Alfred Weber and Subsequent Developments in Industrial Location Theory


  1. Why are we interested in Weberian Triangles? Objectives of deriving Weberian principles and least-cost location theory.

  2. Setting up the theoretical model: the constraints (assumptions)
    1. the "objective function" for this "normative" model
      1. starting with transport cost minimization
      2. overall cost minimization
      3. profit maximization
    2. Assumptions related to organization and, importantly, to production process and production function [the initial Weber model is based on linear production relations with no scale economies and no input substitution; "Leontief-type production function".
    3. Assumptions related to inputs used in the production process
      • Inputs are available in unlimited supply at given (fixed) prices independent of location
      • These material inputs are either localized at a limited number of locations or ubiquitously available ( = everywhere).
      • "pure" versus weight-losing materials
      • competitive price formation on markets for inputs (input prices are independent of production levels)
    4. Assumptions related to markets
      • Demand is fixed and concentrated at a limited number of (known) locations (points)
      • competitive price formation (given prices at market, i.e. prices are independent of production levels)
    5. Assumptions related to the transportation process and transport costs.
      • Transport is possible in any direction, and transport costs for materials or products are linear, i.e. directly proportional to weight and distance, implying a "flat plain" and an absence of networks and distance & scale economies in transportation.
  3. Precursor: Wilhelm Launhardt (see reading by Pinto)

  4. One-Dimensional Model: One Localized Input / One Localized Market (Review Hoover, 1948, pp.39ff.)

  5. Location Triangle: Two Localized Inputs, one Localized Market
    • Solution procedures (The optimal Weberian location is NOT the center of gravity [which minimizes the sum of the squares of distances], but the spatial median, which minimizes the sum of the distances; see: Kuhn & Kuenne, below).
    • Conditions for interior versus corner locations

  6. Isodapane-based Extensions of the Triangle Solution
    1. Critical Isodapane
    2. Labor and other spatial cost variations, "labor coefficients"
    3. Agglomeration, "joint action spaces" (Weber Ch.5)

  7. David Smith:

  8. Analysis of Effects of Variations in Selected Assumptions
    1. non-linear transport cost functions
    2. non-linear production functions
      • Definition and kinds of "production function"
      • Nature of linear, fixed-factor production function
        (right angled isoquants)
      • Linear homogenous production function of the frist degree
        (constant returns to scale)
      • Non-linear production functions (Leon Moses)
        • increasing returns to scale
        • decreasing returns to scale
      • Equilibrium at any one isoquant/ level of output: iso-cost lines
      • Iso-cost lines and scale: structure of factor input markets
    3. The Moses Model (see Moses Reading) [ JSTORS-PDF]
    4. Product (Output) Oriented Production Function (Hamilton 1974), allowing for
      • Multiple products
      • Substitution between outputs
      • Continuous substitution among and between inputs & outputs
      • Environmental interpretations and insights
    5. Considerations related to the structure and price mechanisms on on input and output markets and the market for transport services
    6. Entrepreneurship, organization, subsidies, chance, personal factors
    7. Externalities, agglomeration,"business climates", etc.
    8. Multi-location problems (warehouses, branch plants etc.)


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