Question

2 Location and Land Value Suppose now that there are 1,001 villagers that all own a piece of land of an acre each. Villagers grew tired of eating potatoes and are now exporting all potato production through the port at price Pp 60 per ton. Alternatively to potatoes, villagers can let cattle graze on their land and export their milk through the same port at price Pn-110 per thousand gallons. Each of the 1,001 acres of land own by the 1,001 villagers can either produce Qp-100 tons of potatoes, or Qm 50 thousand gallons of milk. The labor costs Cp-20 per ton of potatoes produced while milk costs Cnn = 10 per thousand gallons produced. Each of the acres of land is a certain distance x (in thousands of feet) from the port where potatoes and milk are exported. For simplicity, assume that acre j is j thousand feet away from the port; that is, Acre 0 is zero thousand feet away from the port (i.e. right next to the port), Acre 1 is one thousand feet away from the port, Acre 2 is two thousand feet away from the port, and so on, up to Acre 1,000 which is 1,000,000 feet away from the port. The costs to transport one ton of potatoes to the port are given by, T)1000 while the costs of transporting one thousand gallons of milk to the port are given by, 50 1000 Tm(x) since milk needs refrigeration during transportation (a) Should the villager that owns Acre 250 produce potatoes or milk? What profit would this villager make if she produces potatoes? What profit would this villager make if she produces milk? Show your work. [0.5 point] (b) Should the villager that owns Acre 750 produce potatoes or milk? What profit would this villager make if he produces potatoes? What profit would this villager make if he produces milk? Show your work. [0.5 point] (c) Which Acre j is the villager indifferent between producing potatoes and milk? What profit would this villager make if she produces potatoes? What profit would this villager make if she produces milk? Show your work. [1 point]

Answer 1

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