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Partial Answers: Final Practice Questions May 5, 2006 Question 1 Solve for the price of stocks, p t Let’s assume that the total income of the young is y t , so per capita income of the young is y t / (1 δ ) (we could assume y t is per capita income for the young - the expressions would end up slightly di ff erent, but with exactly the same fl avor) Given the conjecture for individual consumption rules, aggregate consump- tion is given by C t = (1 δ ) P a =1 δ a 1 c a t = (1 δ ) (1 βδ ) y t 1 δ + δ (1 βδ )( s 2 t ( p t + d t )) + δ 2 (1 βδ )( s 3 t ( p t + d t )) + ... ¸ = (1 δ )(1 βδ ) y t 1 δ + δ ( s 2 t ( p t + d t )) + δ 2 ( s 3 t ( p t + d t )) + ... ¸ = (1 βδ ) y t + (1 δ )(1 βδ )( p t + d t ) £ δ ( s 2 t ) + δ 2 ( s 3 t ) + ... ¤ = (1 βδ )( y t + p t + d t ) where in the last step we use the fact that the old, in total, hold all the shares, so (1 δ ) £ δ ( s 2 t ) + δ 2 ( s 3 t ) + ... ¤ = 1 From market clearing C t = y t + d t Combining the two expressions for C t gives the equilibrium price p t = βδ ( y t + d t ) 1 βδ

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