The appropriate resource constraint, Mathematics, Microeconomics

Assignment Help:
Consider a person''s decision problem in trying to decide how many children to have. Although she cares about children and would like to have as many as possible, she knows that children are "costly" in the sense that there are costs to their upbringing as well as the time that she will have to take off from work in order to have children. Her utility function over her own consumption (x), her own leisure (l) and the number of children (n) is given by the following utility function:

U(x,l,n) = x1/6l1/6n1/6

For tractability (and to be able to use calculus), we will assume that the number of children, n is a continuous variable (i.e. it can take any nonnegative value, including decimal values like 2.15 etc.). This individual is endowed with a total of T units of time in her life, which she can divide between working, leisure and having children. For having each child, she will have to take time t off from work, during which she will not earn anything. Besides this, there is a per child cost of n for upbringing expenses.

Her wage rate is w; she uses her total income to purchase good x for her own consumption, as well as to provide for the upbringing expenses of her children. Assume that good x is priced at p per unit.

(a) Write the consumer''s optimization problem with the appropriate resource constraint, and derive her Marshalian demand for children n.

[Hint: Instead of redoing the whole calculations, can you make use of your results from Problem 1?]

(b) Suppose the government introduces child benefits i.e. for every child she has, the government provides her an amount s. How will this affect her decision on how many children to have i.e. is dn/sn greater or less than 0?

Related Discussions:- The appropriate resource constraint, Mathematics

Major air pollutants, Major air pollutants can be sub divided into 2 catexa...

Major air pollutants can be sub divided into 2 catexampleories: Inorganic gases and particular gases. (A) Inorganic gases 1. Carbon monoxide (CO) CO is a colourless, lethal gas

Black economy public policy interface, Black Economy Public Policy Interfac...

Black Economy Public Policy Interface: The above mode of functioning and expansion of the black economy became an important basis for policy disruption in India. The undergrou

Majority minority, Are there any economic effects to non-Hispanic whites, g...

Are there any economic effects to non-Hispanic whites, given that they no longer represent the majority of the population? Why are these examples important from an economic standpo

Demand and supply, If demand goes down what happens to the equilibrium?

If demand goes down what happens to the equilibrium?

Define Gibb''s Energy, Gibb''s energy In every chemical system, the substa...

Gibb''s energy In every chemical system, the substance moves in a direction in which there is a decrease in free energy, for example i.e. ?G is negative. G = H - TS where, G is

Williamson model of managerial discretion, how the equilibrium output and p...

how the equilibrium output and price is determined in williamson model of managerial discretion?

I am concerned that if we get into price war with Ev, I am concerned that i...

I am concerned that if we get into price war with Everest Solution

Production, what is cob duglus production function?

what is cob duglus production function?

Criticisms of world trade organisation, Criticisms of World trade organisat...

Criticisms of World trade organisation:   There are critics too of the WTO. It is believed that the WTO will emerge out destructive of biodiversity and people's livelihoods by

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