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

Individual demand, INDIVIDUAL DEMAND * Price Changes - Using figures...

INDIVIDUAL DEMAND * Price Changes - Using figures developed earlier, the impact of a change in price of food can be shown by using indifference curves.  Effect of Price

Surplus, Surplus The surplus is a condition under that supply for a goo...

Surplus The surplus is a condition under that supply for a good or service is in excess of the demand for that good or service. When this happens, there is commonly a reduction

Cost, Relatiön between TC ,TFC and TVC

Relatiön between TC ,TFC and TVC

Value of intermediate products, Value Added:Value added in a particular sta...

Value Added:Value added in a particular stage of production equals value of total output, less the value of intermediate products (comprising raw materials, capital equipment and o

Supply and demand, Suppose scientists discover that eating soybeans prevent...

Suppose scientists discover that eating soybeans prevents cancer and heart disease

How are consequences of economists used, How are consequences of economists...

How are consequences of economists used? Economists generally use efficiency, information, equilibrium and incentive compatibility like focal points, and examine the consequenc

Total sales of industry, The sales of a company are the part of the total s...

The sales of a company are the part of the total sales of industry. If the conditions of industry changes then the sales of each of the firm in the industry is affected. All teh ti

Contribution of foreign trade to economic development, Contribution of Fore...

Contribution of Foreign Trade to Economic Development: Foreign trade contributes to economic development in a number of ways.  •  It provides flow of technology which al

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