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Unformatted text preview: EC314-Fall 2010 Solutions Problem Set 4 Matt Turner (updated: 18 August 2010) . 1. 2. (a.) n l f = 1 f = 2 k = wn + lk (isocost) 2 a a 2 b b n l f = 1 f = 2 k = w n + l k (isocost) 2 a a 2 b b (b.) To minimize costs, we always want to be at the corner of the isoquant, along the dashed line in the figures. Along this locus, we have n a = l b . 1 3. 4. 5. (a.) We have u ( x ) = w- r ( x )- cx . Let u = 0 and let x denote the edge of the city. Then x satisfies u ( x ) = w- c x = 0, so that x = w c . In equilibrium, the rent gradient adjusts so that utility is equal throughout the city, u ( x ) = w- cx- r ( x ) = 0, which means that r ( x ) = w- cx for all x x and 0 for more distant locations. (b.) Let be the market discount factor and let = 10 . The land transfer tax requires payments tr ( x ) in years 9,19,29,... Thus, V ( x ) = ( 9 + 19 + 29 + ... ) tr ( x ) = 9 tr ( x )( 1 + 1 + 20 + ... ) = 9 tr ( x )( 1 + + 2 + ... ) = 9 tr ( x ) t = t 2 =...
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