3. (25) Now consider Cornelius and Wheaton as consumers. Both derive utility not only from consuming what they can grow themselves, but also from the crop grown by the other farmer. Denote Cornelius' consumption of corn by q and wheat by qu, and Wheaton's consumption of corn by q" and wheat by qu. (Note: We use the subscript to denote the good consumed, and the superscript the consumer.) Their utility functions are u ( ge, q) = = log ge + - log qu u" (q" , qw) = - log qe + - log qu (a) (5) Find the total income earned by Cornelius /" and Wheaton I". (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 Qu =; "was a function of his share of corn consumption of = (d) (5) Find each consumer's demand for corn, q(Pc, Pw) and q" (Pc, Pu), and wheat, qu (Pc, Pw) and qu (Pc, Pu). (e) (5) Find the market demands for corn q(Pc, Pw) and wheat qu (Pc, Pw)