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

Production cost, how can draw the table and diagram of production function ...

how can draw the table and diagram of production function function with one veriable

Labour supply, Discuss how the opportunity cost principle influence a suppl...

Discuss how the opportunity cost principle influence a supplier''s decision to supply labour

Traditional food processing methods, discuss african traditional methods of...

discuss african traditional methods of production and processing of food

Discounting principle, The owner of a firm Mr. Rajneesh expects to make a p...

The owner of a firm Mr. Rajneesh expects to make a profit of Rs.5,50,000, Rs.6,50,000, Rs.7,50,000 and Rs.8,50,000 at the end of the 1st, 2nd, 3rd and 4th year respectively. Rajne

Explain supply and demand diagrams, During the 1990s, technological advance...

During the 1990s, technological advance reduced the cost of computer chips. Explain, with the use of supply and demand diagrams, how the following markets are affected in terms of

Economics, define economics in plural sense. .

define economics in plural sense. .

Structural unemployment, Structural Unemployment: This is unemploymen...

Structural Unemployment: This is unemployment resulting from changes in the pattern of demand for goods and services or changes in technology.These changes may in turn alter

Inflation, how measure the inflation

how measure the inflation

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