Read e-book online Advanced macroeconomics: Solutions manual PDF

By Romer D.

ISBN-10: 0070536686

ISBN-13: 9780070536685

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0; x2 / D 0 for all x2 0). However, u is stringently quasiconcave. x1 ; x2 / W x1 > 0; x2 0g is convex. t/, a strictly increasing function; then x 7! i /). Hence, u is stringently quasiconcave by Proposition 1. i v/. It is well-known that more can P be said, although this is not of importance for my applications. i i a/ the same is true for the CES utility function. Results from [5] or [12] can be invoked to derive such additional properties: see Remark 4 in [5, p. 3 and its Examples 5, 6 in [12].

Journal of Mathematical Economics 37, 259–267. 33. , Economic Theory 11, 403–412. 34. Ng, Y-K, 1972, Step-optimization, secondary constraints, and Giffen goods, Canadian Journal of Economics 5(4), 553–560. 35. , 1896, Cours d ’´economie politique, Rouge, Lausanne. 36. , 1925, Memorials of Alfred Marshall 1842–1924, Macmillan, London. 37. , 1999, Potato paradoxes, Journal of Political Economy 107(6), S294-S313. 38. , 1948, Economics: An introductory analysis, McGraw-Hill, New York. 39. Silberberg, E.

J. 1 t/p xO y by the given budget-balancedness of x (observe that p xO > 0 by xO 6D 0). This contradicts xO 2 B. d / First, if y D 0 then B D f0g, so x D 0 is the unique optimal solution. t; t; : : : ; t/ belongs to B for t > 0 small enough and because u is strictly monotone. Now suppose that x and x were two different optimal solutions of (1). 0/ by the previous argument. x /. This contradicts the optimality of x . So the optimal solution is unique. c/ with uniqueness. t u Remark 1. i / Without monotonicity in Theorem 1, the budget-balancedness of the optimal solution can obviously not be maintained, but a fair part of Theorem 1 continues to hold when u is nondecreasing and the details are as follows.

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Advanced macroeconomics: Solutions manual by Romer D.

by Ronald

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