Urban Economics PSet 1 – Von-Thünen Model I

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Urban Economics PSet 1 – Von-Thünen Model I

Urban EconomicsProblem Set #1Due, Fri, Sep 30, 10pm , ONLY ONLINE!You can only upload one single file. No multiple file submissions.Upload a Word file, avoid scans/photographs of handwritten setsNo late problem sets.(1) Von-Thünen Model IBarely can only be sold at a central market place M. All producers that do notproduce it at M need to haul it there in order to sell it and will incurtransportation cost. People are willing to pay $201.50 per ton of barely; itsmarginal production cost equals $20 per ton. Freight cost per ton and mile isgiven by T=1.5×2, where x denotes the distance from M in miles.(a) Calculate the maximum distance to the east of M at which the good will beproduced.(b) Do the transportation cost exhibit increasing, decreasing or constanteconomies to distance?(2) Von-Thünen Model IISuppose a certain good (e.g., wheat) can only be sold at a central market place M.All producers that do not produce it at M need to haul it there in order to sell itand will incur transportation cost. Consider onlyPeople are willing to pay $20 for the product; freight cost is $3.50 per piece andmile. The total production cost is given by the function C=10+0.1q(a) Calculate the maximum production distance from M(b) Referring to the one-directional (just to the east) Von-Thünen Model,calculate the overall production cost, the overall transportation cost and theoverall land rent paid.(3) Locations of Transfer-Oriented FirmsAssume the distance between the resource (R ) and the market (M) is 10 miles. Afirm’s procurement cost is given by PC=4x, where x is the distance from theresource measured in miles. The firm’s distribution cost is given by DC=2(10-x)2.Again, x is the distance from the resource.(a) What is the Total Freight Cost at x=10, x=5, x=0. Where should the firmlocate?(b) How does your answer to all parts under (a) change if the marginalprocurement cost decrease from 4 to 1?(4) Suppose customers are distributed on a one-directional path (e.g., to the east) asfollows.LocationDistance from ANumber of customersA03B12C81D22E61F182A company has to deliver a unit of its good to each customer and incurs a cost of$1 per unit and mile. Each unit needs to delivered separately.(a) Where is the median customer located?(b) Where is the delivery cost minimizing location and what is its delivery cost?(5) Suppose a transport cost oriented firm consumes two inputs (one fromsource A, the other from source B) in order to produce one output, which isconsumed at the output market.a) Based on the numbers provided in the graph below, where will thecompany locate?b) Now assume the monetary weight of input source B increases to $44 (allelse stays the same), where will the company locate now?c) If the all monetary weights (output as well as inputs) were equal to $10,where will the firm locate? Explain.d) Is it possible that the firm’s transfer-cost-minimizing location can beanywhere? If yes, under what circumstances? If no, why not?