Concise answers only please in details.

PRELIMINARY EXAMINATION FOR THE Ph.D. DEGREE Directions: Answer all questions. Short Answer Questions - Keep your answers short and concise. (Each question is worth 5 points.) 1. Consider two closed economies that have the same real interest rate. If consump- tion growth is higher and less volatile in Economy A relative to Economy B, what implications does this have for preferences in the two economies? 2. One of the stylized facts of growth is a growing wage rate and a (relatively) constant labor supply. What restrictions does this place on agents' preferences? 3. In the Solow model, what happens when there is a permanent increase in the savings rate? Describe both the transition and steady-state effects. What economic forces are at work? 4. An equity is a claim to a stream of future dividends. Suppose that dividends grow at a constant rate g and are discounted at a constant rate r, with r > 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.Given this environment, do the following: (a) Write down the agents' maximization problem. (b) Derive and interpret the associated necessary conditions. (c) Define a recursive competitive equilibrium in this economy. (d) Prove that, in equilibrium, equity prices are procyclical while interest rates are countercyclical. (e) Give an intuitive proof for the sign of the equity premium in this economy. 8. Consider an exchange cash-in-advance economy similiar to that studied by Alan Stockman in which the money supply, Mr, grows at the (gross) constant rate / > 0 so that My = /M-1. The endowment in this economy is stochastic and can take on two values (x1, x7) with x1