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1、Chapter Twenty-OneCost CurvesStructureuTypes of cost curvesFixed,variable and total cost functionsAverage fixed,average variable and average cost functionsuMarginal cost functionsuMarginal and variable cost functionsuMarginal and average cost functionsuShort run and long run cost curvesTypes of Cost
2、 CurvesuA total cost curve（总成本曲线）总成本曲线）is the graph of a firms total cost function.uA variable cost curve（可变成本曲线）可变成本曲线）is the graph of a firms variable cost function.uAn average total cost curve（平均成平均成本曲线）本曲线）is the graph of a firms average total cost function.Types of Cost CurvesuAn average variab
3、le cost curve（平平均可变成本曲线）均可变成本曲线）is the graph of a firms average variable cost function.uAn average fixed cost curve（平均固平均固定成本曲线）定成本曲线）is the graph of a firms average fixed cost function.uA marginal cost curve（边际成本曲线）边际成本曲线）is the graph of a firms marginal cost function.Types of Cost CurvesuHow are t
4、hese cost curves related to each other?uHow are a firms 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 firms fixed cost,does not vary with the firms output level.ucv(y)is the total cost to a
5、firm of its variable inputs（可变投入）可变投入）when producing y output units.cv(y)is the firms 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 firms tot
6、al cost function;y$Fy$cv(y)y$Fcv(y)y$Fcv(y)c(y)FAv.Fixed,Av.Variable&Av.Total Cost CurvesuThe firms total cost function isFor y 0,the firms average total cost function isAv.Fixed,Av.Variable&Av.Total Cost CurvesuWhat does an average fixed cost curve look like?uAFC(y)is a rectangular hyperbola so its
7、 graph looks like.$/output unitAFC(y)y0AFC(y)0 as y Av.Fixed,Av.Variable&Av.Total Cost CurvesuIn a short-run with a fixed amount of at least one input,the Law of Diminishing(Marginal)Returns must apply,causing the firms average variable cost of production to increase eventually.$/output unitAVC(y)y0
8、$/output unitAFC(y)AVC(y)y0Av.Fixed,Av.Variable&Av.Total Cost CurvesuAnd ATC(y)=AFC(y)+AVC(y)$/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$/output unitAFC(y)AVC(y
9、)ATC(y)y0Since AFC(y)0 as y ,ATC(y)AVC(y)as y .And since short-run AVC(y)musteventually increase,ATC(y)must eventually increase in a short-run.Marginal Cost FunctionuMarginal cost is the rate-of-change of variable production cost as the output level changes.That is,Marginal Cost FunctionuThe firms t
10、otal cost function isand the fixed cost F does not change with the output level y,souMC is the slope of both the variable cost and the total cost functions.Marginal and Variable Cost FunctionsuSince MC(y)is the derivative of cv(y),cv(y)must be the integral of MC(y).That is,Marginal and Variable Cost
11、 FunctionsMC(y)y0Area is the variablecost of making y units$/output unitMarginal&Average Cost FunctionsuHow is marginal cost related to average variable cost?Marginal&Average Cost FunctionsSinceMarginal&Average Cost FunctionsSinceTherefore,asMarginal&Average Cost FunctionsSinceTherefore,asas$/output
12、 unityAVC(y)MC(y)$/output unityAVC(y)MC(y)$/output unityAVC(y)MC(y)$/output unityAVC(y)MC(y)$/output unityAVC(y)MC(y)The short-run MC curve intersectsthe short-run AVC curve frombelow at the AVC curves minimum.Marginal&Average Cost FunctionsSimilarly,sinceMarginal&Average Cost FunctionsSimilarly,sin
13、ceTherefore,asMarginal&Average Cost FunctionsSimilarly,sinceTherefore,asas$/output unityMC(y)ATC(y)asMarginal&Average Cost FunctionsuThe short-run MC curve intersects the short-run AVC curve from below at the AVC curves minimum.uAnd,similarly,the short-run MC curve intersects the short-run ATC curve
