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Unformatted text preview: Macroeconomics 1. Master APE. 2009-2010. TD6 Prof. Xavier Ragot / T.A : Eric Monnet To work on these exercises, you can use your classnotes on overlapping gener- ation models, and Chapter 2 - part B of Romer's textbook for example. If you have not done it yet, rst nish the exercise on RBC. 1 Diamond Overlapping Generations Model Consider the Diamond overlapping generations model. L t individuals are born in period t and live for two periods, working and saving in the rst and living o capital in the second period. Assume population is growing at a constant rate, n , and technological progress occurs at exogenous rate g . Markets are competi- tive and labor and capital are paid their marginal products. There is no capital depreciation. Utility is logarithmic with individual discount rate > ρ >- 1 . U = log ( c t ) + 1 1 + ρ log ( c t +1 ) The production function is Cobb-Douglas , with output (Y), capital (K), labor(L), and 'knowledge' or 'e ectiveness of labor'(A) to which g applies : Y = F ( K,AL ) ....
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- Fall '09