Explore BrainMass
Share

lexicographic order

This content was STOLEN from BrainMass.com - View the original, and get the already-completed solution here!

The Complement A of an r-subset A of {1,2...,n} is the (n-r)-subset of {1,2,...,n} consisting of all those elements that do not belong to A. Let M= C(n,r), the number of r subsets and at the same time the number of (n-r)-subsets of {1,2...,n}. Prove that if A1,A2,A3...AM are the r subsets in lexigraphic order then complements Am,...,A3,A2,A1 are the (n-r)-subsets in lexiographic order.

(so the last Am,...,A3, A2,A1 are compliments)

© BrainMass Inc. brainmass.com October 25, 2018, 1:46 am ad1c9bdddf
https://brainmass.com/math/combinatorics/lexicographic-order-274133

Solution Summary

This post assesses lexicographic order.

$2.19
See Also This Related BrainMass Solution

Microeconomic Theory - lexicographic, cardinal/ordinal utility,envelope, Hotelling's lemma, utility maximization

1. In the context of the usual utility maximization problem involving n(>2) goods, prove that not all goods can be net complements and that at least one good must be normal.

2. Prove the envelope theorem and use it to derive Hotelling's lemma.

3. Explain:
(a) Why lexicographic preferences do not yield a continuous utility function.
(b) The difference between cardinal and ordinal utility.
(c) Why profit maximization is not an assumption in the competitive general equilibrium model.

4. Average costs fall as output increases if and only if the production function is homogeneous of degree p>1. True or false? Explain your answers.

5. Consider the problems of maximizing utility u(x) subject to px ≤ y and minimizing expenditure px subject to u(x) ≥ u. Assuming that the utility function is continuous and strictly monotonic increasing and that solutions to both problems exist. Prove that utility maximization implies and is implied by expenditure minimization.

View Full Posting Details