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7. Consider an overlapping generations version of the Lucas tree model. Specifically, an exchange economy is characterized by a random total endowment of x, each period. It is assumed that x, is distributed identically and independently over time. Each period a new generation (that lives for two periods) is born. There is no population growth so you can think of the economy at any point in time consisting of a repre- sentative young person and a representative old person. At birth, each agent receives a fraction yx, of the endowment (with 0 g. There is no uncertainty. The price of the equity is the present discounted value of this dividend stream. What is the price-dividend ratio? (Hint: I would do this in continuous time, but you don't have to.) 5. Re question (4), what happens to the price-dividend ratio when there is a permanent increase in r? How about when there is a permanent increase in g? Briefly provide economic intuition for each. Longer Answer Questions (Each question is worth 25 points.) 6. Risk neutrality v. certainty equivalence: Imagine a consumer with time-separable preferences, E: Esco Bu(Cits), where 0