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

Dalton''s law of partial pressures, Describe Dalton''s law of partial press...

Describe Dalton''s law of partial pressures, specification of Dalton''s law of partial pressures, Dalton''s law states that, at a given known temperature total pressure exerted b

Explain elasticity coefficient, The elasticity coefficient is a number meas...

The elasticity coefficient is a number measured using price and quantity data to verify how responsive consumers are to changes in the price of a commodity.  The elasticity coeffic

Political economy, Consider the model of corruption explored by Shleifer an...

Consider the model of corruption explored by Shleifer and Vishni’s where there is one government-produced good X. There is a demand for that good described by the inverse demand eq

Marginal utility, discuss how economic theory explains the optimum pattern ...

discuss how economic theory explains the optimum pattern of consumption of an individual consumer

Organization becoming too large to effectively manage, Economies of scale a...

Economies of scale are advantages obtained from a company becoming large and diseconomies of scale are additional costs inflicted because a firm has become very large.  The causes

Find contract curve, Consider two individuals  M and F who must split 20 un...

Consider two individuals  M and F who must split 20 units of good X and 10 units of good Y. Suppose we can represent M's preference with the utility function Um =X ^2 mYm and Fs

How change in the exchange rate affect the domestic economy, How might a ch...

How might a change in the exchange rate affect the domestic economy of the country? A change in the exchange rate - ceteris paribus - will alter relative prices between trading

Factors that calculate price elasticity of demand, Factors that calculate p...

Factors that calculate price elasticity of demand: The proportion of Income spent on the Commodity If the price of a good is relatively low such the expenditure on it is a

Corporations price and output in the short run, Consider that the governmen...

Consider that the government tells a large monopolistic firm that maximizes profits that it has to pay a fee to the Reelect the President Committee same to one third of its total p

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