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A . Location Theories Models
1. Von Thunen Model
2. Alonso Model
3. Weber Model
4. Moses Model
5. Christaller Model
B. Comparison between the location theories models
Definition
• Location theory is concerned with the geographic location of economic activity; it has become an integral part of economic geography, regional science and spatial economics.
• Location theory addresses the questions of what economic activities are located where and why.
• Location theory rests — like microeconomic theory generally — on the assumption that agents act in their own self interest.
• Thus firms choose locations that maximize their profits and individuals choose locations that maximize their utility.
• The location of economic activities can be determined on a broad level such as a region or metropolitan area, or on a narrow one such as a zone, neighborhood, city block, or an individual site
1. Von Thunen Model
• Johann Heinrich Von Thunen, a Prussian landowner introduced an early theory of agricultural location known as The Isolated State on 1826.
• The model predicts the emergence of a series of concentric zones characterised by different patterns and intensities of land use.
• Principles of the Model
- The model suggests that accessibility to the market (town) can create a complete system of agricultural land use.
- This model also envisaged a single market surrounded by farmland, both situated on a plain of complete physical homogeneity
• Assumptions
– The city is located centrally within an "Isolated State."
– The Isolated State is surrounded by wilderness.
– The land is completely flat and has no rivers or mountains.
– Soil quality and climate are consistent.
– Farmers in the Isolated State transport their own goods to market via oxcart, across land, directly to the central city. There are no roads.
– Farmers behave rationally to maximize profits.
• Location of intensive vs Extensive agriculture
– Intensive agriculture will possess a steep gradient and will located closer to the market than extensive agriculture.
– Different crops will possess different rent gradients.
– Perishable crops such as vegetables and dairy products will possess steep gradient while less perishable crops such grains will possess less steep gradients.
• There are four rings of agricultural activity surrounding the city.
– Zone 1 : Dairying and intensive farming occur in the ring closest to the city. The related products (vegetables, fruit, milk and other dairy products) have the highest profits, but also the highest transportation costs because they are vulnerable and perishable.
– Zone 2 : Timber and firewood will be produced for fuel and building materials. Before industrialization (and coal power), wood was a very important fuel for heating and cooking. Wood is very heavy and therefore difficult and costly to transport.
– Zone 3 : Consists of extensive field crops such as grain for bread. Since grain lasts longer than dairy products and is much lighter than wood transport costs are considered to be lower, allowing a location further from the city. Ranching is located in the final ring surrounding the central city. Animals can be raised far from the city because they are self-transporting and thus have low transport costs.
– Zone 4 : Lies the unoccupied wilderness, which is too great a distance from the central city for any type of agricultural product
• Analytical Tools : Economic Rents
– Economic rent is technical terminology used by economist to define one aspect of the price of goods and services.
– Generally, it designates the difference between the raw costs of everything needed to produce the goods or service and the price.
– In the analysis, economic rent is determined for each of the factors of production that are used to produce the good or service.
– Usually economic rent is due to some exclusivity
• Von Thünen developed the basics of the theory of marginal productivity in a mathematically rigorous way, summarizing it in the formula in which
R = Y (p – c) – Y Fm
Where,
R=land rent;
Y=yield per unit of land;
c=production expenses per unit of commodity;
p=market price per unit of commodity;
F=freight rate;
m=distance to market.
2. Alonso Model
• William Alonso (1933-1999), was an Argentineanborn American planner and economist.
• In 1964, he published Location and land use, in which he defined a modelled approach on the formation of land rent in urban environments.
• His model would become one of the pillars of urban economics as from the seventies.
• His famous land use model is Alonso’s Bid Rent Function.
• Alonso's Bid Rent Function
– A "Bid-Price Curve” is a set of combinations of land prices and distances among which the individual is indifferent.
– Principle : The household could pay at each distance in order to achieve a predetermined utility level (thus there is a bid price curve for every utility level).
– Assumptions : As the individual considers residential locations at different locations in the city, i.e. at increasing distances from the city center, what price of land would allow her to buy sufficient amount of land and other goods to enjoy as much satisfaction as a given starting price and amount of land at the city center.
