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

How are the limitations of the economics theory affected, How are the limit...

How are the limitations of the economics theory affected? Limitation of Economic Theory: While examining the generality of an economic theory, one must realize any assump

Physical accounting, Normal 0 false false false EN-IN ...

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

Utility-expenditure duality, Utility-Expenditure Duality: Consider the...

Utility-Expenditure Duality: Consider the minimisation of the  expenditures necessary to achieve a specified utility level. The solution for qi yields the compensated demand f

Production theory and analysis in managerial economi, dicuss the relevance ...

dicuss the relevance of studing production theory and analysis inn your career as a student of manegerial economics

Draw an indifference curve for consumption, Draw an indifference curve for ...

Draw an indifference curve for consumption and hours of work. (Hint: in class we discussed indifference curves for consumption and hours of leisure, this is different.)

Diminishing marginal returns, law of diminishing marginal returns does no...

law of diminishing marginal returns does not hold then output of the world can be produced in a flower pot. Explain?

Explain the duality between direct and indirect utility, Explain about the ...

Explain about the duality between direct and indirect utility. Duality between Direct and Indirect Utility: While seen how one can recover an indirect utility function by ob

Consumer choice, Suppose a family earns £1,500 per month and can either pay...

Suppose a family earns £1,500 per month and can either pay £0.50 per square foot in monthly rent for an apartment in the private rental market, or accept a 1,500 square foot house

Market supply labour, use a graphical illustration to describe briefly what...

use a graphical illustration to describe briefly what the influence of each of the following be on the market supply of labour,(a) an increase in immigrants, (b) a reduction in wag

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