Von-Thünen Model II Suppose a certain good (e.g., wheat) can only be sold at a c
ID: 1139155 • Letter: V
Question
Von-Thünen Model II Suppose 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 and will incur transportation cost. Consider the one directional von-Thünen model to the right only.
a) People are willing to pay $6 for the product; marginal production cost m equals 2. If the maximum distance at which people grow wheat is x*=16, what is marginal transportation cost t?
b) If wheat production were equally distributed over the entire distance between M and x*, you could calculate the sum of all costs, i.e., production w/o FC, transportation cost and rent as the areas of your chart; see the sketch below. For the data given at (a), calculate the size of these cost components.
Rent Transp Cost Production CostExplanation / Answer
a) Here the price paid by people for the 1 unit of wheat is $6 or p is $6.The marginal production cost is or c is $2 and the maximum distance between the market center and the place of production is x*=16.Let the marginal rent from land be r and marginal transportation cost as t.
To maximize profit the price obtained by the producers or the marginal revenue from wheat sale has to equal the marginal cost of production and the marginal transportation cost paid for transporting each unit of wheat to the market.
Thus,based on the profit maximizing condition in this case,we can state:-
6=2+t
6-2=t
4=t
Thus,the marginal transportation cost or t at the profit maximizing point would be $4 and the total transportation cost would be=(x*t)=(10*4)=$40.Notice in the figure given that the additional rent is 0 or has dissappeared at the profit maximizing level of production as the marginal revenue from production is equal to the sum of marginal cost of production and the marginal transportation cost.
b) Now,let y denotes the y denotes the yield per unit of land and R represents the total rent obtained from the production.
The total cost of the producer=2y and the total transportation cost=ytx*
Based on the Von Thunen model of marginal productivity,we can state:-
R=y(p-c)-ytx*
R=y(6-2)-10ty[Pluging the respective values given in part a)]
R=6y-2y-10ty
R=4y-10ty
R=2y(2-5t)
R/2(2-5t)=y
Thus,total cost of production=(2*R/2(2-5t))=R/(2-5t)
Total transportation cost=(R/2(2-5t)*10t)=5tR/(2-5t)
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.