Presentation on theme: "Main Points Wrong in Proposals FOCUS: What you say in your RQ, OBs and TEs must follow from your context. You cannot add stuff in later just because you."— Presentation transcript:
Main Points Wrong in Proposals FOCUS: What you say in your RQ, OBs and TEs must follow from your context. You cannot add stuff in later just because you thought of it. Context sets everything up. It must have: What is the topic you are doing and why. Where? (Region, nation, area). When (time period(s), pre- post a date) and logic? Quantifiable variables to be used (GDP, fertility rates, etc)? And all in half a page tops. SPIRAL, SPIRAL, SPIRAL DOWN: This means that every section must not only follow from your context but must narrow it down further and further until you have testable expectations that explicitly say this variable will do that quantitative thing, here, and when it will do it.
Really, really annoying things... STOP… …using “Hypothesis” unless you are doing real inference. trying to use data that does not exist. …trying to use too short a timeline to see any change. …forgetting about relative growth and decline. …forgetting about constant dollars. …making your assignment about the topic instead of the process. …doing a project that would take an expert their lifetime. …using rhetoric: I will do this and this and this and… START: Reading the handouts! All of them! Every last one. Title, page, font, margins, length, headings, sequence, etc, etc… This was really annoying.
Be Aware of… The “Where”: Is your paper about one region/nation/area? Is it comparing a region/nation/area with another? The “When”: Is it a comparison or description of a variable(s) over a time period? Is it a before and after a date comparison? Is it a compare period #1 with #2? The “What”: Are your variables quantitative? Available for the time and place you want? Comparable over time (e.g. dollars)? The Expectation…Does your RQ say that the variable: Will increase, decrease, stay the same, do all three? Across the period? Before this date ? After that date? All of them?
Central Place Theory Developed by German geographer Walter Christaller in the early 1930s. Asked the question whether there was regularity in the spatial distribution of towns and cities and if so why should such regularity exist? Thus this is an urban settlement system model and not a retail model. He recognised that places have specialised roles – manufacturing, political, resource – but all places served one role: the distribution of goods and services to consumers. The types of goods and services distributed depended on the size of the place doing the distribution.
Christaller’s school atlas with his first polygons around settlements of various sizes in France.
The Central Place Hierarchies Christaller recognised that smaller places distributed fewer, less expensive and more frequently required goods than did larger places. He also recognised that all places served local and trade area populations, and that small places had smaller trade areas than large places. This led to two hierarchies: Places: there would be a few large places, several medium sized places and many smaller places. Goods: there would be also be a hierarchy ranging between low order goods and high order goods.
Low Order and High Order Goods Low Order Goods: Goods that are required more frequently and are less expensive – e.g. food, gasoline. High Order Goods: Goods that are required less frequently and are more expensive – e.g. automobiles, university education. All goods would fit into a hierarchy ranging from low order to high order, with medium order goods in between. The hierarchy of places and the hierarchy of goods combined to give a “central place hierarchy”.
The Central Place Hierarchy The central place hierarchy would be comprised of small places providing only low order goods and services, and large places providing both low order and high order goods and services. Type of place (order, number of) in the Central Place Hierarchy Order of Good or Service University (high) Clothing (medium) Groceries (low) City (high, few)XXX Town (medium, several)XX Village (low, many)X So far so obvious, you might think. But the real question is: why should we get low and high order goods/services and places?
Range and Threshold Christaller postulated that two economic concepts would govern the distribution that he saw in the central place hierarchy – range and threshold. Range is based on distance decay and is defined as the maximum distance someone is willing to travel to a good or service. Threshold is based on margins of profitability and is defined as the number of people (or their income) needed by a merchant to stay in the business of providing a good/service. This leads to the following implications:
Implications of Range and Threshold When range and threshold are combined with the central place hierarchy we get: A small number of establishments with high thresholds and ranges providing high order goods/services in a few places. A large number of establishments with low thresholds and ranges providing low order goods/services in a large number of places. In Summary: Low order goodsHigh order goods Low thresholdsHigh thresholds Low rangesHigh ranges Large number of establishmentsSmall number of establishments Large number of settlementsSmall number of settlements
Putting it all together If we go back to Christaller’s original question from his school atlas experiments: “Is there a regularity in the spatial distribution of places and if so, why?” We get an answer: There is a regular pattern in the spacing of settlements and their trade areas, superimposed on… … a regular pattern in the size of settlements and their trade areas. And the pattern is created by the operation of the economic concepts of range and threshold, which are actually…
Spatial Supply and Spatial Demand Curves Once again we use supply and demand curves but this time (as we shall see) they are based on spatial supply (threshold) and spatial demand (range). Price/revenue of a product per unit Quantity of units SupplyDemand …price thus demand is governed by how much money you have to spend on a particular good. …supply is governed by how much revenue you need to supply a particular good. BASIC ECONOMIC CONCEPTS USED
Spatial Supply and Demand Equilibrium Again, when the two curves get put together we end up with an equilibrium price (quantity q will be supplied and bought at price p) being established by the market: the revenue is high enough to make it worth while for stores to provide the product and consumers have enough money left after travel costs to buy the product. Price of a product per unit Quantity of units Supply Demand p q BASIC ECONOMIC CONCEPTS USED
Assumptions and Principles of Order Christaller built what he called a static model of the central place hierarchy based on a on a set of principles and concepts and a set of assumptions. The assumptions and principles would give rise to a “static” model of the tertiary economy based on a regular and measurable arithmetic and geometry for the size and spacing of settlements. The static model simply means that all things except travel costs are held constant again.
