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ECON 366 Notes (09.22.2008)

# ECON 366 Notes (09.22.2008) - Econ 366 Notes If input...

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Econ 366 Notes 9/22/2008 If input substitution is possible - at small values of u, land is more expensive than capital as R(u) rises linearly - thus at small values of u, the input ratio that is optimum (makes profits = 0) at large values of u would not be optimum at small values of u - therefore if R(u) rises linearly as u decreases profits will be positive at small values of u - R(u) must rise faster than linearly as u becomes small, if profit is to be 0 at each u - More capital is substituted for land (heights of buildings grow as one approaches the city center) Model - Two marginl productivity conditions (1), (2) o MPK(u)[p – tu] = r ((MPK at distance u)*(net price at exp point) = r) o MPL(u)[p-tu] = R(u) ((MPL at distance u)*(net price at exp point) = land rent at distance u) - Equation relating land use to land available o L(u) = (Circle with line through middle)/2(u) 2 - Production function Q = F(K, L) o Determine land, capital, output, and land rent at each u - Overall demand supply equation and - Equation R(u*) = R* o Determines the price of commodity, radius of urban area Households -

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