Question 1 Monogamy and polygamy
(a) (10 points) Suppose we have a society with Nm men and Nf 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 Nm > Nf , women will receive all the gains from marriage at the monogamous equilibrium point em.
(b) (10 points) Show that if Nm > Nf polygamy doesn't raise women's payoff from marriage. Why not?
(c) (20 points) Consider an economy with two types of men, type A and type B. All women are identical. Let MPA1f > MPA2f > MPA3f > MP1Bf > Zf >MPA4f > MPB2f , and 2NA m + NB m < Nf < 3NA m + NB m. 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) (10 points) Why is there less polygamy worldwide today than 300 years ago?
家庭经济学代写As depicted in figure 1, the market equilibrium will happen at the intersection point ( ) of supply curve and demand curve. Only man will get married. All women will get an income of at the equilibrium point, thus they will receive all the gains from marriage (the gray striped area).
(b) Since , there are more men than women in the market, so no man would get a second wife even under polygamy. Therefore there will be man marrying one wife, while the rest ( ) men will be bachelor forever. This is the same situation with the case of monogamy. Women’s gain from the market will stay the same as depicted in the striped area of figure 1. Therefore, polygamy would not raise women’s payoff.
(c) Case of Monogamy: since the total number of women is larger than the total number of man( ), all men will get married with one wife. The supply and demand situation can be depicted in figure 2家庭经济学代写:
In the figure above, is the marginal product of first wife for type A man ( ); is the marginal product of first wife for type B man ( ). At the equilibrium point , women will get an income of , which is the same as their single output; type A man will get an income of ; type B man will get an income of . Therefore the type A man’s gain from marriage will be the green striped area; type B man’s gains from marriage will be the gray striped area. Women will be indifferent between marriage or single since their gains from marriage is zero.