– The residential bid price curve is "the set of prices for land the individual could pay at various distances while deriving a constant level of satisfaction.“
– Alonso stresses three points in his characterization of the bid price curve:
• every individual or household has her own bid price curve. Others have other curves
• every bid price curve represents a given utility level. There is family of bid price curves representing different utility levels, analogous to the well-known indifference curves
• prices represented by the bid price curve have no necessary relations to actual prices:
"A bid price is hypothetical, merely saying that, if the price of land were such, the individual would be satisfied to a given degree."
– The bid price function for the urban firm would be defined as follows:
It describes the prices which the firm is willing to pay at different locations (distances from the city center) in order to achieve a certain level of profits.
3. Weber Theory
• Alfred Weber (1868 – 1958) was a German economist, geographer, sociologist and theoretician of culture whose work was influential in the development of modern economic geography.
• In 1929, he introduced a model of industrial location which assumes that industrialists choose a least cost location for the development of new industry.
• Least-Cost Location means a site chosen for industrial development where total costs are theoretically at their lowest, as opposed to location at the point of maximum revenue.
• The theory is based on a number of assumptions, among them that markets are fixed at certain specific points, that transport costs are proportional to the weight of the goods and the distance covered by a raw material or a finished product, that perfect competition exists, and that decisions are made by economic man.
• Economic Man means a theoretical being who has perfect knowledge of an economy and has the ability to act in his or her own interests to maximize profits.
• The idea of economic man has proved a useful tool in neoclassical economics but other writers suggest that the concept of the satisfier is more realistic.
• Alfred Weber formulated a theory of industrial location in which an industry is located where the transportation costs of raw materials and final product is a minimum.
• Also known as the Location Triangle sought the optimum location for the production of a good based on the fixed locations of the market and two raw material sources, which geographically form a triangle.
• He sought to determine the least-cost production location within the triangle by figuring the total costs of transporting raw material from both sites to the production site and product from the production site to the market.
• The weight of the raw materials and the final commodity are important determinants of the transport costs and the location of production.
• Commodities that lose mass during production can be transported less expensively from the production site to the market than from the raw material site to the production site.
• The production site, therefore, will be located near the raw material sources.
• Where there is no great loss of mass during production, total transportation costs will be lower when located near the market.
• Principles of the Model
– He singled out two special cases. In one the weight of the final product is less than the weight of the raw material going into making the product.
– This is the weight losing case. In the other the final product is heavier than the raw materials that require transport.
– Usually this is a case of some ubiquitous (available everywhere) raw material such as water being incorporated into the product.
– This is called the weight-gaining case.
Analytical Tools
– Material Index
• The ratio of the weight of localized materials used in the manufacture of a product to the weight of the finished product.
• A material index of much greater than 1 indicates that there is a considerable loss of weight during the manufacturing process (as in ‘instant’ mashed potato) so the factory should have a material orientation, while a material index of less than 1 (where weight is gained during manufacturing) would suggest a market orientation.
• An index of less than 1 could be achieved by an industry using largely ubiquitous materials, like water, as in the brewing industry.
– Isodapane is a line joining up places of equal total transport costs for industrial production and delivery between the points where the raw materials are located and the markets.
– Isotims are lines representing points of equal transport costs from one source of a raw material or to one market.
– The Critical isodapane
• is that isodapane (out of the family of isodapanes which signifies the outer limit for alternative locations (alternative to the location with minimum aggregate transport costs) in a Weberian locational triangle or other polygon.
• Its specification is dependent on the savings (labor cost, scale- or agglomeration economies) associated with such an alternative; beyond the critical isodapane, savings are not sufficient to compensate for the additional transport costs.
Industrial Location
4. Moses Location
- Production Model
• Leon Nathan Moses (1924-) is an American who introduced the Location-Production Model in 1958.
• This model originally adopted the principle in Weber Model and still maintain the assumption “a linear production function”.
• The aim of this model is to place the theory of location within the main body of economic theory.
