Explain what is meant by an effectively altruistic head

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Reference no: EM131298144

Assignment 1 -

Q1. Efficient sorting in marriage markets Consider a marriage market with four men and four women. Women are indexed by i ∈ {1, 2, 3, 4} and men by j ∈ {1, 2, 3, 4}. The 4x4 matrix of marital outputs is given by:

 

men

1

2

3

4

women

1

7

8

8

5

2

6

5

6

4

3

2

7

7

0

4

5

6

7

2

Note that you can get full marks for (a) and (c) if you just give me the right answer but if you give the wrong answer, an explanation will be worth partial marks and an unexplained wrong answer is a zero.

(a) What is the efficient sorting?

(b) Without proving it, explain intuitively why a set of marital incomes exist for which the sorting from (a) will be stable.

(c) Which man and which woman do you expect to receive the highest incomes in the efficient and stable sorting?

(d) The result that the efficient sorting is the equilibrium sorting in this marriage market is due to the assumption of transferability of income within marriage: the only restriction on marital incomes is that Zm_if_j = Zm_i + Zf_j. Suppose instead that marital output is a non-transferable public good, which means that in a marriage between man i and woman j, Zm_if_j = Zm_i = Zf_j. Will it still be the case that the efficient sorting is stable?

Q2. Sorting on traits Economic theory suggests that couples should sort positively on traits, such as personality, that help convert income into utility but negatively on traits, such as wages, that allow them to generate income. Explain.

Q3. Demand for children

Suppose you have a utility function for children given by U(n, q) = n.95 + q.95 where n is the number of children and q is the quality per child (we ignore demand for non-child commodities Z). Your income is I = 100, and your budget constraint is given by pnn + pcnq = I, where pn is the fixed cost of having another child regardless of its quality, and pc is the cost of a unit of quality for one child. Equality of the budget constraint comes from the non-satiation of the utility function in both arguments. If pc = 5 and pn = 2, what is the solution for n and q? What if pc = 5 and pn = 3? Do you find your mathematical answers to be intuitively credible?

Assignment 2 - Investments in children

Q1. Investments in children I:

Suppose I have one child and I value my child's adult income and my own consumption with utility function U(Zt, It+1) = Zαt/a + I1-αt+1/1-α. I can make only transfers of wealth to my child yt where the return at t + 1 is (1 + rt)yt and my child's adult income is It+1 = et+1 + (1 + rt)yt. (For simplicity, there is no luck ut+1.) Also, I can borrow against my kid's future resources et+1 freely at market interest rt. Derive the parent's optimality condition relating Zt to It+1 given Ut(·). What happens to It+1 and Zt if my kid's natural ability et+1 increases by 1%?

2. Investments in children II:

Following the analysis in the Chapter 7 notes, if parents are not able to borrow against their children's future earnings, it is likely that rich families will remain (relatively) rich while poor families will remain poor from one generation to the next, even if the heredity of endowments h is fairly low (close to zero)?

3. Altruism:

If a parent is altruistic toward his p children, he has utility:

Uh = Uh(Zh, U1, U2, ..., Up);  ∂Uh/∂Zh > 0; ∂Uh/∂Ui > 0; i = 1, ..., p

The budget constraint of the altruistic head is:

Zh + k=1p yk = Ih

where Ih is the head's private income and yk are the transfers to each child k. Each of the children k = 1, ..., p therefore have private income Ik and consumption Ik + yk = Zk.

(a) Explain what is meant by an "effectively altruistic" head.

(b) Suppose Tom, Jane, and Mary are the three children of an altruistic head. Explain why, when Tom's income rises, the head's consumption rises even though Ih (and IM and IJ) does not change. Would this also be the case if the altruistic head was not an effective altruist?

(c) If the head is an effective altruist toward all his children, would Tom be willing to accept a reduction of $500 in his income IT if doing so would raise Jane's income IJ by $300 and Mary's income IM by $250? Explain.

(d) Now suppose that, in part (c), the head is not altruistic toward Mary. Now will Tom be willing to accept a reduction of $500 in IT if doing so would raise IJ by $300 and IM by $250? Explain.

Attachment:- Lecture Notes.rar

Reference no: EM131298144

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Reviews

len1298144

12/2/2016 2:59:36 AM

In first assignment for Q1 and Q2, I think you can find related material from second part of the lecture note for Q1 an Q2 I provided, that is chapter 4, starting with page 17. In page 23, Assortative: Matching by Traits, so I believe it's for Q2. For Q3, demand for children, i have also uploaded the lecture note for that question. Please see lecture note for Q3. This is a calculation-based assignment. So the professor expects us to solve it by calculation as much as possible. You can find how to solve these questions from lecture notes. Please try your best. If you think i provided wrong lecture notes or you can't find how to solve these questions from lecture notes, please get contact with me, thanks. In the second assignment this is a calculation-based assignment. So the professor expects us to solve it by calculation as much as possible. You can find how to solve these questions from lecture notes. Please try your best. If you think i provided wrong lecture notes or you can't find how to solve these questions from lecture notes, please get contact with me, thanks.

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