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Now consider Cornelius and Wheaton as consumers who eat a balanced diet of both foods. Denote Cornelius' consumption of corn by qcc and wheat by qwc, and Wheaton's consumption of corn by qcw and wheat by qww. (Note: That is, the subscript denotes the good consumed, and the superscript the consumer.) Their utility functions are uc(qcc,qwc)=119logqcc+112logqwc,uw(qcw,qww)=112logqcw+119logqww. (a) (5) Find the total income earned by Cornelius Ic and Wheaton Iw. (b) (5) Set up each consumer's utility maximization problem, write the Lagrangians, and find the first order conditions. (c) (5) Find an equation that describes the line of Pareto efficient allocations by expressing Cornelius' share of wheat consumption w=qwc+qwwqwc as a function of his share of corn consumption c=qcc+qcwqcc. (d) (5) Find each consumer's demand for corn, qcc(pc,pw) and qcw(pc,pw), and wheat, qwc(pc,pw) and qww(pc,pw). (e) (5) Find the market demands for corn qcd(pc,pw) and wheat qwd(pc,pw)
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