• More specifically, he wish to make the theory of location an integral part of the theory of production and to investigate the implications of factor substitution for the locational equilibrium of the firm.
• Moses argued that the model should be modified to make it consistent with the theory of the firm, in that the chosen combination of inputs depends on their relative prices.
• Moses’ innovation was to argue that these prices would vary from location to location due to transport costs.
• Objectives :
– optimal combination of input
– Optimal level of production at optimal location
– Substitutability of any one level of production
• Assumptions :
– Inputs are sold Freight On Board (f.o.b.)
– The delivered prices are equal to price at the source plus full freight.
– If inputs are sold according to some other geographical pricing technique, delivered prices may be greater or less than f.o.b. prices, but this will not invalidate the analysis.
• Conclusion :
– profit maximization requires a proper adjustment of output, input combination, location and price.
– The optimizing values of these three variables can be determined with analytical tools derived directly from traditional economic theory.
– There is no need for much of the esoteric paraphernalia sometimes employed by location specialists.
Where,
P1, the price of the first input at its source
P2, the price of the second input at its source
r1, the transport rate on the first input
r2, the transport rate on the second input
s1, the distance from M1 to the locus of production of the final product.
s2, the distance from M2 to the locus of production of the final product.
P’1, the price of the first input delivered to the locus of production of the final product
P’2, the price of the second input delivered to the locus of production of the final product
• The figure shows the locational problem.
• M1 and M2 are the sites of the two materials and C is the market point.
• The distances M1, M2, M1C are known.
• The latter two distances will be referred to respectively as “a” and “b”.
• The values of the included angles are also known, though will be concerned only with the angle ( ).
Central Places
5. Christaller Model - Market Areas -
• Walter Christaller (1893 – 1969), was a German geographer whose principal contribution to the discipline is Central Place Theory, first published in 1933.
• This groundbreaking theory was the foundation of the study of cities as systems of cities, rather than simple hierarchies or single entities.
• The primary purpose of a settlement or market town, according to centralplace theory, is the provision of goods and services for the surrounding market area.
• Such towns are centrally located and may be called central places.
• Settlements that provide more goods and services than do other places are called higher-order central places.
• Lower-order central places have small market areas and provide goods and services that are purchased more frequently than higher-order goods and services.
• Higher-order places are more widely distributed and fewer in number than lower-order places.
• Objectives
– concerning the size and distribution of central places (settlements) within a system.
– Central-place theory attempts to illustrate how settlements locate in relation to one another, the amount of market area a central place can control, and why some central places function as hamlets, villages, towns, or cities.
• Assumptions :
– an unbounded isotropic (all flat), homogeneous, limitless surface (abstract space) an evenly distributed population all settlements are equidistant and exist in a triangular lattice pattern
– evenly distributed resources
– distance decay mechanism
– perfect competition and all sellers are economic people maximizing their profits
– consumers are of the same income level and same shopping behaviour
– all consumer have a similar purchasing power and demand for goods and services
– Consumers visit the nearest central places that provide the function which they demand. They minimize the distance to be travelled
– no provider of goods or services is able to earn excess profit(each supplier has a monopoly over a hinterland)
• Principles : the trade areas of these central places who provide a particular good or service must all be of equal size
– there is only one type of transport and this would be equally easy in all directions
– transport cost is proportional to distance traveled in example, the longer the distance traveled, the higher the transport cost
• Concept :
– Threshold is the minimum market (population or income) needed to bring about the selling of a particular good or service.
– Range is the maximum distance consumers are prepared to travel to acquire goods
- at some point the cost or inconvenience will outweigh the need for the good.
• The marketing principle (K=3 system)
– First order service center providing first order services
– Second order service center providing second order services.
– Third order service center providing third order services
• The transportation principle (K=4 system)
– The traffic principles states that the distribution of central places is most favourable when as many important places as possible lie on one traffic route between two important towns, the route being established as straightly and as cheap as possible.
– The more unimportant places may be left aside.
