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

State the difference between indifference curve and isoquant, What is the d...

What is the difference between indifference curve and isoquants?  An indifference curve shows dissimilar combinations which a consumer can buy with a given level of income. Ind

102, why does the quantity of salt tend to be unresponsive to changes in it...

why does the quantity of salt tend to be unresponsive to changes in its price

Find all the equilibrium, The "Battle of Sexes" is a famous game. The story...

The "Battle of Sexes" is a famous game. The story is that a couple tries to decide what to do on a Friday evening. The girl prefers to go to an Opera and the guy prefers to go to t

Marxisism, Hi, Can you help with writing journals homework? It should be in...

Hi, Can you help with writing journals homework? It should be in english as a second language. Ten pages different topics about Karl Marx economics views. I will give you the t

Positive and normative statement, differentiate between normative and posit...

differentiate between normative and positive statements in economics with the help of a statement

Demand Forecasting, what is demand forecasting and defines its techniques

what is demand forecasting and defines its techniques

Market structers, what are the majotr sources of monopoly

what are the majotr sources of monopoly

Rationale for government intervention, Rationale for government interventio...

Rationale for government intervention There are six major functions the government can perform in an economy. 1. The government provides a legal and social framework within which

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