Mathematical derivation of ordinary demand function, Microeconomics

Assignment Help:

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

 


Related Discussions:- Mathematical derivation of ordinary demand function

Mixed economics, Mixed Economic System and how can this system solve the ec...

Mixed Economic System and how can this system solve the economic problem, with example?

Rationale for the intervention of government, 1. Describe why government re...

1. Describe why government regulation is required, citing the major reasons for government involvement in a market economy. 2. Justify the rationale for the intervention of gove

Outline the main components of trade liberalization, Problem: "Mauritiu...

Problem: "Mauritius offers an interesting case study of successful trade liberalization and export-led development in Sub-Saharan Africa. This is a notable achievement given t

Economic growth, Economic Growth: Economic Growth refers to an increas...

Economic Growth: Economic Growth refers to an increase in real aggregate output (real GDP) reflected in increased real per capita income. A country is said to experience econo

Technical economies, Technical Economies: They are economies that acc...

Technical Economies: They are economies that accrue from the use of large machines with emphasis on full utilization and efficiency in production. First, there are some equip

What is yuen’s profit function, Yuen, a travelling salesman for snake oil, ...

Yuen, a travelling salesman for snake oil, can produce the stuff at a marginal cost of 1. There are 100 potential customers in Vernon, each of whom has the following demand functio

Example of insurance - reducing risk, The Value of Title Insurance While Bu...

The Value of Title Insurance While Buying a House *  A Scenario: - Price of house is $200,000 - 5% chance that seller does not own house *  Risk neutral buyer would pa

Marginal social benefit, Consider the following information relating to the...

Consider the following information relating to the pulp market.   Demand     Supply   Output(tonnes/ da

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd