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

Economic reforms and reduction of regional disparities, Economic Reforms an...

Economic Reforms and Reduction of Regional Disparities: Another important objective of development is to reduce regional disparities. Government has been helping the backward

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

Global business etiquette, Your company has a product that it is interested...

Your company has a product that it is interested in marketing in a foreign country. Using one of the following Websites, click on a country of your choice to learn about Etiquette,

Microeconomics, determinants of demand and determinants of supply

determinants of demand and determinants of supply

Educational financing, Normal 0 false false false EN-IN...

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

Economic growth, Summarize the four supply factors in economic growth.

Summarize the four supply factors in economic growth.

What is the price of a call option on stock, Consider an economy with three...

Consider an economy with three states. The following set of stocks is traded:   x 1 =(2,2,0)    x 2 =(1,0,3)  x 3 =(0,2,4). The t=0 prices of these stocks are given as follow

International financial institutions, Conditionality: International financi...

Conditionality: International financial institutions (such as World Bank andInternational Monetary Fund) usually attach strong conditions to emergency loans they make to developing

Explain how the price system eliminates a surplus, Explain how the price sy...

Explain how the price system eliminates a surplus. The meaning of surplus is that quantity demanded is less as compared to the quantity supplied.  This will lead to downward pr

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