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1、Chapter Twenty-One,Cost Curves,Structure,Types of cost curvesFixed,variable and total cost functionsAverage fixed,average variable and average cost functionsMarginal cost functionsMarginal and variable cost functionsMarginal and average cost functionsShort run and long run cost curves,Types of Cost
2、Curves,A total cost curve（总成本曲线）is the graph of a firms total cost function.A variable cost curve（可变成本曲线）is the graph of a firms variable cost function.An average total cost curve（平均成本曲线）is the graph of a firms average total cost function.,Types of Cost Curves,An average variable cost curve（平均可变成本曲线
3、）is the graph of a firms average variable cost function.An average fixed cost curve（平均固定成本曲线）is the graph of a firms average fixed cost function.A marginal cost curve（边际成本曲线）is the graph of a firms marginal cost function.,Types of Cost Curves,How are these cost curves related to each other?How are a
4、 firms long-run and short-run cost curves related?,Fixed,Variable&Total Cost Functions,F is the total cost to a firm of its short-run fixed inputs（固定投入）.F,the firms fixed cost,does not vary with the firms output level.cv(y)is the total cost to a firm of its variable inputs（可变投入）when producing y outp
5、ut units.cv(y)is the firms variable cost function.cv(y)depends upon the levels of the fixed inputs.,Fixed,Variable&Total Cost Functions,c(y)is the total cost of all inputs,fixed and variable,when producing y output units.c(y)is the firms total cost function;,y,$,F,y,$,cv(y),y,$,F,cv(y),y,$,F,cv(y),c
6、(y),F,Av.Fixed,Av.Variable&Av.Total Cost Curves,The firms total cost function isFor y 0,the firms average total cost function is,Av.Fixed,Av.Variable&Av.Total Cost Curves,What does an average fixed cost curve look like?AFC(y)is a rectangular hyperbola so its graph looks like.,$/output unit,AFC(y),y,
7、0,AFC(y)0 as y,Av.Fixed,Av.Variable&Av.Total Cost Curves,In a short-run with a fixed amount of at least one input,the Law of Diminishing(Marginal)Returns must apply,causing the firms average variable cost of production to increase eventually.,$/output unit,AVC(y),y,0,$/output unit,AFC(y),AVC(y),y,0,
8、Av.Fixed,Av.Variable&Av.Total Cost Curves,And ATC(y)=AFC(y)+AVC(y),$/output unit,AFC(y),AVC(y),ATC(y),y,0,ATC(y)=AFC(y)+AVC(y),$/output unit,AFC(y),AVC(y),ATC(y),y,0,AFC(y)=ATC(y)-AVC(y),AFC,$/output unit,AFC(y),AVC(y),ATC(y),y,0,Since AFC(y)0 as y,ATC(y)AVC(y)as y.,AFC,$/output unit,AFC(y),AVC(y),A
9、TC(y),y,0,Since AFC(y)0 as y,ATC(y)AVC(y)as y.,And since short-run AVC(y)musteventually increase,ATC(y)must eventually increase in a short-run.,Marginal Cost Function,Marginal cost is the rate-of-change of variable production cost as the output level changes.That is,Marginal Cost Function,The firms
10、total cost function isand the fixed cost F does not change with the output level y,soMC is the slope of both the variable cost and the total cost functions.,Marginal and Variable Cost Functions,Since MC(y)is the derivative of cv(y),cv(y)must be the integral of MC(y).That is,Marginal and Variable Cos
11、t Functions,MC(y),y,0,Area is the variablecost of making y units,$/output unit,Marginal&Average Cost Functions,How is marginal cost related to average variable cost?,Marginal&Average Cost Functions,Since,Marginal&Average Cost Functions,Since,Therefore,as,Marginal&Average Cost Functions,Since,Therefo
12、re,as,as,$/output unit,y,AVC(y),MC(y),$/output unit,y,AVC(y),MC(y),$/output unit,y,AVC(y),MC(y),$/output unit,y,AVC(y),MC(y),$/output unit,y,AVC(y),MC(y),The short-run MC curve intersectsthe short-run AVC curve frombelow at the AVC curves minimum.,Marginal&Average Cost Functions,Similarly,since,Marg
13、inal&Average Cost Functions,Similarly,since,Therefore,as,Marginal&Average Cost Functions,Similarly,since,Therefore,as,as,$/output unit,y,MC(y),ATC(y),as,Marginal&Average Cost Functions,The short-run MC curve intersects the short-run AVC curve from below at the AVC curves minimum.And,similarly,the sh
14、ort-run MC curve intersects the short-run ATC curve from below at the ATC curves minimum.,$/output unit,y,AVC(y),MC(y),ATC(y),Short-Run&Long-Run Total Cost Curves,A firm has a different short-run total cost curve for each possible short-run circumstance.Suppose the firm can be in one of just three s
