4. Let X be a set, R be an order relation in X. (a) Say R...

 

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4. Let X be a set, R be an order relation in X. (a) Say R is a total order on X. What is the set of equivalence classes? (b) Say R P is a strict order on X. What is the set of equivalence classes? (c) Say X is a consumption set equal to R2. Say the consumers preferences Rare are represented by u(x) = x1+x2. What are the equivalence classes? Now, apply the "level set optimization" approach discussed in class to re-represent that Marshallian demand. That is, solve out for a representation of the equiv- alence classes of u(x), show they are functions, and continuous and increasing in fixed utility level. Then construct the set of feasible utilities. Finally, show if we max equivalence classes over the feasible utilities, we can represents that Marshallian demand problem. (i) Show R is a complete transitive reflexive order. (ii) Show the equivalence classes of R form a totally ordered set in X. Are the equivalence classes for R a strict order? What is a "point" in the equivalence class ordering? 4. Let X be a set, R be an order relation in X. (a) Say R is a total order on X. What is the set of equivalence classes? (b) Say R P is a strict order on X. What is the set of equivalence classes? (c) Say X is a consumption set equal to R2. Say the consumers preferences Rare are represented by u(x) = x1+x2. What are the equivalence classes? Now, apply the "level set optimization" approach discussed in class to re-represent that Marshallian demand. That is, solve out for a representation of the equiv- alence classes of u(x), show they are functions, and continuous and increasing in fixed utility level. Then construct the set of feasible utilities. Finally, show if we max equivalence classes over the feasible utilities, we can represents that Marshallian demand problem. (i) Show R is a complete transitive reflexive order. (ii) Show the equivalence classes of R form a totally ordered set in X. Are the equivalence classes for R a strict order? What is a "point" in the equivalence class ordering?

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4 Let X be a set R be an order relation in X a Say R is a total order on X What is the set of equival ence classes ANS WER The set of equival ence classes is the set of all ordered pairs x y such that ... View the full answer