Unformatted text preview: Demography/Economics 175 Professor Ronald Lee Problem Set 3 Due: Tuesday February 23, 2010 by 2pm [Submit paper preparation question separately via email; see page 3] Please turn in a hard copy of the problem set either at the beginning of class on February 23rd or anytime this week into the box located at the foot of the stairs in the Department of Demography (2232 Piedmont Ave). 1) Marriage and Divorce a) Define the terms “positive assortative mating” and “negative assortative mating.” Briefly describe the trait pairing of a hypothetical couple that exemplifies each term [in two sentences or less.] b) Use the following facts to answer the sub‐questions below: Shannon can earn 55 when working 100% time. Erin can earn 90 when working 100% time. Cameron can earn 35 when working 100% time. Each person absolutely requires home production tasks that would take half of the potential time for earning money, but alternatively his/her spouse could complete all of the home production so that he/she could work full‐time if doing so would maximize utility. For each individual, utility equals money income plus 10 from the necessary home production. i) Calculate the utility of each person when single, assuming they devote 50% time to money earnings and 50% time to home production. ii) Compute the total utility of the Shannon/Erin pairing. iii) Compute the total utility of the Cameron/Erin pairing. iv) Compute the gains to marriage for each pair. v) According to the economic theory, when will a couple decide to divorce? Describe four factors that could be destabilizing to a marriage and explain why they could lead to divorce, with reference to gains from marriage [one sentence each]. Questions? (1) Ask a GSI during Office Hours or sections; or (2) send an email with your Q to [email protected]; or (3) check bSpace announcements and view/post on bSpace forums. For bSpace go to “Forums” ‐> “Problem sets” ‐> “Problem set #3”. If your question has not already been asked, click on “Post new thread” to write your question, together with the “title” of the question. Try to phrase it in such a way so as to not give away the answer to other students still working on the assignment. Thanks. Page 1 of 3 Demog/Econ 175 Professor Ron Lee Spring 2010 Problem Set 3 Due Feb 23, 2010 by 2pm Submit paper prep separately via email 2) Fertility: Value of Time and Quantity‐Quality Theory Standard Model of Fertility: n = Number of children x = Consumption by parents (goods) Y = Non‐wife’s income I = Total family income tc = Time mother must spend for each child. q = Goods that must be given to each child pq = Price of these child goods px = Price of parental consumption goods w = Wife’s potential or actual wage rate U = U(x, n) is the couple’s utility T = Total discretionary time per day, e.g. 14 hours Simplifying Assumptions: ‐ The wife does all child care, and the husband does none ‐ The amount of time spent per child by the mother is fixed ‐ The amount of goods given per child is fixed ‐ The amount of work by the husband is fixed ‐ The wife’s allocation of time to child rearing or the labor market is the choice variable ‐ Children are divisible, so one can have 2.38 children! a) Write expressions for the wife’s income from work, the total family money income, the total family money expenditures, and the family budget constraint. b) What is the shadow price of a child? Write the expression and explain in words. c) In a diagram, draw the budget constraint and indifference curve. Label the axes, the optimum (x*, n*), and nmax. d) Suppose that the wife’s wage decreases. In the same diagram draw the new optimum (x*’, n*’). e) Decompose the shift from (x*, n*) to (x*’, n*’) into an income and substitution effect. Label the intermediary (hypothetical) optimum (x**, n**). Which effect is larger? What explanation can you give for this set of shifts? f) Now suppose that parents care about the “quality” of their children as well so that the utility function becomes U=U(x, n, q) where q is the quality of children. According to Becker’s quality‐quantity theory, what happens to the demand for n and q as income rises? Explain. And is the answer different if income falls? Page 2 of 3 Demog/Econ 175 Professor Ron Lee Spring 2010 Problem Set 3 Due Feb 23, 2010 by 2pm Submit paper prep separately via email 3) Paper Preparation Exercise Logistics: The following questions should be answered and sent as an email to [email protected] with the subject heading “PS3 Paper Prep [First Name Last Name].” For example John Smith would send an email with the subject heading “PS3 Paper Prep John Smith.” You are encouraged to send us your email on February 23rd with the rest of the assignment but you are granted an automatic extension until Friday February 26th by 5pm PST for this paper preparation exercise if needed [not the rest of PS3!]. Instructions: In order to get started, provide answers (1 to 2 sentences) to each question below. You may want to reread syllabus sections about the term paper first. There are no incorrect answers, and you do not have to write your term paper based on your answers to these questions. The sole purpose of this exercise is to help you get started thinking about your paper long before it is due. If you need help with your paper topic ideas, see a GSI during office hours or Professor Lee. a) What is your research question? Try to state your hypothesis. b) Why is your question important and interesting? Why should we care about the answer to your question? c) What kind of data you need to answer your question? For example: what is your expected unit of observation (individuals, communities, states, countries)? d) Are the data you describe in c) available? Where? (Name a publication or web site where the data are available, and the organization that gathers the data.) If not, tell us what data you could try to use instead. PAPER PREPARATION RESPONSES SUBMITTED AS PART OF THE WRITTEN PROBLEM SET ANSWERS ON FEBRUARY 23rd WILL BE IGNORED – we need you to send one email directly to GSIs at [email protected] for feedback. Please resend your paper prep email only if you have not received comments by March 15th. Thanks. Page 3 of 3 ...
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