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

Stockholders and managers, Normal 0 false false false E...

Normal 0 false false false EN-IN X-NONE X-NONE MicrosoftInternetExplorer4 1. Suppose that the

Physical capital, Physical Capital: A tangible tool, machine, building or o...

Physical Capital: A tangible tool, machine, building or other productive asset that is used to produce other goods or services. Pollution: Many economic activities involve disch

Production, what is cob duglus production function?

what is cob duglus production function?

I am doing micro assignment, how to write the conclusion,i am doing the nik...

how to write the conclusion,i am doing the nike company.

Subsidies and welfare, Ask question #Minimum 100 areanycurrentsubsidyorwelf...

Ask question #Minimum 100 areanycurrentsubsidyorwelfareissueddiscussedoraddressedinparliamentwords accepted#

Moving average methods, Moving Average Methods: Under this methods the movi...

Moving Average Methods: Under this methods the moving average to the sales of the past years is computed. The computed moving average is taken as forecast for the next year or peri

Describe stabilisation policies as by the imf, Describe stabilisation polic...

Describe stabilisation policies as by the International Monetary Fund (IMF). Define stabilisation policies as basically a list of demands set forward by the IMF to a debtor nat

Demand and supply, what happens when price is fix and there is a change of ...

what happens when price is fix and there is a change of the supply and demand curve

Why is it considered well to bring all bop to zero, Why is it considered we...

Why is it considered well to bring all BOP's to zero?   If BOP of any country is zero, it reflects that the present account of that country has sufficient balance to meet the n

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