332_Classics - Some Handy Notation to Know in xi x1 x2 x3...

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1 Slide 1 Classical Models Some Handy Notation to Know i n x i x 1 + x 2 + x 3 + … + x n (e.g. 2 + 4 + 6 +…+ 10) i n x i x 1 x 2 x 3 x n ( is multiplication) is defined to be there exists x for all x a b a implies b a B a is an element of the set B {a,b,c} B set {a,b,c} is a subset of set B wrt with respect to (an abbreviation I use often) Slide 2 Classical Models Net Locational Value = Accessibility NLV i = B i -C i + Σ j n-1 (B j -C j / d ij ) NLV i = net locational value at node (“place”) i d ij = distance between place i and j B j -C j = net benefit of place j, (friends, enemies, etc.) n = number of places.
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2 Slide 3 Classical Models Potential Accessibility (Market Potential) A i = P i + Σ j n-1 ( P j / d ij ) A i = potential accessibility at node i d ij = distance between place i and j P j = relevant attributes of each place, such as its population, retailing surface, parking space, etc. n = number of places. Slide 4 Classical Models Locational Rent von Thünen’s Simplifying Assumptions (1783-1850, von Thünen owned an agricultural estate in rural Germany for 40 years) 1. An ‘ isolated state ’ (no links with the rest of the world) with one city at the centre of an agricultural area. 2. The city is the sole market for the surplus production from the agricultural area, and the agricultural area is the sole supplier to the city. At the city all fanners receive the same price for a particular crop at anyone time . 3. This agricultural area is a uniform plain over which soil fertility, climate, and other physical factors do not vary. There are no physical barriers to movement across the plain. 4. All farmers act as economic [agents ] ; this means that they aim to maximize their profits and have full knowledge of the needs of the market. 5. There is only one form of transport (in those days, horse and cart). 6. The cost of this transport is directly proportional to distance . Bradford and Kent Human Geography: Theories and Their Applications (1977, page 34)
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3 Slide 5 Classical Models von Thünen’s Equation for Locational Rent Location Rent (LR) = Ym - Yc - Ytd = Y(m - c - td) = Revenue – Production Costs – Transportation Costs where: LR = locational rent per unit of land Y = yield (in commodity units) per unit of land m = market price per unit of commodity c = production cost per unit of commodity t = transport cost per unit of commodity per mile d = distance from the market For example, a commodity unit might be a bushel, or a ton, or per gallon. Bradford and Kent Human Geography: Theories and Their Applications (1977, page 33) Slide 6 Classical Models von Thünen’s Equation in a Diagram Stutz and de Souza The World Economy (1998, page 264)
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4 Slide 7 Classical Models Location Rent versus Distance for 2 Crops Bradford and Kent Human Geography: Theories and Their Applications (1977, page 31) Slide 8 Classical Models Location Rent versus Distance for 3 Crops, with 2D Bradford and Kent Human Geography: Theories and Their Applications (1977, page 32)
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