Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,Theories of Plant Location,Median Location Principle,Linear Market Competition(Hotelling),Weber,L,sch,Isards Space Economy,Smiths Spatial Margins,Webbers Uncertainty Effect,Median Location Principle:Minimize Transport Cost,Hotellings Vendors on the Beach Solution to such Competition,Essentially iterative competitive movements within the,agglomeration space,A,B,C,D,E,If seller 1 starts at A,then,seller 2 jumps to B,then seller 1 jumps to C,and seller 2 could proceed,to D,but that is inferior,to also locating at C,splitting the market in,half.,Webers Model of Manufacturing Industry Production,Developed in the early 20th Century in southern Germany,Input factors are not ubiquitous,This means that:,physical resources are not found everywhere,human labor is differentiated by skill&ability,capital availability varies,other inputs are also differentiated,Weber hypothesized that:,Given market prices,producers would seek to minimize production costs to maximize profits.,This leads to a taxonomy of production cost situations,considering,factor costs,transport costs on products,transport costs on finished goods,In the Weber Model,If producers Minimize Costs,then:,Min:Ipiqi+Iriqidi+rqqdj,e.g.,Minimize sum of factor costs+transport costs,on factor inputs+transport cost on shipment of product to the market,If factor costs are“given,then the problem becomes how to minimize transport costs.,The Material Index Principle as a guide to manufacturing location,Material index=weight of localized material,weight of product(unit),If M.I.or=1.0,locate at market,Material types:,“Pure materials:no weight loss in production,“Weight-losing materials,“ubiquities,Webers Cost Minimizing Model&the Principle of Material Orientation,Example:2T local materials,3T ubiquities,MI=2/5=.4,locate at market,Alternative Situations,(1)Ubiquities only,MI=0,locate at market,(2)Pure Materials only,(a)1 pure material,MI=1,M,C,Material Index Cases,Cont.,(b)1 pure material+ubiquities,MI 1,locate at market,(c)several pure materials only,MI=1,locate at market,(d)several pure materials+ubiquities,MI 1,locate at material location,M,C,Material Index Cases,Cont.,(b)1 weight losing material+ubiquities,If MI 1,locate at material site,If MI 1,locate at market,If MI=1?,probably at market,(c)Several weight losing materials,M,1,M,2,C,Locate away from C,An Example of(c),P,1,=10,q,1,=2,r,1,=.1 r,q,=.1,q=5,p,2,=5,q,2,=4,r,2,=.1 MI=6/5=1.2,M,1,C,M,2,7,7,5,At M1:40+0+2.0+3.5=45.5,At M2:40+1+0 +3.5 =44.5,At C:40+1.4+2.8+0=44.2,At L:40+1.225+2.45+.5=44.175,L,6.125,6.125,1,Material Index Situations,Cont.,(d)Several weight-losing materials+pure materials:MI decreases,outcomes as in(b)above,(e)Several weight-losing materials+pure,materials+ubiquities:outcomes as in(d),Upshot:Most situations are like c,d,and e.,3 classic locational outcomes:1.Market,2.Resource,and 3.Intermediate,sometimes“footloose,Labor Cost Deviation,M,1,M,2,C,P,L,1,L,2,P-Transport Cost Minimum Location,L,1,L,2,-Low Labor Cost Locations,C -Market,M,1,M,2,-Raw Material Sites,Critical,Isodapane,Webers Approach to Agglomeration Economies,Scale of Output,$,Q,1,Q,2,a,1,a,2,For some index of agglomeration(e.g.a,1,or a,2,):,A,C,B,Separate,Market,Regions,e.g.A,B,C,or agglomeration,A,B,C,Critical,Isodapanes,Competition for Location in Agglomerations,S,T,U,T,T,S,S,U,U,S,1,T,1,U,1,S,T,and U can get agglomeration savings at T1,S1,and U1,but need to bargain to move to a location realizing them in,S,T,and U are separate Markets,whose critical isodapanes are,SS,TT,and UU,Critique of Weber,Conception of market demand limited,Transport costs not defined realistically,Labor is typically mobile,not fixed in space,Many manufacturing plants produce complex sets of products with complex sets of inputs,Treatment of agglomeration is rigid,L,sch:Location based on maximum profit,not minimum cost,Isards Substitution Framework,Input-factors can often be used substitutability,although the degree of substitution can vary by scale and by technology,A,B,Q,1,Q,2,“Perfect substitutability,A,B,No substitution,Q,1,Q,2,Q,3,Substitution possibilities,Isoquants-Equal levels of output,Substitution is possible over a range,A,B,Q,1,Q,2,but factor proportions change,Substitution possibilities,Isocosts-Equal levels of cost,C,1,C,2,C,3,A,B,Q,1,Q,2,Q,1,Q,2,C,1,C,1,C,2,C,3,C,2,C,3,Y,X,X is the ideal amount of A,Y is the ideal amount of B,for production at level Q,1,Expansion Curve-joins optimal factor combinations across scale of output,Factor X,Factor Y,Q,1,Q,2,Q,3,Q,1,Q,2,Q,3,C,1,C,1,C,2,C,2,C,3,C,3,Expansion Path,Spacing of isoquants and scale economies and/or diseconomies,Factor X,Output,Diseconomies,Linear,Scale Economies,Isoquants displaying scale economies&diseconomies,Factor X,Factor X,Factor Y,Factor Y,10,20,30,10,20,30,40,Diseconomies,Economies,Isards Substitution Model:,two point location model-pure materials,M,C,Transformation Li