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The Location Invariance Theorem in Weberian Space Under Uncertainty
Author(s) -
Tan LinTi,
Hsu SongKen
Publication year - 2001
Publication title -
journal of regional science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.171
H-Index - 79
eISSN - 1467-9787
pISSN - 0022-4146
DOI - 10.1111/0022-4146.00209
Subject(s) - homothetic transformation , production (economics) , economics , function (biology) , product (mathematics) , invariant (physics) , product topology , location model , space (punctuation) , demand curve , mathematical economics , homogeneous , econometrics , mathematics , microeconomics , mathematical optimization , computer science , mathematical analysis , geometry , combinatorics , evolutionary biology , mathematical physics , biology , operating system
This paper examines the validity of the location invariance theorem in Weberian space under various types of uncertainty. The main results are: Given that the firm's location is constrained to remain at a specified distance from the output market, the optimal location is invariant to any change in product demand if and only if the production function is homothetic for a firm facing demand price uncertainty, or if the production function is homothetic and both inputs are risk‐neutral for a firm facing technological uncertainty. Alternatively, given that the distance from the firm's location to the output market is a variable, location invariance occurs for a firm facing demand price uncertainty if the production function is linear homogeneous. In the presence of input price uncertainty the optimal location always varies with a change in product demand. The results can include those previously obtained for linear stochastic location models as special cases and some are new contributions to the literature.