible av. total production cost.uThe long-run av. total cost curve must be the lower envelope of all of the firm’s short-run av. total cost curves. Short-Run & Long-Run Average Total Cost CurvesuE.g. suppose again that the firm can be in one of just three short-runs;x2 = x2¢ or x2 = x2¢¢ (x2¢ < x2¢¢ < x2¢¢¢)or x2 = x2¢¢¢then the firm’s three short-run average total cost curves are ...y$/output unitACs(y;x2¢¢¢)ACs(y;x2¢¢)ACs(y;x2¢)Short-Run & Long-Run Average Total Cost CurvesuThe firm’s long-run average total cost curve is the lower envelope of the short-run average total cost curves ...y$/output unitACs(y;x2¢¢¢)ACs(y;x2¢¢)ACs(y;x2¢)AC(y)The long-run av. total costcurve is the lower envelopeof the short-run av. total cost curves.Short-Run & Long-Run Marginal Cost CurvesuQ: Is the long-run marginal cost curve the lower envelope of the firm’s short-run marginal cost curves?Short-Run & Long-Run Marginal Cost CurvesuQ: Is the long-run marginal cost curve the lower envelope of the firm’s short-run marginal cost curves?uA: No.Short-Run & Long-Run Marginal Cost CurvesuThe firm’s three short-run average total cost curves are ...y$/output unitACs(y;x2¢¢¢)ACs(y;x2¢¢)ACs(y;x2¢)y$/output unitACs(y;x2¢¢¢)ACs(y;x2¢¢)ACs(y;x2¢)MCs(y;x2¢) MCs(y;x2¢¢)MCs(y;x2¢¢¢)y$/output unitACs(y;x2¢¢¢)ACs(y;x2¢¢)ACs(y;x2¢)MCs(y;x2¢) MCs(y;x2¢¢)MCs(y;x2¢¢¢)AC(y)y$/output unitACs(y;x2¢¢¢)ACs(y;x2¢¢)ACs(y;x2¢)MCs(y;x2¢) MCs(y;x2¢¢)MCs(y;x2¢¢¢)AC(y)y$/output unitACs(y;x2¢¢¢)ACs(y;x2¢¢)ACs(y;x2¢)MCs(y;x2¢) MCs(y;x2¢¢)MCs(y;x2¢¢¢)MC(y), the long-run marginalcost curve.Short-Run & Long-Run Marginal Cost CurvesuFor any output level y > 0, the long-run marginal cost of production equals to the short-run marginal cost of output chosen by the firm.Short-Run & Long-Run Marginal Cost CurvesuThis is always true, no matter how many and which short-run circumstances exist for the firm.uSo for the continuous case, where x2 can be fixed at any value of zero or more, the relationship between the long-run marginal cost and all of the short-run marginal costs is ...Short-Run & Long-Run Marginal Cost CurvesAC(y)$/output unitySRACsShort-Run & Long-Run Marginal Cost CurvesAC(y)$/output unitySRMCsShort-Run & Long-Run Marginal Cost CurvesAC(y)MC(y)$/output unitySRMCsuFor each y > 0, the long-run MC equals theMC for the short-run chosen by the firm.。