[精选]生产者理论知识29212.pptx

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1、李永波The Firm:ProductionAdvanced MicroEconomicsIn this lecture we set out some of the elements needed for an analysis of the firmlTechnical efficiencylReturns to scalelConvexitylSubstitutabilitylMarginal products.and(for next time)assuming a competitive environment.We do it within the context of a sin

2、gle-output firm.But first we need the building blocks of a model.The basics of production.ziamount of input iQamount of outputThe basics of production.input vector z:=(z1,z2,.,zm)wiprice of input iw:=(w1,w2,.,wm)input price vector Pprice of outputNotation:PricesQ G(z1,z2,.,zm)The single-output produ

3、ction functionWritten more compactlyQ G(z)technologyoutputYes,but why not=sign here?inputsThe meaning of the functionthe maximum amount of output that can be producedfrom this list of inputsUse this relation to distinguish two cases.Components of the relationshipQ G(z)Q=G(z)21The case where producti

4、on is technically efficientThe case where production is(technically)inefficientTechnical efficiencyG(z)zi_iG(z):=where differentiableSome handy notation.z2Qz10 G(z,z)1 2outputinput 2input 1Q G(z,z)1 2infeasiblepointsQ=G(z,z)1 2technically efficient pointsNow lets slice this set up to get some useful

5、 toolsThe full production functionn Pick a particular output level QZ(Q):=z:G(z)Qn Find a feasible input vector z G(z)Qn Repeat to find all such input vectorsInput requirement setsZ(Q):=z:G(z)Qthe set of input vectors that meet the technical feasibility condition for output level Q.but what would Z

6、look like?This depends on the assumptions we make about production.First,a“standard”case.?What is this thing.?z1z2G(z,z)=Q1 2 infeasible points _ Z(Q)technically efficient points feasible,but inefficient pointsG(z,z)Q1 2The input requirement set:z1z2l z l z Pick two boundary pointsDraw the line betw

7、een themIntermediate points must lie in the interior of Zmeaning:a combination of two techniques may produce more outputG(z)=QG(z)=QG(z)QBut what if we changed some of the assumptions here?_ Z(Q)Case 1:Z is smooth and strictly convexz1z2 _ Z(Q)l z l z Pick any two points in ZDraw the line between th

8、emIntermediate points must lie in Zmeaning:a combination of feasible techniques is also feasibleCase 2:Z convex but not strictly convexz1z2 this point isnot feasible _ Z(Q)This region causes a problemmeaning:in this region there is an indivisibilityCase 3:Z is smooth but not convexAn Example.LondonN

9、ew York313 1z1z2slope undefinedat this point the only efficient point for Q=Q _ Z(Q)Case 4:Z is convex but not smoothz1z2z1z2z1z2z1z2Standard case,but strong assumptions about divisibility and smoothnessalmost conventional case:mixtures may be just as good as single techniquesPresents problems:the d

10、ent represents an indivisibilityunusual case:only one efficient point and not smooth.But not perverse.Summary:4 possibilities for the input requirement set Z z:G(z)=Q This is the isoquant.Lets look at its shape.n Pick an output level Qn Find the input requirement set Z(Q)n Draw the boundary of this

11、setIsoquants z:G(z)=Q Az1inputs requiredto produce at Az2Isoquant at QSlope=z2/z1The input ratio describes the particular techniqueThe isoquant is the boundary of ZThe isoquant through A(Q)Marginal rate of technical substitutionlThe slope of the isoquant is the marginal rate of substitution at A.lIt

12、 measures the implicit“price”of input 1 in terms of input 2.lThe higher is this“price”,the smaller is the relative usage of input 1z1z2l Al AG1(z)/G2(z)l The responsiveness of the input ratio to the MRTS is given by the elasticity of substitution-log(z1/z2)log(G1/G2)l Can be seen as the isoquants“cu

13、rvature”input ratioNow for aspecial case.A constant elasticity of substitution:Increase the elasticity of substitution.z1z2Now look at the structure of the contour map.z1z2Homothetic contoursz1z2Qt z2t ztQr1G(t z)=t G(z)rContours of a homogeneous functionlThe isoquants form a contour map.lIf we look

14、ed at the“parent”diagram,what would we see?lLets do this for 2 inputs,one output.Lets rebuild from the isoquantsz2Qz1expansionrayl 0G(t z)=t G(z)constant returns to scaleProportional increase in all inputsz2Qz10t1 G(t z)t G(z)Increasing returns to scaleProportional increase in all inputsz2Qz10t1 G(t

15、 z)t G(z)Decreasing returns to scaleProportional increase in all inputsz2Qz1isoquantQ=Q0Take a horizontalsection.to get the isoquant againl z2Qz10this gives us our next conceptNow take a vertical section.l n Pick a technically efficient input vectorn Keep all but one input constant Q=G(z)n Measure c

16、hange in output w.r.t.this inputG(z)zi_MPi=Gi(z)=Marginal productsz1QG(z)z1QG(z)z1QG(z)possible relationships between output and one inputz1QG(z)Lets take the conventional case feasible setG(z)Qz1input 1 is essentialSet of technically efficient pointsTake the relationship between output and input 1.

17、If z1=0then Q=0z1QG(z)G1 falls with z1 if G is concaveMarginal productslope=G1(z)n Technical efficiencyThats for next time.Thats for next time.n Returns to scalen Convexityn MRTSn Marginal productAll of these are important in All of these are important in the firms optimisation problemthe firms optimisation problemKey concepts演讲完毕，谢谢观看！