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Unformatted text preview: Problem Set 6: Innovation and Growth Econ720. Fall 2009. Prof. Lutz Hendricks 1 Stochastic patent duration [Due to Matt Doyle] Consider a version of the &Expanding Variety of Goods model in which innovatorsmonopoly power diminishes over time. Otherwise the model is standard. Demographics: There is a single representative household. Endowments: The household is endowed with L units of labor, which can only be used for work. Preferences: U = Z 1 c 1 & & & 1 1 & & e & t dt: (1) Technology: Final goods are produced from labor and intermediate inputs according to Y i = AL 1 & i N X j =1 ( X ij ) ; (2) where < < 1 , Y i is output, L i is labor input, X ij is the input of the j th type of the intermediate good, and N is the number of varieties. It takes one unit of nal goods to produce one unit of intermediates: X j = Y j (3) It costs units of the nal good to create a new type of intermediate good....
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