CPT Principles of Order As you will see shortly, we have used some of these before in bid rent theory and economic base theory. Centralisation. Centres and their trade areas. Centrality, nodality, local consumption. Central, auxiliary, deficit places. Range and threshold. Hierarchies. Along with the assumptions they make the static model.
CPT Assumptions Again, you should remember these as basic to all models: An isotropic plain. Equal distribution of income. Same tastes in goods/services. Equal distribution of population. There can be no unserved areas. No excess profits can be made by a merchant. Consumers and merchants are rational in their choices. Consumers go to the closest centre for the good/service. In the same way as Von Thunen, Christaller fixed all variable attributes of the landscape in order to see what the effect of distance – or at least the cost of overcoming it – had on the spatial distribution of places.
Ode to Assumptions In the land of Ceteris Paribus. On the isotropic plain. Lived people with the same income, same sex, same tastes, same name.
Centralisation and Trade Areas This is the same idea that Alonso used with urban rent theory: that on an isotropic plain the centre is the closest point to all other points on average. This means that: Merchants will try and centralise themselves in their potential market areas on the plain, and… Customers will patronise the closet supply point which, because of the merchant’s choice, will be the centre of the customers’ density distribution on the plain. This leads to a starting distribution of merchants and customers as follows:
Centralisation and Trade Areas Customers ● Supply point (merchant) Trade Area ●●
Nodality, Centrality, Local Consumption These three terms are used to account for the activity within a central place system in a similar way as in economic base theory. The total activity in a CP system is given by: N = C + L Where: N = nodality or total sales in a place. C = centrality or the place’s trade area proportion of sales. L = local consumption or the place’s own proportion of sales. It should be clear that centrality and local consumption are equivalent to the basic and non basic components in EBT. Therefore a place’s importance is directly related to the size of its trade area.
Central, Auxiliary, Deficit Places Not all places are central places; a place is a central place only when its centrality is positive – i.e. it trades. Places that serve only their own place population are called auxiliary places, and places that cannot even do that but must rely on other centres for goods/services are called deficit places. NLCType of place Place A$10m$5m$5Central Place B$10m $0Auxiliary Place C$10m$15m-$5Deficit IMPORTANT Any spatial arithmetic or geometry of places will be based on the central places and their trade areas only and not on auxiliary or deficit places.
The Range of a Good – Outer Range Range and threshold are the fundamental economic operators underlying CPT and both are actually manifestations of the range of a good. The outer range is the furthest distance people are willing to travel for a good or service, and is based on the economics of distance decay. Money available distance Maximum Distance customer will travel Store RANGE Maximum distance customer will travel
The Economics of the Outer Range The economics of the outer range arises out of the price and cost considerations in obtaining a good. The real price of a product is a function of the market price plus the travel costs to get it: Cost of product distance Store Market Price (shelf price) Travel Costs Since the real price increases with distance travelled, then there will be an outer limit to the amount of money someone is willing to pay for the product. This is found at the outer range (blue dotted line). This transportation cost is a fundamental attribute of spatial models – we all pay it and we all pay attention to it. Price limit consumer is willing to pay Real price = shelf price + travel costs Maximum Distance customer will travel
The inner range or threshold is the minimum number of customers (or revenue actually) required by a merchant to stay in business. It is based on the market model: Threshold = population * income * propensity to spend Given the CPT assumption of equal population density a minimum area is required to encompass the minimum population needed to sustain the good. People required Distance Store RANGE Minimum number of customers required Population density The Range of a Good – Inner Range
The Economics of the Inner Range On the CPT isotropic plain population density is equally distributed (green line). The larger the area, the higher the cumulative population becomes as indicated by the solid brown line, which increases away from the store. At point Rm the necessary minimum number of customers (or revenue available) is reached to achieve the inner range. This distance is the trade area minimum for the store to achieve its threshold. Revenue available distance Store Rm Population density Minimum # of customers (or revenue) required or threshold. Cumulative Population Store RANGE Minimum number of customers required
The Economics of Range and Threshold Together If the inner range and outer range coincide, then the trade area boundary is established. In economic terms, at point Pc the aggregate ‘price’ customers are willing to pay is the same as the aggregate ‘revenue’ at point Rm a merchant must get. This point is the price equilibrium point of the spatial supply/demand schedule. Q required distance Store Pc Rm This distance is the trade area minimum for the store to achieve its threshold AND the maximum distance people will travel from for the good.
