Exercise5 - to . The government budget constraint is = T s...

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EC813A. PROBLEM SET 5. PLEASE HAND IN FRIDAY OCTOBER 21 ST . 1. (Durables and Money) . Consider the following model. Assume that the household can hold its financial wealth in money or foreign bonds with gross interest rate R . The household derives utility from consumption of a durable and a non-durable good, and from real money balances. Taking the government’s behavior as given, the household chooses to save by investing in the durable good, money or foreign bonds to maximize its lifetime utility of consumption and real money balances β s t s = t uc s () + vD s , M s p s subject to the budget constraint s . t . B s + 1 = RB s + Y s C s C s d T s M s p s + M s 1 p s The output, Y s , is produced using the durable good Y s = FD s () and the law of motion of the stock of durable good is D s = D s 1 + C s d . Note that the durable good cannot be produced domestically but must be purchased in the world market at the relative price of 1. The government follows a money supply rule, setting the constant money growth rate
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Unformatted text preview: to . The government budget constraint is = T s + M s p s M s 1 p s i) Find the state and control variables and define the value function and Bellman equation. ii) Derive the Euler conditions. iii) Assume R =1. Define a stationary equilibrium for this economy and derive the inflation rate (you do not need to derive durable and non-durable consumption explicitely). Is money neutral and/or superneutral in this economy? Show and explain. Hint: Contrast the case v D s , M s p s = ln D s + M s p s and v D s , M s p s = ln D s ( ) + ln M s p s . 2. Discuss the concepts of neutrality and super-neutrality of money. 3. Discuss the different theories of money and the drawbacks associated with each of them....
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