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

Sample Exams, Hi, My Econ prof gives out a sample exam two days before we t...

Hi, My Econ prof gives out a sample exam two days before we take the real exam. If I were to submit the sample exam to you, how long would it take to get the answers back?

Instant help from economics tutors Environmental economics, Environmental e...

Environmental economics goes back to the 19th century. Economists who research the planet are mainly worried with the idea of externalities, rare organic sources, and with the pro

Price mechanism, how does the prices system affect a country

how does the prices system affect a country

Gay lussac''s law of gaseous volumes, Gay Lussac''s law of gaseous volumes:...

Gay Lussac''s law of gaseous volumes: While gases react with each other they always do so in volumes that bears a simple ratio to one and another or to the volumes of the products

Economic value, The monetary calculate of the welfare associated with the c...

The monetary calculate of the welfare associated with the change in the provision of some good. It is not to be confused with monetary value, unless the latter is explicitly desig

Explain about the integrability problem, Explain about the integrability pr...

Explain about the integrability problem. The Integrability Problem: Provide a system of demand functions x(p, m). Is there essentially a utility function by which such deman

Determine the non orthogonal - anova, 1. The two-way ANOVA, non-orthogonal ...

1. The two-way ANOVA, non-orthogonal case, has been a vexing problem for ANOVA researchers for many years.  Please answer the following questions concerning the two-way non-orthogo

Atmospheric Pollution, Earth is completely surrounded by thick envelope of ...

Earth is completely surrounded by thick envelope of gases called atmosphere. Atmosphere is sub divided into different layers depending upon the distance from the sea level. The

Definition, the definition of exceptional supply curve

the definition of exceptional supply curve

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