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

Level of aggregate demand in economy, Q. Level of aggregate demand in econo...

Q. Level of aggregate demand in economy? Demand-pull inflation takes place when there is an increase in level of aggregate demand in economy. Aggregate demand comprises five co

Explain the price inflation and wage inflation, What is the difference betw...

What is the difference between Price inflation and Wage Inflation?  Price inflation is the rate of enhance in the prices of goods and services whereas the wage inflation is ra

What is economic efficiency, Q. What is Economic efficiency? Economic ef...

Q. What is Economic efficiency? Economic efficiency Explain a situation where the total value of the end uses, to which the resources are put, is maximised. A consequence is th

Demand functions for one product facing two markets, Suppose a firm faces t...

Suppose a firm faces two markets for the same product. In market A, the demand function is PA=60-QA, while in market B the demand function is PB=36-0.5QB. The total cost function i

What do you meant by deficit, Q. What do you meant by Deficit? Deficit:...

Q. What do you meant by Deficit? Deficit: When a business, government or household spends more in a given period of time than they generate in income, they suffer a deficit. A

Determine the rule of divergence in general, Determine The Rule of Divergen...

Determine The Rule of Divergence in General Though even if attention is confined to non-communist-ruled economies there still has been huge divergence in relative output per w

What are the properties of cost function, What are the properties of cost f...

What are the properties of cost function? Properties of Cost Functions: Some similarities are here with consumer theory. Such similarities are actually exact while one compa

Barometric forecasting, It is also known a sleadig indicators forecasting N...

It is also known a sleadig indicators forecasting National Bureau of Economic Research of U. S.A has identified three types of indicate Leading indicators coincidental indicators a

Product transformation curve, Production: - Firms should choose how muc...

Production: - Firms should choose how much of each to produce. - The alternative quantities can be illustrated by using product transformation curves. Product Transforma

Find the average residential water under the current split, Suppose you are...

Suppose you are a regulator in charge of allocating water between residential and agricultural users (farmers) in Southern California. You conduct a survey that finds that under th

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