The appropriate resource constraint, Mathematics, Microeconomics

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?
Posted Date: 10/12/2016 11:06:43 AM | Location : Canada

Related Discussions:- The appropriate resource constraint, Mathematics, Assignment Help, Ask Question on The appropriate resource constraint, Mathematics, Get Answer, Expert's Help, The appropriate resource constraint, Mathematics Discussions

Write discussion on The appropriate resource constraint, Mathematics
Your posts are moderated
Related Questions
determination of optimal solution mathematical presentation

Strategic Importance of Supply Chain Management This describes the scope of supply chain management (SCM), including the management of procurement, logistics and materials. It

Control of Monopolies and Restrictive Trade Practices Monopoly hampers economic growth by lowering output and increasing prices and has an anti-social impact. In India, the Monopo

Economic Development The word development is from the Latin root ‘Voloper’ which meant wrap up, envelop. The English used this word along with ‘des’ meaning ‘undo’. The word

What is What is Critical Temperature? Why Critical Temperature is Specified in Equation? Describe critical temperature specification...

#question.suppose the # of producers of electric cars increases causing the supply curve to shift to the right. If the demand curve stays stationary what will happen to the produce

1. Cost minimizing firms must be profit maximizing as well. False, why??