Mathematical derivation of ordinary demand function, Microeconomics

Mathematical Derivation of ordinary demand function:

Here we present the mathematical and more general proof of the above result. Consider, again, the initial price income situation (p0, M0), where x0 is the chosen bundle. Prices change from p0 to p1, where p0>p1, and consumer's real income changes (in this case increases). Suppose we adjust consumer's money income in such a way that her  purchasing power remains the same. Consumer's money income is changed to M1 = p1x0. Suppose x" is the bundle consumer buys with her adjusted money income viz., 

1852_Mathematical Derivation of ordinary demand function.png

Since with (p1, M1) consumer chooses x" while x0 was available, so x" is revealed preferred to x0 and therefore was not available when x0 was chosen while (p0, M0) prevailed. Thus,  

2102_Mathematical Derivation of ordinary demand function1.png

15_Mathematical Derivation of ordinary demand function5.png

Suppose only price of ith good changes, other prices remaining constant. Therefore,  

 (pi0 - pi1) (xi" - xi0) < 0 

So, quantity change is in opposite direction of the price change. Hence, substitution effect is negative. Now, dp = (dp1, dp2,...,dpi,...,dpn) and dx = (dx1, dx2,...,dxi,...,dxn)T, so that   

367_Mathematical Derivation of ordinary demand function4.png

 

Posted Date: 10/26/2012 3:54:53 AM | Location : United States







Related Discussions:- Mathematical derivation of ordinary demand function, Assignment Help, Ask Question on Mathematical derivation of ordinary demand function, Get Answer, Expert's Help, Mathematical derivation of ordinary demand function Discussions

Write discussion on Mathematical derivation of ordinary demand function
Your posts are moderated
Related Questions
Austrian economics is a brand of neo-classical economics that was established in Vienna during the late 19th century & first half of the 20th century. Austrian economics was strong

The Snob Effect - If network is negative externality, a snob effect exists. * The snob effect refers to desire to own unique or exclusive goods. * The quantity demanded o

(a) Reasons of Urban Growth (b) Characteristics of Urban Growth (c) Economic Life of a Building (d) Zone of Transition (e) Location Theory (f) Patterns of Growth Theory (g) Growth

Is Indian companies running a risk by not giving attention to cost cutting

During a given interval a nation''s overall productivity grows at a compounded rate of 2%. Its population growth rate and degree of labor-force participation do not change over thi


A MANUFACTURING UNIT IS INTERESTED IN DEVELOPING A BENEFIT SEGMENTATION OF THE CAMERA MARKET. SUGGEST SOME MAJOR BENEFIT SEGMENT WITH MARKET TARGETING STRATEGIES?

A Period of Deterioration: The entire period was very difficult for India's BOP, partly because of slow growth of exports in relation to import requirements and partly because


Expected Utility: Theory Assume that a utility index exists which conforms to the five axioms. The expected utility for the two-outcome lottery L = (P, A, B) is given by,