Baskets of Goods and Services So far then, we know that ceteris paribus inner and outer ranges will coincide due to their underlying economics. These economics are different for every different good/service, but to simplify things we classify goods/services into orders – low, medium, high. These are called baskets of goods/services and each will have its coincident range and threshold. It follows from this that low order baskets will be found in low order places that will have the appropriate low order trade area. Each next higher order basket will be found at the next higher order place along with all the lower order baskets below that level.
Number of threshold units (people) needed for each good/service. Number of threshold units (people) available in place Hamlet 1 Village 2 Town 3 City 4 Groceries= 1XXXXXXXXXX Bank = 2XXXX Optician = 3XX Dept. store = 4X Hierarchies of Central Places This leads us back to the concept of a hierarchy of places each supplying increasingly higher order goods/services and increasing multiples of the lower order goods/services. Thus there are many lower order goods at many low order places and an increasingly fewer higher order goods at increasingly fewer larger places. 0 0 0 0 0 0 Marginal good
The Static Model Christaller called his theoretical model the static model because it was made static by his assumptions. In other words, like all models it was not dynamic insofar as it included real world attributes. Christaller developed three ‘K’ systems (where ‘K’ stood for the German word Konstante or constant). The ‘K’ systems referred to the ‘constant’ or the number that underlay the arithmetic of each, and they were: K=3 or marketing principle K=4 or transportation principle K=7 or administrative principle And these were based on his assumptions so to review his assumptions…
Assumptions An isotropic plain. Equal distribution of income. Same tastes in goods/services. Equal distribution of population. There can be no unserved areas. No excess profits can be made by a merchant. Consumers and merchants are rational in their choices. Consumers go to the closest centre for the good/service. As with Von Thunen these can all be relaxed to provide a more realistic landscape – which we will do later. For now the K systems.
The K=3 Static Model Christaller built his static model by starting with the geometry of its trade areas – in this case the K=3 model. Circular trade areas violate assumptions: no un-served areas allowed. Hexagonal trade areas ‘pack’ a landscape most efficiently. Overlapping trade areas violate assumptions: customers go to the nearest place. ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●
The K=3 Static Model – Level 1 Low Order Trade Areas The K=3 Static Model – Level 2 Middle Order Trade Areas
The K=3 Static Model – Level 1 Low Order Trade Areas The K=3 Static Model – Level 2 Middle Order Trade Areas Arithmetic of K=3 System The next level will have 1 full trade lower trade area plus 6 * ⅓ of the surrounding trade areas 1 + 6 * ⅓ = 3 K = 3
The K=3 Static Model Geometry Levels 1&2 Nested Hierarchy of Trade Areas v c v v v v v v v
The K=3 Static Model – Level 3 High Order Trade Areas v v v v v v
v v v v v v Arithmetic of K=3 System The next level will have 1 full trade lower trade area plus 6 * ⅓ of the surrounding trade areas 1 + 6* ⅓ = 3 K = 3
c v v v v v v v The K=3 Static Model – Level 3 High Order Trade Areas
c v v v v v v v The K=3 Static Model – Number of Central Places ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ●●●● ● ●●● ●
The Arithmetic of Central Place Theory Christaller recognised that there would be a regularity to the geometry of trade areas, and also to the arithmetic of the central places. For the K=3 system, it would follow what he called the the rule of ‘3s’. For the K=4 and K=7 systems, it would follow the rules of 4 and 7. But no central place landscape is comprised of just one of these ‘K’ systems. Even on the theoretical and assumption bound isotropic plain the landscape had to ‘mix’ these K systems. But first the K=3 arithmetic…
The Arithmetic of K=3 Trade Area NestingEach trade area would encompass 3 trade areas from the next lower level Therefore the arithmetic progression would be 1,3,9, … or 3 1, 3 2, 3 3, etc Area of Trade AreasThe area of a trade area is three times that of a trade area of the next lower level. Frequency of Occurrence of Central Places The frequency of occurrence of different orders of central places follows the arithmetic progression 1,2,6,18,64… Distance Between Places