15、hort-runs;x2=x2 or x2=x2 x2 x2 x2.or x2=x2.,y,0,F=w2x2,F,cs(y;x2),$,y,F,0,F=w2x2,F,F=w2x2,cs(y;x2),cs(y;x2),$,y,F,0,F=w2x2,F=w2x2,A larger amount of the fixedinput increases the firmsfixed cost.,cs(y;x2),cs(y;x2),$,F,y,F,0,F=w2x2,F=w2x2,A larger amount of the fixedinput increases the firmsfixed cost
16、.,Why does a larger amount of the fixed input reduce the slope of the firms total cost curve?,cs(y;x2),cs(y;x2),$,F,MP1 is the marginal physical productivityof the variable input 1,so one extra unit ofinput 1 gives MP1 extra output units.Therefore,the extra amount of input 1needed for 1 extra output
17、 unit is,Short-Run&Long-Run Total Cost Curves,units of input 1.,MP1 is the marginal physical productivityof the variable input 1,so one extra unit ofinput 1 gives MP1 extra output units.Therefore,the extra amount of input 1needed for 1 extra output unit is,Short-Run&Long-Run Total Cost Curves,units
18、of input 1.Each unit of input 1 costs w1,so the firmsextra cost from producing one extra unitof output is,Short-Run&Long-Run Total Cost Curves,is the slope of the firms total cost curve.,Short-Run&Long-Run Total Cost Curves,is the slope of the firms total cost curve.,If input 2 is a complement to in
19、put 1 thenMP1 is higher for higher x2.Hence,MC is lower for higher x2.,That is,a short-run total cost curve startshigher and has a lower slope if x2 is larger.,y,F,0,F=w2x2,F=w2x2,F,F=w2x2,cs(y;x2),cs(y;x2),cs(y;x2),$,F,Short-Run&Long-Run Total Cost Curves,The firm has three short-run total cost cur
20、ves.In 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.How does the firm make this choice?,y,F,0,F,y,y,For 0 y y,choose x2=x2.,cs(y;x2),cs(y;x2),cs(y;x2),$,F,y,F,0,F,y,y,For 0 y y,choose x2=x2.,For y y y,choose x2=x2.,cs(y;x2),cs(
21、y;x2),cs(y;x2),$,F,y,F,0,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.,cs(y;x2),cs(y;x2),$,F,y,F,0,cs(y;x2),cs(y;x2),F,cs(y;x2),y,y,For 0 y y,choose x2=x2.,For y y y,choose x2=x2.,For y y,choose x2=x2.,c(y),thefirms long-run totalcost curve.,$,F,Short-Run&Long-
22、Run Total Cost Curves,The firms 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 Curves,If input 2 is available in continuous amounts then th
23、ere 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.,$,y,F,0,F,cs(y;x2),cs(y;x2),cs(y;x2),c(y),F,Short-Run&Long-Run Average Total Cost Curves,For any output level y,the long-run total cost curve alw
24、ays gives the lowest possible total production cost.Therefore,the long-run av.total cost curve must always give the lowest possible av.total production cost.The long-run av.total cost curve must be the lower envelope of all of the firms short-run av.total cost curves.,Short-Run&Long-Run Average Tota
25、l Cost Curves,E.g.suppose again that the firm can be in one of just three short-runs;x2=x2 or x2=x2(x2 x2 x2)or x2=x2then the firms three short-run average total cost curves are.,y,$/output unit,ACs(y;x2),ACs(y;x2),ACs(y;x2),Short-Run&Long-Run Average Total Cost Curves,The firms long-run average tot
26、al cost curve is the lower envelope of the short-run average total cost curves.,y,$/output unit,ACs(y;x2),ACs(y;x2),ACs(y;x2),AC(y),The long-run av.total costcurve is the lower envelopeof the short-run av.total cost curves.,Short-Run&Long-Run Marginal Cost Curves,Q:Is the long-run marginal cost curv
27、e the lower envelope of the firms short-run marginal cost curves?,Short-Run&Long-Run Marginal Cost Curves,Q:Is the long-run marginal cost curve the lower envelope of the firms short-run marginal cost curves?A:No.,Short-Run&Long-Run Marginal Cost Curves,The firms three short-run average total cost cu
28、rves are.,y,$/output unit,ACs(y;x2),ACs(y;x2),ACs(y;x2),y,$/output unit,ACs(y;x2),ACs(y;x2),ACs(y;x2),MCs(y;x2),MCs(y;x2),MCs(y;x2),y,$/output unit,ACs(y;x2),ACs(y;x2),ACs(y;x2),MCs(y;x2),MCs(y;x2),MCs(y;x2),AC(y),y,$/output unit,ACs(y;x2),ACs(y;x2),ACs(y;x2),MCs(y;x2),MCs(y;x2),MCs(y;x2),AC(y),y,$/
29、output unit,ACs(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 Curves,For 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-
30、Run Marginal Cost Curves,This is always true,no matter how many and which short-run circumstances exist for the firm.So 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 Curves,AC(y),$/output unit,y,SRACs,Short-Run&Long-Run Marginal Cost Curves,AC(y),$/output unit,y,SRMCs,Short-Run&Long-Run Marginal Cost Curves,AC(y),MC(y),$/output unit,y,SRMCs,For each y 0,the long-run MC equals theMC for the short-run chosen by the firm.,
