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Suppose that we have an economy consisting of two farmers, Cornelius and Wheaton, who unsurprisingly farm corn c and wheat w, respectively. Assume that both farmers produce their crop of choice using a single input, land , of which there are a total of =100 acres, with c=20 owned by Cornelius and w=80 by Wheaton. However, neither is required to farm only his own land and each may rent a portion to the other, so that if Cornelius is farming c acres and Wheaton w, the quantities of each crop produced are given by the production functions qc=c,qw=w. Let pc and pw denote the prices of corn and wheat, respectively, and let r denote the rental price of land. (a) (5) Set up each farmer's profit maximization problem, and find the first order conditions. (b) (5) Find the land demand functions for Cornelius cd(r,pc) and Wheaton wd(r,pw). (c) (5) Knowing that the supply of land is fixed, find the equilibrium rental price of land in terms of the crop prices to grow r(pc,pw). (d) (5) Find the supply of corn qcs(pc,pw) and wheat qws(pc,pw). (e) (5) Find the profits earned by Cornelius c(pc,pw) and Wheaton w(pc,pw)