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RandD_PS

RandD_PS - Problem Set 6 Innovation and Growth Econ720 Fall...

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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 innovators²monopoly 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 0 c 1 ° ° ° 1 1 ° ° ± e ° ±t dt: (1) Technology: ² Final goods are produced from labor and intermediate inputs according to Y i = AL 1 ° ² i ± N X j =1 ( X ij ) ² ; (2) where 0 < ± < 1 , Y i is output, L i is labor input, X ij is the input of the j 0 th type of the intermediate good, and N is the number of varieties. ² It takes one unit of ³nal goods to produce one unit of intermediates: X j = Y j (3) ² It costs ² units of the ³nal good to create a new type of intermediate good. Market arrangements: ² The ³nal goods sector is perfectly competitive.

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