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

Price adjustments under fixed exchange rate, PRICE ADJUSTMENTS UNDER FIXED ...

PRICE ADJUSTMENTS UNDER FIXED EXCHANGE RATE: In a flexible exchange rate regime trade deficits (surpluses) are automatically corrected by a depreciation (appreciation) of a co

Substitute product, If we have two products, A and B, which are substitutes...

If we have two products, A and B, which are substitutes, we can expect that a rise in the price of A (or B) will cause the demand for B (or A) to go up.” Examine this statement wit

Describe labour market segmentation, Q. Describe Labour Market Segmentation...

Q. Describe Labour Market Segmentation? Labour Market Segmentation: Deep and systematic differences among various groups of workers, in which different types of workers are eff

Population information, What population information is needed by local auth...

What population information is needed by local authorities to provide the right number of primary and secondary school places? How would such information affect the plans of the lo

Types of taxes, Taxes: Compulsory government levies collected to pay for pu...

Taxes: Compulsory government levies collected to pay for public spending. There are numerous types of taxes (corporate, income, wealth, sales, environmentaland payroll taxes); each

Microeconomics help, Review: Full, Anonymous: No Answer each of the follo...

Review: Full, Anonymous: No Answer each of the following questions using economic theory covered in this lesson. 1. Marginal revenue product is defined as the change in total

Determination of exchange rates, DETERMINATION OF EXCHANGE RATES: When...

DETERMINATION OF EXCHANGE RATES: When we study the determinants of exchange rates, we must distinguish between long run determinants and short run because the determinants in

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