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Unformatted text preview: Problem Set 3: In&nite Horizon Model Econ720. Fall 2009. Lutz Hendricks 1 Land Prices with Capital Accumulation Consider the following economy with land and capital. There is a single good produced from land L and capital K according to K t +1 = A F ( K t ; L t ) + (1 & & ) K t & c t (1) where A is an exogenous productivity factor, & is the depreciation rate of capital, and c is consumption. The production function has constant returns to scale. Production takes place in a representative &rm which rents capital and land from households. The rental prices are r t and q t . The purchase price of land is p t . The aggregate endowment of land, L , is &xed. A single representative household orders consumption sequences according to P 1 t =0 t u ( c t ) . He receives income only from holding capital and land. (a) Set up the households Bellman equation. De&ne a solution to the household problem....
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