lecture6 - Lecture 6 The Ramsey Model Pareto Efficiency An...

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Lecture 6 The Ramsey Model
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ECON 7240 VI - 2 Pareto Efficiency An allocation of goods across a group of people is called Pareto efficient if there is no way to reallocate the goods to make someone better off without making someone worse off. This is equivalent to the allocation maximizing some Pareto social welfare function . A linear combination of the utility functions of every member of the group.
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ECON 7240 VI - 3 A Representative Agent Pareto efficiency concept simplifies if there is a representative agent. There is only one agent. Pareto social welfare function must be the utility function of this agent. In Cass-Koopmans model, a technologically feasible allocation that maximizes the utility function is Pareto optimal. Pareto optimality does not involve markets.
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ECON 7240 VI - 4 The Ramsey Problem Given K (0), the social planner chooses C ( t ) and K ( t ) to maximize subject to dt t C u t L e t - 0 )) ( ( ) ( ρ ). ( )) ( ) ( ), ( ( ) ( ) ( ) ( t K t L t A t K F dt t dK t C t L δ - = +
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ECON 7240 VI - 5 The Ramsey Hamiltonian
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