Aflevering-2.pdf - Macroeconomics 3 Assignment 2 1 Consider...

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Macroeconomics 3 - Assignment 2 1) Consider an economy where individuals live for two periods, and population is constant. Utility for young individuals born in period t is U t = c 1 t + β ln( c 2 t +1 ) , β > 0 where c 1 t is consumption when young, and c 2 t +1 consumption when old. Young agents work a unit of time (i.e. their labor income is equal to the wage they receive). Old agents do not work and must provide consumption through saving (in capital and/or government debt, if this exists). Production for firm i that hires labor and capital is given by Y i t = A ( K i t ) α ( K t N i t ) 1 - α where A (1 - α ) > 1, K is the aggregate capital stock in the economy, K i and N i are the amounts of capital and labor hired by the firm (since there is no population growth, take the aggregate amount of labor, N , to be normalized to one). Markets for factors are com- petitive resulting in factors being rewarded their marginal products, r and w . Although the economy might trade with the rest of the world, it is assumed that production factors

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