3 Exercise: Business Cycle and Consumption Smooth- ing = Consider a 2-period economy in which Yt AtKt. The households start with a quantity aj > 0 of initial assets and maximize lifetime utility given a per-period utility function u (c) = ln (c). = 1. Do households earn any labor income? Solve the household's Euler Equa- tion. 2. Solve the firms' problem. Is the production function constant returns to scale? Do firms make any profits? 3. Define an equilibrium for this economy. > = = 4. Solve for the equilibrium of this economy. Solving for the equilibrium means finding the value of all equilibrium objects as a function of the parameters of the model: A1, A2, a, b, d, a1 5. Assume that Aj = A = 1 and A2 1. What is ri equal to? 6. Assume that A1 = Af = 1- A and A2 = 1. What is ri equal to? 7. What is the percentage difference between A and A ? That is, find the value of x such that Ai = (1 + x) A. What is the percentage difference between r and ri ? How do these two differences relate to each other and what does this connection remind you of? = = 3 Exercise: Business Cycle and Consumption Smooth- ing = Consider a 2-period economy in which Yt AtKt. The households start with a quantity aj > 0 of initial assets and maximize lifetime utility given a per-period utility function u (c) = ln (c). = 1. Do households earn any labor income? Solve the household's Euler Equa- tion. 2. Solve the firms' problem. Is the production function constant returns to scale? Do firms make any profits? 3. Define an equilibrium for this economy. > = = 4. Solve for the equilibrium of this economy. Solving for the equilibrium means finding the value of all equilibrium objects as a function of the parameters of the model: A1, A2, a, b, d, a1 5. Assume that Aj = A = 1 and A2 1. What is ri equal to? 6. Assume that A1 = Af = 1- A and A2 = 1. What is ri equal to? 7. What is the percentage difference between A and A ? That is, find the value of x such that Ai = (1 + x) A. What is the percentage difference between r and ri ? How do these two differences relate to each other and what does this connection remind you of? = =