View Question
Q: Microeconomics - Theory of the Firm - Production Technology ( Answered,   2 Comments )
 Question
 Subject: Microeconomics - Theory of the Firm - Production Technology Category: Business and Money > Economics Asked by: la2005-ga List Price: \$50.00 Posted: 14 Oct 2005 23:17 PDT Expires: 13 Nov 2005 22:17 PST Question ID: 580526
 ```Hi I need a response for the following question: Suppose you own a circular island with radius R which can be used for either growing pineapples or renting to tourism industry. The production technology for pineapples is: Q = min{alpha1 * L, alpha2 * A} with Q being the quantity of pineapples grown, L for labor, A for area of land used for pineapples. The wage for labor is w, while the price for pineapples is p. The rental price P for the land to the tourist industry is a decreasing function of distance of land from edge of island, r: P = P(r), P'(r) <0 for all r. How will you use the land? What will be the shape of the plot of land for pineapple farming and what fraction of the total island will it occupy? What is your supply function for pineapples? Thanks. I need a response as soon as possible. I will TIP an answer that I believe requires more compensation than that already given.```
 ```Dear la2005, Because renting land to the tourist industry involves essentially no labor or capital investment, we will want to exploit coastal areas of the island to this end. But land that is far enough from the coast can be more profitably used to grow pineapples, so we will also want to devote some of the land to pineapple farming. The plot of land used for pineapple farming must be circular, like the island itself, with its center coinciding with that of the island. This is because the nearer a parcel of land is to the center of the island, the less it is worth to the tourist industry. The border between the pineapple-farming circle and the tourist-area perimeter strip demarcates the point where tourism and pineapple cultivation are equally profitable. Pineapples are more profitable on the inland side of this line, while tourism is more profitable on the coastal side. Assuming that the only cost of growing Q pineapples is the labor cost Lw, and given that y is the radius of the pineapple-farming plot, the profit function for pineapple farming alone is profit_0(y) = Qp - Lw = min{alpha1 * L, alpha2 * A}p - Lw = min{alpha1 * L, alpha2 * pi*y^2} - Lw . The width of the perimeter strip rented to the tourist industry is R-y. Thus, we gain a revenue of profit_1(y) = P(R-y) from tourism rentals. The total profit that we earn from both uses of the land can be expressed as profit_T(y) = profit_0(y) + profit_1(y) = Qp - Lw + P(R-ry) = min{alpha1 * L, alpha2 * pi*y^2} * p - Lw + P(R-y) . The radius r' of the pineapple plot, and therefore the fraction of the total island pi*y^2 / A = pi*y^2 / pi*(R-y)^2 devoted to pineapple farming, is determined by the value of y that maximizes the total profit function profit_T(y). Using this value y_max, the supply function for pineapples becomes Q = min{alpha1 * L, alpha2 * pi * y_max * y_max} . Regards, leapinglizard```
 ```Google Answers discourages and may remove questions that are homework or exam assignments```
 `I assure you this is not a homework or exam assignment.`