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

Elasticity of market supply, Elasticity of Market Supply • Perfe...

Elasticity of Market Supply • Perfectly inelastic short run supply arises when industry's plant and equipment are so fully utilized that new plants should be built to ac

Risk loving persons, Risk Loving - A person is a risk loving if they sh...

Risk Loving - A person is a risk loving if they show a preference toward the uncertain income over a certain income having same expected value. Examples: Gambling, some

Learning curve in practice, Learning Curve in Practice * Scenario - ...

Learning Curve in Practice * Scenario - A new firm enters chemical processing industry. * Do they: 1) Produce a low level output and sell at high price? 2) Produce

Explicit costs are accounting costs, An economist's view of costs contains ...

An economist's view of costs contains both explicit and implicit costs.  Explicit costs are accounting costs, and implicit costs are the opportunity costs of an allocation of resou

What are the three major types of unemployment, What are the three major ty...

What are the three major types of unemployment?   a) Frictional b) Structural and c) Cyclical unemployment. Cyclical unemployment is broadly spread by an economy durin

Duality theorems, Duality Theorems: The relationship between the direc...

Duality Theorems: The relationship between the direct and indirect utility functions may be described by a set of duality theorems. The following illustrative theorems are pro

Linkage of education with poverty and income distribution, Normal 0 ...

Normal 0 false false false EN-IN X-NONE X-NONE MicrosoftInternetExplorer4

What are the possibilities of returns to scale in production, What are the ...

What are the possibilities of returns to scale in production technology? Three possibilities are there as: technology exhibits (a) constant returns to scale; (b) decreasing ret

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