SUPPLY ARMS AND OPTIMAL SPATIAL STRUCTURE*

ABSTRACT. A multi-plant producer has sole access to a region, and each of the plants processes a raw material which is drawn from its own exclusive supply area. Under these conditions what spatial structure of production (in terms of plant scale, plant frequency, supply-area size and supply-area shape) will enable region-wide or multi-plant profit to be maximized? The form of this optimal structure is shown to vary with prevailing level of price, which is exogenously determined.     

City size distributions and urban density functions: some interrelationships

This paper is concerned with "relating the apparent regularities of the population distribution within individual cities to the regularities with which the urban population of a nation is distributed among cities....An attempt is first made to draw the two distributions together in mathematical terms. The discussion then turns to a theoretical consideration of possible interrelations between the two distributions, after which the temporal variation of the parameters of each distribution is examined. This leads to the outlining of an evolutionary model of urban-system development, based on the passage through a number of stages." The analysis focuses on urban systems in Europe and North America.     

Mapping schools' NAPLAN results: a spatial inequality of school outcomes in Australia

This article identifies spatial dimensions of educational outcomes using maps of the 2016 Grade 5 reading results for Australia's National Assessment Program–Literacy and Numeracy for all Australian schools. A geographical information system (GIS) was used to overlay schools' results onto suburbs' advantage or disadvantage to visualise spatial patterns. We then examined the extent to which school results “cluster” in socio‐economically advantaged and disadvantaged suburbs and considered the consistency of spatial patterns for results across major cities. That work illustrates both how GIS can foreground educational inequality and how “the spatial” is more than corollary for student socio‐economic status. Results show substantial differences between urban and remote areas and towns of different size. Maps of cities visualise spatial “clustering” patterns of school results, with most schools in advantaged suburbs having high results and almost no schools in disadvantaged suburbs having high results. Educational outcomes strongly align to local socio‐demographic characteristics, and parallel host communities’ levels of advantage or disadvantage. Differences between public and private schools are less significant than within‐sector differences for schools in advantaged or disadvantaged locales. Patterns in all cities are consistent—schools in advantaged suburbs predominantly have high results, whereas non‐government schools generally perform better than government schools in disadvantaged suburbs. Most concerning is the persistent and increasing trajectory of results in advantaged, and more so in disadvantaged suburbs, of all cities since the first National Assessment Program–Literacy and Numeracy in 2008. Ameliorating spatial inequality between primary schools is one of the greatest challenges for Australians.