The Arithmetic of K=3 Trade Area NestingEach trade area would encompass 3 trade areas from the next lower level. Therefore the arithmetic progression would be 1,3,9,27… or 3 1, 3 2, 3 3, etc Area of Trade AreasThe area of a trade area is three times that of a trade area of the next lower level. Frequency of Occurrence of Central Places The frequency of occurrence of different orders of central places follows the arithmetic progression 1,2,6,18,64… Distance Between Places
The Arithmetic of K = 3 And the numbers for the K=3 system would be (where n is a value pertaining to the level in the hierarchy)… Hierarchical Level Number of Central Places (3*n) Number of Trade Areas (3 n ) 0. Capital11091 1. Large City2633 2. Medium City6369 3. Small City182127 4. Large Town541281 5. Small Town162 (3*54=162) 243 (3 5 =243) 6. Village4864729
The K = 4 and K = 7 Systems In order to accommodate more realistic landscapes Christaller also developed two other K systems and a mixed hierarchical system. The K=4 system incorporated transportation networks, ensuring that higher order centres were linked more directly than lower order centres. This system would follow the ‘rule of 4s’ The K=7 system ensured that each trade area must include all of the next lower level’s trade areas – no partial trade areas were allowed. This was to ensure administrative efficiency. This system would follow the ‘rule of 7s’
The K = 4 System With Three Levels 1 ½ ½ ½ ½ ½ ½ 1+½+½+½+½+½+½= K = 4
The K = 7 System With Three Levels 1+1+1+1+1+1+1= K = 7
The Mixed Hierarchy Model Further work looked at the arithmetic of mixed hierarchies and their matches to reality. Number of Trade Areas Hierarchical Level K = 3K = 4MixedFinlandAustria 111111 2343.4834 391610.33912 4276437.23639 581256147.2151141
Varying the density of population gives a pattern of increasingly larger trade areas away from the central places. Varying Population Density
Research from the Niagara Peninsula shows a distinct pattern of numbers of functions by hierarchical order of the place. Functions and Rank Order of Places Number of Functions Rank order of Centre Rank order high - city Rank order low - villages
Research from the Niagara Peninsula shows a distinct pattern of numbers of functions by hierarchical order of the place. Functions and Rank Order of Places Number of Functions Population Large places Small places
For Eastern Ontario, the desire line maps show limited travel patterns for grocery purchases. Spatial Pattern of Food Purchases Ottawa Cornwall
For Eastern Ontario, the desire line maps show much wider travel patterns for optical purchases. Spatial Pattern of Optical Purchases Ottawa Cornwall
For Devon in the U.K., the desire line maps show extended travel patterns for clothing purchases. Spatial Pattern of Clothing Purchases Plymouth
Spatial Pattern of Grocery Purchases For Devon in the U.K., the desire line maps show limited travel patterns for clothing purchases. Plymouth
Clothing Purchases for Old Order Mennonites, Waterloo County, Ontario Cultural Differences and Clothing Purchases Clothing Purchases for Non-Mennonites, Waterloo County, Ontario Waterloo Old Order Mennonites make their own clothing from yard goods that have little variety, that they can buy locally.
Banking for Old Order Mennonites, Waterloo County, Ontario Cultural Differences and Banking Banking for Non- Mennonites, Waterloo County, Ontario Waterloo Banking is banking, even for Old Order Mennonites.
Edmonton Area Low Order Trade Areas - 44 Groceries, hardware, school and church attendance. Edmonton
Edmonton Area Middle Order Trade Areas - 25 Place of work, haircuts, curling, banking Edmonton
Edmonton Area High Order Trade Areas - 12 Health care, newspaper distribution, car/truck purchases Edmonton
Zurich Area Travel for Various Goods/Services Neighborhood Business District Regional Business Centre Central Business Centre Others Increasing order of good Increasing order of centre
Conclusions Central Place Theory is best suited for the historical economic landscapes of 50 years ago than it is for modern metropolitan areas. But hierarchies of goods and services still exist, as do hierarchies of places. The theory was never designed to work with anything but complete urban systems, so the dynamics of large metropolitan areas such as Toronto are beyond its scope. The advent of big box retailing has created pseudo “towns” providing all levels of goods and some services. But few would drive to Wal-Mart just to buy groceries.