Indirect utility functions, Microeconomics

Assignment Help:

Indirect Utility Functions:

Let qi denotes commodity i and pi is the price of that commodity. Let y denotes money income of the consumer. Suppose vi = pi/y. The budget constraint now may be written as  

854_Indirect Utility Functions.png

Since optimal solutions in the demand functions are homogeneous of degree zero in income and prices, nothing essential is lost by this transformation to "normalised" prices. The utility function U = f (q1, qn) together with equation (a) gives the following first order conditions of utility maximisation:   

1058_Indirect Utility Functions1.png

It gives the maximum utility as a function of normalised prices. The direct utility function describes preferences independent of market phenomena. The indirect utility function reflects a degree of optimisation and market prices. Applying the composite function rule of calculus to equation (c), we get  

1722_Indirect Utility Functions2.png

where the second equalities are based on equation (b). Partial differentiation of equation (a) with respect to vj yields  

2308_Indirect Utility Functions3.png

which is called the Roy's identity. Optimal commodity demands are related to the derivatives of the indirect utility function and the optimal value of the Lagrange multiplier (i.e., the marginal utility of income). Substituting equation (e) into the last equation of equation (b) gives  

2267_Indirect Utility Functions4.png

to provide an alternative form of Roy's identity. Now consider an optimisation problem in which equation (c) is minimised subject to equation (a) with normalised prices as variables and quantities as parameters. From the function, 1179_Indirect Utility Functions5.pngand setting its partials equal to zero, we get   

2390_Indirect Utility Functions6.png

"Inverse demand functions" are obtained by solving equation (f) for the prices as functions of quantities:  

603_Indirect Utility Functions7.png

This provides a parallel to the direct problem in which quantities are variables and prices are parameters.  


Related Discussions:- Indirect utility functions

Average total cost, Average Total Cost (ATC): ATC is the total cost per uni...

Average Total Cost (ATC): ATC is the total cost per unit of output. ATC = TC/y = (TFC + TVC)/y = AFC +AVC ATC falls sharply at the beginning of the production process because

Explain change in quantity demanded and a change in demand, Explain the dif...

Explain the difference between a change in quantity demanded and a change in demand. Change in quantity demanded" refers to movement with the demand curve.  For instance, if th

Movements in demand, diagram of extension and contraction in demand?

diagram of extension and contraction in demand?

Demand, what are tne methots of demand forecasting ?

what are tne methots of demand forecasting ?

...., Homework 4 Q1. Suppose a consumer has utility function (u) = xy where...

Homework 4 Q1. Suppose a consumer has utility function (u) = xy where x and y are amounts of two commodities that this consumer consume. Suppose this consumer’s income is $120, pri

Government Stimulus Package, The government decides to implement a new econ...

The government decides to implement a new economic stimulus package targeted at American Farmers. The stimulus package gives every household a $300 prepaid credit card that may on

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