Models of City Size and Urban Growth

Why do Cities Grow? - Why do some cities get bigger than others? - Why do cities tend to locate in certain places? - Why do firms locate in certain cities, and not others? - How does firm choice reinforce city growth? - What are the limits to the number of services in a city? The Perspective of the Firm - we assume that the point of a firm is to maximize profit - if they do not make money, there is no point in running a business - the question confronting management is: where do we physically locate our operations, so that we can maximize utility, efficiency, and thus profit? - multi-dimensional tug-of-war - what economic forces pull a firm in different directions? - firms need to take into account such factors as: + transport costs + worker productivity + locations of other firms, which create external economies of production + low energy costs + location of markets + fiscal regulations Transport-Intensive Firms - a firm whose transport costs make up a relatively large fraction of total cost - the firm's objective is to choose a location which minimizes total transport costs - transport costs can be defined as the sum of the input transport cost (for transporting materials from this source to the production site), and the output transport cost (for transporting from the production site to the output market) - there is a classic model of the transport intensive firm - In this scenario, the main question is what is the distance from the source, and what is the distance to the market? + the relative strengths of these costs will determine the minimum cost - hence, a firm which has to get coal from the mountains by railroad, but sells via lorry, will locate closer to the source is the railroad costs are high, but locate close to the markets if the lorry costs are higher - 2 types of transport-intensive firms: 1. Resource-Oriented firms - relatively high cost of transporting its input + e.g., a baseball bat firm, which uses 5 tons of wood to make 1 ton of bats + the input cost of 1 dollar/ton/mile is 5 + the output cost at 2 dollars/ton/mile is 2 + so, 5 tons going into the firm, 1 ton coming out - because the cost of input transport is larger than the cost of output transport, the firm will locate closer to the location of origin of the input (e.g., wood chopping area) + but how close to the location of origin will the firm locate? - answer: you would want to locate at the source 2. Market-Oriented Firms - this is a firm with a relatively high cost of transporting output to the market + e.g., a bottling firm which uses 1 ton of sugar and 4 tons of water to produce 5 tons of bottled beverages (i.e., ubiquitous input) + the firm is involved in weight-gaining activity because its output is heavier than its transportable input (the water is ubiquitous and does not need to be transported, according to the model) + in this case, the firm will locate near its market because the cost of transporting output is higher than the cost of transporting input Median Location - to take account of multiple inputs and/or multiple markets, you have to add together the distances to the various locations to which you travel (and pay for transport) - in general, the principle of Median Location says that, you should locate yourself in a way which minimizes the distance to all locations - this will tend to be the “median location”, which means, the location which has an equal number of both to one side and the other - no matter how far away you are from the customers, if you move outside of the median location, you will be increasing transport costs - in theory, the best location is M - this is the median location as there would be 10 customers on one side and 10 on the other - when calculating monetary weight, the math should show that this is indeed the best location for your money - if you move to C, the monetary weight will be unbalanced - this principle tend towards self-reinforcement - if the large city D becomes larger (because of job availability…), then a step West will increase travel cost to a minority of customers - while it will decrease travel costs to the majority of customers - thus, the total transport cost will be lessened - and the larger city D becomes, the greater will be the pull of that city, as the median number of customers will now outweigh a larger number of smaller cities with fewer customers - as firms move towards D, other firms will do the same, thus self-reinforcing the growth of the large city Median Location and Transhipment Points - a transhipment point is a point where goods are offloaded and onloaded + e.g., from railroads to lorries, from ships to railroad, cars… - the location of industrial firms in port cities means that port cities host both shipping and manufacturing firms - in the next mode, we assume that a furniture factory gets inputs of both cloth and wood which are connected to a port by highways. The factory then ships goods to market M overseas by ship Other Factors - in recent decades, locations matter less to the cost of transport - this is because transportation technology has reduced costs with huge container ships - - - - also the weight of inputs has gone down + e.g., the amount of coal and ore required to produce one ton of steel has gone down steadily labour costs are also about 75% of the total costs, so these tend to matter a lot in general, many firms will follow the labour markets, and locate where people are as wages increase 10%, business activity will tend to decrease about 10% . + there is a -1.0 elasticity (unit elastic) weather has proven to be a draw as well as more people have become mobile, especially in countries with a lot of automobiles, then people tend to move to the places with better weather + thus, firms locate with them also, energy went from being local (coal and watersheds) to being powered by electricity, which means that they are relatively freed from one location due to energy constraints still, some firms locate in areas with cheap electricity and/or natural gas and of course, agglomeration effects have to be mentioned for completeness Case Study: the US manufacturing Belt - Why did manufacturing happen where it did in the US? - innovations in production allowed firms to exploit scale economies - manufacturing belt had access to coal, iron ore, and oil - it also was located on water, which was much cheaper for transport - and the location of other firms meant that both agglomeration effects accumulated - and markets were nearby (near population) - Why did the belt decline into the Rust Belt? - many were relocated overseas - technology/robots replaced many jobs - other factories located in the South, following cheap labour - others were freed from cold constraints on inputs/markets - cities with low human capital (e.g., low education such as college) tended to shrink, while those with higher human capital did well in the new service economy, and have grown. Some have experienced renaissance