14、 from below at the ATC curves minimum.$/output unityAVC(y)MC(y)ATC(y)Short-Run&Long-Run Total Cost CurvesuA firm has a different short-run total cost curve for each possible short-run circumstance.uSuppose the firm can be in one of just three short-runs;x2=x2 or x2=x2 x2 x2 x2.or x2=x2.y0F =w2x2 F c
15、s(y;x2)$yF 0F =w2x2 F F =w2x2 cs(y;x2)cs(y;x2)$yF 0F =w2x2 F =w2x2 A larger amount of the fixedinput increases the firmsfixed cost.cs(y;x2)cs(y;x2)$F yF 0F =w2x2 F =w2x2 A larger amount of the fixedinput increases the firmsfixed cost.Why does a larger amount of the fixed input reduce the slope of th
16、e firms total cost curve?cs(y;x2)cs(y;x2)$F MP1 is the marginal physical productivityof the variable input 1,so one extra unit ofinput 1 gives MP1 extra output units.Therefore,the extra amount of input 1needed for 1 extra output unit isShort-Run&Long-Run Total Cost Curves units of input 1.MP1 is the
17、 marginal physical productivityof the variable input 1,so one extra unit ofinput 1 gives MP1 extra output units.Therefore,the extra amount of input 1needed for 1 extra output unit isShort-Run&Long-Run Total Cost Curves units of input 1.Each unit of input 1 costs w1,so the firmsextra cost from produc
18、ing one extra unitof output isShort-Run&Long-Run Total Cost Curvesis the slope of the firms total cost curve.Short-Run&Long-Run Total Cost Curvesis the slope of the firms total cost curve.If input 2 is a complement to input 1 thenMP1 is higher for higher x2.Hence,MC is lower for higher x2.That is,a
19、short-run total cost curve startshigher and has a lower slope if x2 is larger.yF 0F =w2x2 F =w2x2 F F =w2x2 cs(y;x2)cs(y;x2)cs(y;x2)$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
20、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 x
21、2=x2.cs(y;x2)cs(y;x2)$F yF 0cs(y;x2)cs(y;x2)F cs(y;x2)y y For 0 y y,choose x2=x2.For y y y,choose x2=x2.For y y,choose x2=x2.c(y),thefirms long-run totalcost curve.$F Short-Run&Long-Run Total Cost CurvesuThe firms long-run total cost curve consists of the lowest parts of the short-run total cost cur
22、ves.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
23、of the short-run total cost curves.$yF 0F cs(y;x2)cs(y;x2)cs(y;x2)c(y)F Short-Run&Long-Run Average Total Cost CurvesuFor any output level y,the long-run total cost curve always gives the lowest possible total production cost.uTherefore,the long-run av.total cost curve must always give the lowest pos
24、sible av.total production cost.uThe long-run av.total cost curve must be the lower envelope of all of the firms short-run av.total cost curves.Short-Run&Long-Run Average Total Cost CurvesuE.g.suppose again that the firm can be in one of just three short-runs;x2=x2 or x2=x2 (x2 x2 0,the long-run marg
25、inal cost of production equals to the short-run marginal cost of output chosen by the firm.Short-Run&Long-Run Marginal Cost CurvesuThis is always true,no matter how many and which short-run circumstances exist for the firm.uSo for the continuous case,where x2 can be fixed at any value of zero or mor
26、e,the relationship between the long-run marginal cost and all of the short-run marginal costs is.Short-Run&Long-Run Marginal Cost CurvesAC(y)$/output unitySRACsShort-Run&Long-Run Marginal Cost CurvesAC(y)$/output unitySRMCsShort-Run&Long-Run Marginal Cost CurvesAC(y)MC(y)$/output unitySRMCsuFor each y 0,the long-run MC equals theMC for the short-run chosen by the firm.