Only for Question4.

3 Exercise: Business Cycle and Consumption Smooth- ing Consider a 2-period economy in which Y; = A Kt. The households start with a quantity Q1 > 0 of initial assets and maximize lifetime utility given a per-period utility function u(e) = ln(e). 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 mcans finding the value of all cquilibrium objects as a function of the parameters of the model: A1, A2, a, b, d, a1 5. Assume that A1 = A = 1 and A2 = 1. What is requal to? 6. Assume that A1 = A=1-A and A2 = 1. What is ri cqual to? 7. What is the percentage difference between A and A ? That is, find the value of r such that Aj = (1+2) A. What is the percentage difference between rand r1? How do these two differences relate to cach other and what does this connection remind you of? 3 Exercise: Business Cycle and Consumption Smooth- ing Consider a 2-period economy in which Y; = A Kt. The households start with a quantity Q1 > 0 of initial assets and maximize lifetime utility given a per-period utility function u(e) = ln(e). 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 mcans finding the value of all cquilibrium objects as a function of the parameters of the model: A1, A2, a, b, d, a1 5. Assume that A1 = A = 1 and A2 = 1. What is requal to? 6. Assume that A1 = A=1-A and A2 = 1. What is ri cqual to? 7. What is the percentage difference between A and A ? That is, find the value of r such that Aj = (1+2) A. What is the percentage difference between rand r1? How do these two differences relate to cach other and what does this connection remind you of