中級微觀經(jīng)濟(jì)學(xué)課件輝英語第21章

1、Chapter Twenty-OneCost Curves成本曲線成本曲線StructureuTypes of cost curves Fixed, variable and total cost functions Average fixed, average variable and average cost functionsuMarginal cost functionsuMarginal and variable cost functionsuMarginal and average cost functionsuShort run and long run cost curvesT

2、ypes of Cost CurvesuA total cost curve （總成本曲線）總成本曲線）is the graph of a firms total cost function.uA variable cost curve （可變成本曲線可變成本曲線）is the graph of a firms variable cost function.uAn average total cost curve （平均成平均成本曲線）本曲線）is the graph of a firms average total cost function.Types of Cost CurvesuAn

3、average variable cost curve （平平均可變成本曲線）均可變成本曲線）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線）定成本曲線）is the graph of a firms average fixed cost function.uA marginal cost curve （邊際成本曲線邊際成本曲線）is the graph of a firms marginal cost function.Types of Cost

4、CurvesuHow are these 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)

5、 is the total cost to a firm of its variable inputs （可變投入）可變投入）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

6、 output units. c(y) is the firms total cost function;c yFcyv( )( ). y$Fy$cv(y)y$Fcv(y)y$Fcv(y)c(y)Fc yFcyv( )( ) Av. Fixed, Av. Variable & Av. Total Cost CurvesuThe firms total cost function isFor y 0, the firms average total cost function isc yFcyv( )( ). AC yFycyyAFC yAVC yv( )( )( )( ). Av. Fixed

7、, 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 .AFC yFy( ) $/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, t

8、he Law of Diminishing (Marginal) Returns must apply, causing the firms average variable cost of production to increase eventually.$/output unitAVC(y)y0$/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(

9、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

10、 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,MC ycyyv( )( ). Marginal Cost FunctionuThe firms total cost function isand the fixed cost F does not change with the output level y, souMC is the slope

11、 of both the variable cost and the total cost functions.c yFcyv( )( ) MC ycyyc yyv( )( )( ). Marginal and Variable Cost FunctionsuSince MC(y) is the derivative of cv(y), cv(y) must be the integral of MC(y). That is,MC ycyyv( )( ) cyMC z dzvy( )( ).0Marginal and Variable Cost FunctionsMC(y)y0cyMC z d

12、zvy()( ) 0 yArea is the variablecost of making y units$/output unitMarginal & Average Cost FunctionsuHow is marginal cost related to average variable cost?Marginal & Average Cost FunctionsSinceAVC ycyyv( )( ), AVC yyyMC ycyyv( )( )( ). 12Marginal & Average Cost FunctionsSinceAVC ycyyv( )( ), AVC yyy

13、MC ycyyv( )( )( ). 12Therefore, AVC yy( ) 0yMC ycyv ( )( ).asMarginal & Average Cost FunctionsSinceAVC ycyyv( )( ), AVC yyyMC ycyyv( )( )( ). 12Therefore, AVC yy( ) 0yMC ycyv ( )( ).asMC ycyyAVC yv( )( )( ). as AVC yy( ) 0$/output unityAVC(y)MC(y)$/output unityAVC(y)MC(y)MC yAVC yAVC yy( )( )( ) 0$/

14、output unityAVC(y)MC(y)MC yAVC yAVC yy( )( )( ) 0$/output unityAVC(y)MC(y)MC yAVC yAVC yy( )( )( ) 0$/output unityAVC(y)MC(y)MC yAVC yAVC yy( )( )( ) 0The short-run MC curve intersectsthe short-run AVC curve frombelow at the AVC curves minimum.Marginal & Average Cost FunctionsSimilarly, sinceATC yc

15、yy( )( ), ATC yyyMC yc yy( )( )( ). 12Marginal & Average Cost FunctionsSimilarly, sinceATC yc yy( )( ), ATC yyyMC yc yy( )( )( ). 12Therefore, ATC yy( ) 0yMC yc y ( )( ).asMarginal & Average Cost FunctionsSimilarly, sinceATC yc yy( )( ), ATC yyyMC yc yy( )( )( ). 12Therefore, ATC yy( ) 0yMC yc y ( )

16、( ).asMC yc yyATC y( )( )( ). as ATC yy( ) 0$/output unityMC(y)ATC(y)MC yATC y( )( ) as ATC yy( ) 0Marginal & 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 cur

17、ve 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 .y

18、0F = 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 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 inp

19、ut 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 unit isShort-Run & Long-Run Total Cost Cur

20、ves units of input 1.1MP/1MP1 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 CurvesMCwMP 11. units of input 1.Each unit of in

21、put 1 costs w1, so the firmsextra cost from producing one extra unitof output is1MP/1Short-Run & Long-Run Total Cost CurvesMCwMP 11is the slope of the firms total cost curve.Short-Run & Long-Run Total Cost CurvesMCwMP 11is the slope of the firms total cost curve.If input 2 is a complement to input 1

22、 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 cur

23、ves.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

24、.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), thefirms long-run totalc

25、ost 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 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 availab

26、le 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