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

What is the difference between scarcity and shortage, What is the differenc...

What is the difference between 'scarcity' and 'shortage'?  'Scarcity' and 'shortage' have dissimilar definitions. In reality, when most of the goods and resources are scarce go

1, price falls and demand is elstic

price falls and demand is elstic

Demand Supply, Ask quAsk qIf the supply and demand curves for labor are rep...

Ask quAsk qIf the supply and demand curves for labor are represented by the following equations: Wd= -- (1/100)Ld + 30 Ws= (1/200)Ls Ws=Wd Ld=Ld a. Graph the results and show the

Malthus and the food crisis, Malthus and the Food Crisis - Malthus pred...

Malthus and the Food Crisis - Malthus predicted starvation as diminishing returns limited agricultural output and the population continued to grow. - Why did Malthus' predic

Explain how a perfact market responds to changes in consumer, explain how a...

explain how a perfact market responds to changes in consumer demand?

Problem in measuring depreciation, Economists view depreciation as capital ...

Economists view depreciation as capital consumption for them, there are two distinct ways of charging for depreciation (1) the depreciation of equipment must equal its opportunity

Compute the after-tax cost of debenture, A 5-years Rs.100 debenture of a fi...

A 5-years Rs.100 debenture of a firm can be sold for a net price of Rs. 96.50. The coupon rate of interest is 14 per cent per annum, and the debenture will be redeemed at 5 per cen

Boltzmann distribution, Boltzmann Distribution: In most cases of interest o...

Boltzmann Distribution: In most cases of interest of chemistry the particles adopt the Boltzmann distribution. Qualitative considerations: the general expression for W given by eq

Demand and supply, draw the demand curve,when there is rise in the price of...

draw the demand curve,when there is rise in the price of a product on the demand of the product

Survey methods, Survey Methods: The most direct method of forecasting dema...

Survey Methods: The most direct method of forecasting demand in the short run is survey method. Surveys are conducted to collect information about future purchase plans of the

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