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2. (20) An economy is populated by identical, infinitely-lived agents (there is no population growth) that maximize the present discounted value of lifetime utility given by Coined; BE (0,1) where c denotes consumption. Output is produced via a standard Cobb-Douglas production function: where k, denotes the beginning of period capital stock. (Implicitly it is assumed that labor supply is inelastically supplied by households to firms and that the labor input has been normalized to unity. Hence the labor market is ignored in this analysis.) In addition to consumption, households choose investment. This produces next period's capital stock using the following production function: where 6, denotes a stochastic depreciation factor. It is assumed that this shock, the only source of uncertainty in the economy, is an i.i.d. random variable. Given this environment, do the following: (a) Solve for the recursive competitive equilibrium by solving the associated social planner's problem. In setting up the dynamic programming problem, use two constraints: the typical resource constraint and the capital production constraint. Denote the Lagrange multiplier on the budget constraint as At while the Lagrange multiplier on the capital production constraint is given by the product of Aqr where q is the shadow price of capital (in terms of consumption). (b) Derive the associated Euler equations for the social planner problem. Give an intuitive explanation for the determination of q. (c) Define and solve for the recursive competitive equilibrium in this economy. (Note: This is simplified by first using output (y:) as a state variable and then employing the guess and verify solution method.) (d) Give an intuitive explanation for the behavior of consumption and investment in this economy.1. (10) Briefly discuss the following statements (keep your answers short and concise): (a) The consumption-based capital asset pricing model is inconsistent with high volatility of stock prices. (b) In standard real business cycle models, the MPK is highly procyclical. This implies that interest rates (i.e. real) will be as well