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Consider the following discrete-time optimal growth model with full depreciation:
Assume that u(.) is strictly concave and increasing for c ≥ 0, and f (.) is concave and increasing.
(a) Formulate this maximization problem as a dynamic programming problem.
(b) Prove that there exists a unique value function V (k) and a unique policy rule c = π(k), and that V (k) is continuous and strictly concave and π(k) is continuous and increasing.
(c) When will V (k) be differentiable?
(d) Assuming that V (k) and all other functions are differentiable, characterize the Euler equation that determines the optimal path of consumption and capital accumulation.
(e) Is this Euler equation enough to determine the path of k and c? If not, what other condition do we need to impose? Write down this condition and explain intuitively why it makes sense.
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Use an economic argument to explain why, in your example in part a,it might be profitmaximising for the firm to use both mechanisms rather than just using one mechanism?
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The average revenue schedule of a simple monopolist is: Pmkt = 5000-20Q The total cost schedule of the monopolist is: TC = 50Q2 + 100Q; and marginal cost is: MC = 100Q + 100 a) What is the market-clearing price for the monopolist b) How much will t..
Natural real GDP grows by 3 percent per year over the next five years, but then grows by 4 percent in the second year, 5.5 percent in the third year, 4.2 percent in the fourth year, and 3.5 percent in the fifth year. Calculate the cumulative loss..
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What term describes what these critics are claiming is occurring with regard to U.S.-Mexican trade as a result of NAFTA? Explain your reasoning.
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