Is polygamy likely to exist in this economy

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Reference no: EM131296052

Question 1. Intrahousehold allocations and specialization

Suppose a family consisting of a wife f and a husband m values a commodity Z, which is produced with inputs of home production t'_h and purchased goods x. The household- level utility function is U = U (Z), with Z = f (x, t'_h) = x^.4 t'^.6_h. Household members purchase input x in the market at price p using earned income w_ft_wf + w_mt_wm and unearned income v, where wi is the market wage of, and t_wi is the working time chosen by, member i ∈ {f, m}. Home production t'_h= w_hft_hf+ w_hmt_hm, where w_hiis the home production efficiency of member i ∈ {f, m}. The couple therefore faces the following set of five constraints:

(a) wife's time: t_hf+ t_wf = T
(b) husband's time: t_hm + t_wm = T
(c) income: w_f t_wf + w_mt_wm + v = px
(d) home production: w_hf t_hf + w_hmt_hm = t'_h

(e) commodity production: Z = f (x, t'_h )

(a) Show that f is increasing and concave in both t'_h and x.

(b) Let T = 100, v = 50 and p = 5. When the household members allocate their time optimally, calculate how much Z the household can produce if (i) w_hm = 10, w_m = 0, w_hf= 0, w_f= 10, and (ii) if w_hm = w_hf = 6 and w_m = w_f = 5. What does this imply about the optimal investments in human capital the spouses should make early in life?

(c) Suppose v increases from 50 to 100. What do we expect to happen to t_hf , t_wf , t_hm and t_wm? What about individuals' investments in w and wh at the beginning of life?

2. Monogamy and polygamy

(a) Suppose we have a society with N_m men and N_f women. Using the analysis of the monogamous marriage market from Chapter 3 (see slide 4 of the corresponding notes) where women supply themselves on the marriage market and men demand women as wives, show that if N_m > N_f , women will receive all the gains from marriage at the monogamous equilibrium point e_m.

(b) Show that if N_m > N_f polygamy doesn't raise women's payoff from marriage. Why not?

(c) Consider an economy with two types of men, type A and type B. All women are identical. Let MP_A1f > MP_A2f > MP_A3f > MP_1Bf > Z_f>
MP_A4f > MP_B2f , and 3N_m^A + N_m^B < N_f < 4N_m^A + N_m^B. What are the marriage market payoffs of each type of man and of women under monogamy? What are the marriage market payoffs of each type of man and of women under polygamy? (Use a graph it it helps.) Is polygamy likely to exist in this economy? Explain your reasoning why or why not.

(d) Why is there less polygamy worldwide today than 300 years ago?

Attachment:- economics-Lecture note.rar

Reference no: EM131296052

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Reviews

len1296052

11/30/2016 7:45:03 AM

This is a calculation-based course, so the assignment questions need to be solved by calculation as much as possible. I also provided lecture note for you to solve the assignment. You can find the how to solve the questions from the lecture notes. For question 1, you can start at page 23 of the lecture note i provided for question 1, those material from page 23 to the end covers the question 1, but if you think the lecture note i porvided is wrong, please tell me,or maybe you can find correct material from other place of the lecture note. For question 2, i also provided lecture note for chapter 3 that covers this question, the question also mentioned that you need to see page 4 of the lecture not for chapter 3.

11/30/2016 7:44:52 AM

This is a calculation-based assignment, so please sovle the questions by calculation as much as possible. I also submit lecture notes that relate to this assignment, the material from the lecture note will provide you fomular and other things you need to solve this assignment questions, so please read it and use it if you need

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