– According to the transport principle, the central places would thus be lined up on straight traffic routes which fan out from the central point.
– When Central places are arranged according to the traffic principle, the lower order centers are located at the midpoint of each side of the hexagon rather than at the corner.
– Thus the transport principle produces a hierarchy organized in a k=4 arrangement in which central places are nested according to the rule of four.
• The administrative principle (K=7 system)
– Christaller’s other suggested organizing principle was based upon the realization that from a political or administrative viewpoint centers it was unrealistic for centers to be ‘shared’.
– Any pattern of control which cuts through functional units is potentially problematical.
– Christaller suggested that an arrangement whereby lower order centers were entirely with the hexagon of the higher order center would obviate such problems.
– Such a pattern is shown in the following diagram. – All the six lower order centers are fully subordinate to the higher order center which, therefore, dominates the equivalent of seven market areas at the next lowest level.
• The result of these consumer preferences is that a system of centers of various sizes will emerge.
• Each center will supply particular types of goods forming levels of hierarchy.
• In the functional hierarchies, generalizations can be made regarding the spacing, size and function of settlements.
– The larger the settlements are in size, the fewer in number they will be, i.e. there are many small villages, but few large cities.
– The larger the settlements grow in size, the greater the distance between them, i.e. villages are usually found close together, while cities are spaced much further apart.
– As a settlement increases in size, the range and number of its functions will increase .
– As a settlement increases in size, the number of higher-order services will also increase, i.e. a greater degree of specialization occurs in the services.
• The higher the order of the goods and services (more durable, valuable and variable), the larger the range of the goods and services, the longer the distance people are willing to travel to acquire them.
• At the base of the hierarchy pyramid are shopping centres, newsagents etc which sell low order goods.
• These centres are small.
• At the top of the pyramid are centres selling high order goods.
• These centres are large.
• Examples for low order goods and services are: newspaper stalls, groceries, bakeries and post offices.
• Examples for high order goods and services are: jewellery, large shopping arcades and malls.
• They are supported by a much larger threshold population and demand.
• Conclusion
– The determining factor in the location of any central place is the threshold, which comprises the smallest market area necessary for the goods and services to be economically viable.
– Once a threshold has been established, the central place will seek to expand its market area until the range—i.e., the maximum distance consumers will travel to purchase goods and services—is reached.
– Since the threshold and range define the market area of a central place, market areas for a group of central places offering the same order of goods and services will each extend an equal distance in all directions in circular fashion.
Spatial Competition
- Hotelling Model
• Hotelling's rule defines the net price path as a function of time while maximising economic rent in the time of fully extracting a non-renewable natural resource.
• The maximum rent is also known as Hotelling rent or scarcity rent and is the maximum rent that could be obtained while emptying the stock resource.
• In an efficient exploitation of a non-renewable and nonaugmentable resource, the percentage change in net-price per unit of time should equal the discount rate in order to maximise the present value of the resource capital over the extraction period.
• In other words, this theory proposes that owners of non-renewable resources will only produce a supply of their product if it will yield more than instruments available to them in the markets specifically bonds and other interest-bearing securities. This theory assumes that markets are efficient and that the owners of the nonrenewable resources are motivated by profit. Hotelling's theory is used by economists to attempt to predict the price of oil and other nonrenewable resources, based on prevailing interest rates.
• This concept was the result of analysis of non-renewable resource management by Harold Hotelling, published in the Journal of Political Economy in 1931. Devarajan and Fisher note that a similar result was published by L. C. Gray in 1914, considering the case of a single mine owner.
• The simple rule can be expressed by the equilibrium situation representing the optimal solution.
when P(t) is the unit profit at time t and δ is the discount rate.
• The economic rent obtained is an abnormal rent, often referred to as resource rent, since it generates from a situation where the resource owner has open access to the resource for free.
• In other words, the resource rent is the resource royalty or resource's net price (price received from selling the resource minus costs. In this case costs are zero).
• The resource rent therefore equals the shadow value of the natural resource or natural capital.
• The concept of resource rent also includes biological and other renewable resources.
