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OLG_PS - Problem Set 1 OLG Models Econ720 Fall 2009 Prof...

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Problem Set 1: OLG Models Econ720. Fall 2009. Prof. Lutz Hendricks 1 An Economy with Land Consider a two-period OLG model in which production requires land and labor. Agents hold land as their M units per young household. The cohort size is constant and normalized to one. Each household supplies one unit of labor when young. (a) Write down the household±s budget constraints. Note that the household sells his land holdings at price q t +1 when old. Denote the purchase price of land by q t and its rental price by r t +1 . (b) Derive the household±s FOCs and Euler equation. Utility is u ( c y t ) + ( c o t +1 ) (c) has constant returns in land and labor: F ( M;L ) (d) De&ne a competitive equilibrium.
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