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

Consumer Behavior, Monica consumes only goods A and B. Suppose that her mar...

Monica consumes only goods A and B. Suppose that her marginal uility from consuming good A is equal to 1/Qa, and her marginal utility from consuming good B is 1/Qb. If the price of

Efficiency of a competitive market, The Efficiency of a Competitive Market ...

The Efficiency of a Competitive Market *? When an competitive markets generate an inefficient allocation of the resources or market failure?   1) Externalities Costs

Price elasaticity, why does the quantity of education change in the privat...

why does the quantity of education change in the private universities much more responsive than salt as to changes in price?

Microeconomics, INFO: Suppose that a firm is currently employing 20 workers...

INFO: Suppose that a firm is currently employing 20 workers,(the only variable input), at a wage rate of $60. The average product of labor is $30, the last worker added 12 units to

Corporations price and output in the short run, Consider that the governmen...

Consider that the government tells a large monopolistic firm that maximizes profits that it has to pay a fee to the Reelect the President Committee same to one third of its total p

Total revenue, In fall 2006, Pace University raised its annual tuition from...

In fall 2006, Pace University raised its annual tuition from $24,750 to $29,750. Freshman enrollment declined from 1500 in fall 2005 to 1110 in 2006. assuming the demand curve did

Exchange rate policy, Exchange Rate Policy: LERMS, a dual exchange ra...

Exchange Rate Policy: LERMS, a dual exchange rate system, was introduced in the Budget for 1992-93. Under this system, 40 per cent of foreign exchange earnings were to be sur

FISCAL POLICY, HOW DO YOU ADJUST FISCAL POLICY FOR INTERNAL BALANCE

HOW DO YOU ADJUST FISCAL POLICY FOR INTERNAL BALANCE

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