Write down your name and the last 4 digits of your B-number on your assignment. You do not have to type up your homework. Legible hand writing will do. Plagiarism will lead to zero score. Each question is worth 15 points.
- There are two types of agents in the marriage market: good (g) and bad (b). These characteristics are publicly observable. Suppose a proportion λ of agents in the market is good, and 1- λ bad. The marriage market is decentralized. At rate α, a meeting arrives. Conditional on meeting, with probability λ an unmatched agent will meet a good partner, and probability 1- λ the agent will meet a bad partner.
Match utility with a good partner is x_g. Match utility with a bad partner is x_b. Also, x_g > x_b. Suppose agents obtain no utility when single. To simplify matters, suppose once a marriage is formed, it lasts forever. Denote the value of single and the value of marriage for good and bad agents to be respectively V_g, V_b, W_g, and W_b, and the interest rate r.
(i) Write down the flow value of singlehood for good agents, rV_g. No need to simplify.
(ii) Good agents can either married to only good partners, or married to anyone. Suppose they married to anyone, simplify the value function V_g.
(iii) Work out the incentive constraint for good agents marrying anyone (the condition for them to marry anyone). Interpret it, what is the economics intuition in terms of λ and α?
(iv) Suppose good agents married to good agents only, simplify the value function V_g.