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., 

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,  

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

 (p_i⁰ - p_i¹) (x_i" - x_i⁰) < 0 

So, quantity change is in opposite direction of the price change. Hence, substitution effect is negative. Now, dp = (dp₁, dp₂,...,dp_i,...,d_pⁿ) and dx = (dx₁, dx₂,...,dx_i,...,dx_n)^T, so that   

 

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

Ask an Expert

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

Write your message here..

Related Questions

Canalisation, State trading is often associated with canalisation. Canalisa... State trading is often associated with canalisation. Canalisation means estaolishment of state monomply in foreign trade. In other words, an item that is canalised can be imported

Competitiveness in your industry, a) Collect costs, revenue data, or other ... a) Collect costs, revenue data, or other data from the industry that you deem relevant. Describe how you would modify the data in order to make it relevant to decisions a manager m

Production, factors that affects the volume of production factors that affects the volume of production

ECONOMICS OF UNCERTAINITY WITH EXAMPLE, economics of uncertainty with examp... economics of uncertainty with examples

Monopoly, unique product unique product

Subsitution and income effect, subsitution effect dominate tha income effec... subsitution effect dominate tha income effect in which good case?

What do you meant by derivatives, Q. What do you meant by Derivatives? ... Q. What do you meant by Derivatives? Derivatives: A derivative is a financial asset whose resale value depends on the value of other financial assets at different points in tim

Analyze the characteristics of a monopoly market, Question 1: (a) Descr... Question 1: (a) Describe the three different ways of calculating national income. (b) Does the National Income figure accurately reflect the living standardof a population?

Ppf, You should find two articles, of which one should report on changes th... You should find two articles, of which one should report on changes that make farming more productive (more food per acre, hour or other unit of inputs), and another about changes

Enzyme activity mechanism, The enzymes are highly specific in nature. Durin... The enzymes are highly specific in nature. During enzymatic reaction the enzyme is so built that it binds to the substrate in a specific manner. The stepwise mechanism of enzyme ca