Firms in Competition for Consumer - firms in competition for individual consumers ar the neighbourhood level - we are looking at firms whose main consideration is to locate near the most individual consumers - monopolistic competition in location → saturation point for services + how many of x can you have in an area Locating Near the Consumer - we can discuss the limits of how many choices will be available to consumers in a city or area - What is monopolistic competition (by location)? + perfect competition says that firms are differentiated in no way at all + monopolistic competition means that while firms compete, they still differentiate their products somehow - in our scenario, the main way that firms differentiate is by location (Locational model of monopolistic competition) - monopolistic competition is thus monopolistic in the sense that a firm has monopoly based on location + so their pizza may be the same, but it matters that they are located in a convenient place Equations - Total Cost C(q) = k +cq - meaning that C (total cost) for producing q quantity equals the setup cost (k), plus the marginal cost of production (c) times the quantity produced this is the Total Cost function (where C is a function of the total quantity produced) - Average Cost (per unit) Ac(q) = k/q +c - meaning the Average Cost of producing q units is equal to the total startup cost (k), divided by q units, plus the marginal cost we are only really looking at average cost curves, and the general rule is that the more units you make, the less the average cost becomes, because the startup cost gets divided by more units Monopoly outcome - this graph shows the demand curve, average cost, marginal cost and marginal revenue for a pizza shop which holds a monopoly for an area here, marginal cost is expressed as 2 dollars/pizza - but MC does not represent all the cost, because the pizza shop had startup costs, whose average comes down as you produce more units (i.e., AC) you have to subtract average cost from price, to get economic profit so, if you produce to where MC = MR, then you add the average cost, then the space between the average cost point c, then the price determined by the demand curve at that quantity b, will give you the economic profit rectangle, which is simply average profit per unit + multiply by the number of units and you get total profit When will more firms enter? - i.e., how many pizza restaurants is an area going to get + answer: firms will keep entering as lng as a good profit is being made - this means, uf the profit rectangle is large, then other firms will enter - and in theory, they will continue to enter as long as there is any economic profit at all (the profit rectangle) - they will enter until the economic profit = 0 - meaning they will keep entering, as long as the demand curve is above AC - this means in theory that firms will just make enough to stay in business, but they will not be enough to trigger new entry - Nash Equilibrium - when a new firm enters, they will only get a fraction of the demand - residual demand + split customer base What happens in a Duopoly - a second firm tries to enter the market - this is defined by a 2nd firm which is in the same geographical location - customers will not distinguish between these 2, except that they are both in the same neighbourhood - so now, each firm is left with a residual demand curve + demand left over after the other firm produces - if the total market demand is 400, and each firm produces 200, then residual demand will equal 0 - if one firm supplies 100, then the other firm will be left with a residual demand curve beginning at 300 - when the number of firms increases to 4, the residual demand meets the average cost, meaning that each firm produces enough to stay alive - if a new firm was to enter, they would produce at a loss Firm Entry - as more firms enter the market, the demand curve keeps shifting to the left + it does so until the residual demand for each firm just grazes the average cost curve + in this model, this point is reached at the quadopoly - firms will continue to enter until the residual demand equals average cost at the MR/MC intersection + because this is the point when the economic profit reaches 0 - after this, you will have no more firms entering, because they would make a loss + in this model the neighbourhood can support 4 italian restaurants - this now becomes the long-run or Nash equilibrium Minimum Market Size - What is the startup cost? (relative to demand= - general rule: a city can support a type of firm, if the demand is high relative to the economies of scale created by startup - if there are large economies of scale and high setup cost, then there must be a very high demand + e.g., an Opera house - if there are smaller economies of scale, and relatively low startup cost (e.g., for a bagel shop), then a smaller town with relatively low demand can justify the startup cost required to enter - in brief, a market will support at least one firm if market demand is large relative to the economies of scale in production City Size and Product Variety - another point to consider is the per capita demand of a product - it makes sense that a product with relatively high capita demand will create a large market in even small town - but a product with a low per capita demand will only be found in large cities + e.g., we can assume that there is a high per capita demand for Chinese restaurants, then you expect to find a Chinese restaurant in almost every small town, and many of them in a large town + but if we assume that there is a low per capita demand for a Polish restaurant, then we will expect to find almost no Polish restaurants in small towns, but might expect to find one or two in every large town - you expect to find hairdressers in every town, because the average person needs a haircut every 2 months - but, specialized hospitals are rare, because they offer services that only a few people ever need, and so they are only located in large cities Central Place Theory based on concept of median location + locational monopolistic competition + also the idea of per capita demand varying by business type - in our mode, we have a full spectrum of 3 services + one with low per capita demand will locate in the centre of a city (e.g., clothing) + four with medium per capita demand will locate in the middle and at the 25 and 75 percentiles (groceries) + sixteen with high per capita demand will locate 4 in the centre, 2 in each of the satellite cities, and 8 in the intermediate cities Census Tracts - using the population/firm densities of an area, we can calculate the hierarchy of cities, and the reasons why one city tends to self-reinforce - this is additionally shown by the fact that many services are complementary goods + e.g., shoe stores will locate near clothing stores - and this will reinforce shopping paths, which cause consumers to go to the big city or to locate there despite extra cost