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Unformatted text preview: EC314Fall 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 δ be the market discount factor and let α = δ 10 . The land transfer tax requires payments tr ( x ) in years 9,19,29,... Thus, V ( x ) = ( δ 9 + δ 19 + δ 29 + ... ) tr ( x ) = δ 9 tr ( x )( 1 + δ 1 + δ 20 + ... ) = δ 9 tr ( x )( 1 + α + α 2 + ... ) = δ 9 tr ( x ) Σ ∞ t = α t 2 =...
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This note was uploaded on 11/04/2010 for the course ECO 314 taught by Professor Matthewturner during the Fall '08 term at University of Toronto.
 Fall '08
 MATTHEWTURNER

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