Solve in short simple summary please
8. Consider an exchange cashin-advance economy similiar to that studied by Alan Stockman in which the money supply, it?\" grows at the {gross} constant rate it :- ill sothat If, = hall... The endowment in this economy is stochastic and can take on two values {.n, :1} with x. 1:: :1. it is assumed that x, follows a rst-order Markov process with a symmetric transition probability matrix with diagonal elements of I = [fl At the beginning of the period. agean observe the current value of the endowment and receive the lump sum monetary transfer. Agents first visit the goods market where consumption must be nanced from beginning of period money balances and the monetary transfer. That is. agents face a cash-in-advance constraint. Then agents visit the asset market where one period nominal bonds are traded and new money is acquired. The nominal bonds cost it in period t and return Sit +n.) in period t + l which is received in the asset market. i.e. after the goods market closes in period t + I. Also in the asset market. agents receive the proceeds of the sale of their endowment in the goods market. Agents make consumption and asset choices in order to maximise lifetime expected utility given by: m so [2 ,3: ln a] rut] Given this environment. do the following: {a} Write down the agents\" maximization problem as a dynamic programming problem and derive the associated necessary condition. {b} Amume that the cash-in-advance constraint is always binding. Equilibrium in this economy will be characterized by hvo values for real balances and true values for nominal interest rates. Characterize the behavior of real balances and interest rates in this My. {c} Suppose tea] bonds were introduced into this economy. 1Would the Fisher re- lationship hold? That is, would the real interest rate {1 + n} be equal to the expected real moon on nominal bonds as given by the following expression: P t+n=tt+msI (r11) it is NOT necessary to solve for the the real interest rate in this economy: simply make an intuitive argument based on economic theory. 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 qx, 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 ? How about when there is a permanent increase in g? Briefly provide economic intuition for each 6. Risk neutrality v. certainty equivalence: Imagine a consumer with time-separable preferences, E, Es of u(Cits), where 0
