Duality theorems, Microeconomics

Duality Theorems:

The relationship between the direct and indirect utility functions may be described by a set of duality theorems. The following illustrative theorems are provided without proof. 

Theorem 1: Let f be the finite regular strictly quasi-concave increasing function which obeys the interior assumption (the utility for a commodity combination in which one or more quantities is zero is lower than the utility for any combination in which all quantities are positive). The g determined by equation (c) is a finite regular strictly quassi-convex decreasing function for positive prices. 

Theorem 2:  Let g be a finite regular strictly quassi-convex decreasing function in positive prices. The h determined by equation (g) is a finite regular strictly quassi-concave increasing function. 

Theorem 3: Under the above assumptions 

h(q1,...,qn) = g[V1(q1,...,qn),..., Vn(q1,...,qn)] and

g(q1,..., qn) = h[D1(q1,..., qn),..., D1(q1,..., qn)] 

The direct utility function determined by the indirect is the same as the direct utility function that determined the indirect. 

Duality in consumption forges a much closer link between demand and utility functions for the purposes of empirical demand studies. It is sometimes possible to go from demand functions to the indirect utility function by using Roy's identity, and then to the corresponding direct utility function. Duality is also useful in comparative statics analysis. Homotheticity, separability, and additivity each have counterparts for the indirect utility function. Consequently, many theoretical analyses can be conducted in terms of either the direct or indirect utility function, whichever is more convenient.  

Posted Date: 10/26/2012 4:24:48 AM | Location : United States







Related Discussions:- Duality theorems, Assignment Help, Ask Question on Duality theorems, Get Answer, Expert's Help, Duality theorems Discussions

Write discussion on Duality theorems
Your posts are moderated
Related Questions
what is histogram?

Q. What is Gini Coefficient? Gini Coefficient: A statistical measure of inequality. A Gini score of 0 signifies perfect equality (in which each individual receives the same inc

Current Account: The Current Account can be broken down into two parts, viz., one, balance of trade, and, two, balance on invisibles. The Balance of Trade (BOT) deals only wit

Which assumption of Classic OLS does this model violate?

How base case NPV analysis is applied in financial risk management

Circular Flow of Income: The diagram shows Real Flow (goods and services) and Monetary Flow (Income and expenditure). The bottom pair of arrows depicts the goods market.

when the demand function is 2q-24+3p=0,find marginal revenue when q=3

what is mrs

How has the Haberler''s theory of opportunity cost an improvement over the classical theory of trade

Concept of Stock Replenishment  This concept assumes that stock is always available whether there is demand or not. Consider the demand for constituent items, such as componen