Economies of Scale Average cost falls with increasing quantity High fixed cost Lecture 2 9 5 Saturday September 7 2013 6 54 AM 1 How do people cluster in a space a 3 reasons Why no Clusters 2 a No specialization in productions No bakers weavers Don t depend on others Produce for own consumption No trade i ii iii iv b No economies of scale in transportation No bulk freight or transportation hubs c No economies of scale No factories or mass production i i 3 Why Specialize a Comparative advantage i ii iii iv Find the resources or time needed to make a product In terms of another product find the price Compare one product s price between countries Whoever has lower price has comparative advantage b With trade and specialization i With Specialization 4 Overall increase in production a b But no transportation or scale No clustering i ii No need to since being close to people makes no difference No big factories 5 With Specialization and econ of scale in Transportation Clusters around transportation hubs Trading clusters a b All three a 6 Factory Clusters b c d e c marginal cost of one unit Travel cost time x distance tx X sub 1 1 marginal consumers w cs 0 Urban Econ lecture notes Page 1 e f g X sub 1 1 marginal consumers w cs 0 As long as cs 0 consumers will go to the factory town For x sub 1 i ii WTP p tx distance of x X WTP p t 7 Changes in determinants of Factory Clusters Towns a Change in WTP i The marginal consumer distance will change 1 Find using a X WTP p t Change in transport cost t ii 2 The arms swivel iii Change in price 1 1 2 Keep slope same b These changes can lead to competition between cluster cities 8 Input Orientated Curve a For the firm where to get input for the cheapest b i ii The plant buys beats from the field and is responsible for the freight Has train tracks leading out c Put into graphical form Urban Econ lecture notes Page 2 1 2 3 WTP is of the Firm Variable is how far away the Farmer will locate Transport cost is now basically upside down 9 Multiple firms and their resources i a 10 Profit a Farmer s Profit i ii Will be the surplus between marginal cost for a beat and the price paid Closer to the plant more profit 1 2 But rent will be higher Therefore 0 profit for the farmer iii Is actually landowner s profit b Landowner profit i If land is owned by the farmer 1 2 Profit still canceled out because he is forgoing rent opportunity cost No actual profit Urban Econ lecture notes Page 3 c iii i Put into the Fontaine model 11 Location decision of transfer dependent firms a Where Firms will locate Close to market Close to resources i ii b Assumptions i ii iii 1 single output 1 single output Fixed factor proportions iv Fixed price Resource oriented firm c 1 Certain tonnage of input always certain tonnage of output Input Output Grapes Wine i Physical weight in tons w Transport cost per ton mile t 2 Monetary weight WxT 2 4 1 1 1 ii Find the monetary weight then construct graph d i Construction Sides 1 2 3 Resource Market Define distance between ii Procurement Cost iii Distribution cost 1 Use monetary weight of input from resource 1 Use monetary weight of output from market iv Total Cost 1 Rule to remember PC DC e i ii If add up 2 straight lines you get straight line If 2 straight lines the total cost optimal point will be either at Urban Econ lecture notes Page 4 ii If 2 straight lines the total cost optimal point will be either at resource or the market Urban Econ lecture notes Page 5 Lecture 4 9 12 Thursday September 12 2013 5 56 PM 1 Review Monetary Weight a Physical weight w x Transportation cost t 2 Graphically represent a firms decision for resource or market From resource per mile monetary cost of resource From market monetary cost of the output a b 3 Optimization lowest cost a b c If straight lines the lowest total cost will either be at the resource or the market Economies of scale to distance transportation cost i ii Case 1 1 Case 2 1 Transport cost is constant Concave transport costs Economies of scale Optimal location is either R or M never between a b c iii Case 3 1 Convex transport costs Urban Econ lecture notes Page 6 1 Convex transport costs a b Diseconomies of scale Optimal location will be between R and M never at R or M c 4 Optimal location w more than one input a Nash Equilibrium Stable point Moving away from this point result in a loss for at least one party i ii b Beachfront example i ii Same product ice cream 2 possible locations for vendor 1 Both want to maximize quantity of ice cream sold iii iv People go to the closest location To maximize welfare Picture Xmax 1 4 of beach length to walk E x 1 8th of beech length if everyone is dispersed 1 2 3 v Median location outcome 1 Both will move towards center 5 Theory of Median Location Firm wants to deliver a product to each customer Input cost is same Firm is in charge of delivery cost Locations Number of customers Delivery cost at each location from each other location a b Suppose i ii iii Find i ii iii Location From A etc Distance from A Number of customers c Assume delivery cost of 1 per unit and per mile A 0 1 0 B 1 2 2 C 4 1 4 D 6 2 E 20 1 12 20 38 i Eventually find that location C minimizes transportation cost because it is the median location d It is not important how far apart locations are just median location If you move towards one you move away from 4 others i e Median person not median distance Urban Econ lecture notes Page 7 e Median person not median distance 6 If more than one input source a Find monetary weight of each point i Figure out marginal cost and benefit b Optimal point will usually be at a Port P between market and sources Urban Econ lecture notes Page 8 Lecture 5 9 17 13 Wednesday September 18 2013 5 05 PM 1 If weight of the input changes and not t a b Eg less hops needed for brewing beer Decision for firm to locate will change Chapter 3 Why do firms cluster Measurements 2 Gini coefficient Concentration Ratio CR Hirschman Herfindahl Index HHI 3 Gini Coefficient as Measurement of Firm Clustering Originally measures income inequality graphically Model a b c a b i ii iii iv x axis cumulative of population y axis cumulative of income Line of Equal Division If everyone has same income Slope of 1 v …