Home » 1 Water Supply on Heterogeneous Land Suppose there are two farmers: Farmer 1 and Farmer 2. Both farmers possess a piece of land on which they can…

# 1 Water Supply on Heterogeneous Land Suppose there are two farmers: Farmer 1 and Farmer 2. Both farmers possess a piece of land on which they can…

can you help me with this problem?

Suppose there are two farmers: Farmer 1 and Farmer 2. Both farmers possess a piece of land on

which they can produce soybeans that are sold at a per unit price of Ps = 1. Further suppose that

Farmer 1’s land is more fertile than Farmer 2’s. Soybeans require water to grow, but watering

them too much will drown the crop. Hence, the production of soybeans on Farmer 1 and Farmer

2’s land are respectively given by,

Q1(w1) = 500w1

1 Water Supply on Heterogeneous Land Suppose there are two farmers: Farmer 1 and Farmer 2. Both farmers possess a piece of land onwhich they can produce soybeans that are sold at a per unit price of P3 = 1. Further suppose thatFarmer 1’s land is more fertile than Farmer 2’s. Soybeans require water to grow, but wateringthem too much will drown the crop. Hence, the production of soybeans on Farmer 1 and Farmer 2’s land are respectively given by, Q1 (W1) : 500101 — W12Q2 (W2) 2 200102 * W22 where ml and 102 are respectively the amount of water Farmer 1 and Farmer 2 apply on their land.Finally, assume that if a farmer’s rents are exactly zero, he will still decide to produce soybeans. (a) Suppose that the social planner (i.e. the government) controls the water supply to bothfarmers, and that its objective is to maximize social welfare. (i) Suppose that the cost to supply water to farmers is zero. What per unit water pricesPwl’ and PW; should the social planner charge to Farmer 1 and Farmer 2 respectivelyto maximize social welfare? How much water would each farmer utilize in such a case,i.e. what would be an” and 102* if the social planner chose per unit water prices Pm] *and Pt”; that maximize social welfare? What is the amount of soybeans that eachfarmer produce, i.e. what is (21* : Qlfwl”) and (22* = (22(102′)? How much areFarmer 1’s rents and how much are Farmer 2’s rents? Show your work. [0.25 point]

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