Mathematical presentation of utility maximisation, Microeconomics

Assignment Help:

Mathematical Presentation of Utility maximisation:

Consumer's objective is to maximise her utility by solving UMP. To solve UMP, we set the Lagrange function of the corresponding problem, which is,    L(x1, x2) = U(x1, x2) + λ (M-p1x1-p2x2) Our objective is to maximise this Lagrange function by choosing x1, x2 and λ. For that we differentiate the Lagrange function by x1, x2 and  λ, and set all equal to zero.  

 

547_Mathematical Presentation.png

is the slope of the indifference curve and  p1/p2 is the slope of the budget line. So, at equilibrium we have a slope of the indifference curve that is equal to the slope of the budget line. Again, from equation (f3) we get M = p1x1+p2x2, so budget equation holds with equality sign.   


Related Discussions:- Mathematical presentation of utility maximisation

Explain the difference between actual and potential growth, Use a PPF to ex...

Use a PPF to explain the difference between actual and potential growth. The PPF shows possible output, taking into consideration all factors of production - but de facto outpu

Marginal revenue function and price elasticity of demand, a) Explain the co...

a) Explain the conditions under which a monopolist is able to price discriminate. b) Demonstrate the relationship between a firm's marginal revenue function and its relationship

Understanding the labor market using supply and demand, The market for labo...

The market for labor can be studied use a supply and demand framework.  The demand for labor is from employers who use labor to produce goods and services.  The supply of labor is

Cells electromotive force, Defining Cells Electromotive Force: The main ob...

Defining Cells Electromotive Force: The main objective of this particular aspect of Physical Chemistry is to examine the relation between free energies and the mechanical energy o

Crop patterns, CROP PATTERNS: Analysis of crop patterns in India shoul...

CROP PATTERNS: Analysis of crop patterns in India should relate to the following aspects:  a) The relative significance of different crops/crop groups in the overall area u

Markets, The market structure in the south African mobile telecommunication...

The market structure in the south African mobile telecommunications industry

find the equilibrium quantity and demand curve, Consider a non-renewable r...

Consider a non-renewable resource. There are two periods, now and later. The demand curve in each period (t = 1, 2) is Qt = 10 - Pt. The stock of the resource is 10 units. Extracti

Money multiplier, The Money Multiplier is explained below: If you see c...

The Money Multiplier is explained below: If you see carefully, the money multiplier is nothing but an inverse of a reserve ratio. Therefore, we can write MM = 1/rr, where rr is

Modern economy, Modern economy: It explored the role of money in every...

Modern economy: It explored the role of money in every modern economy.The chapter also revealed that it is necessary for the government to ensure consistency between the quant

Short run costs, A film studio in Hollywood produces movies according to t...

A film studio in Hollywood produces movies according to the function q = F(K;L) = (2=100)K^0.5L^0.5 In the short run, capital (studios, gear) is xed at a level of 100. It costs $

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