ps4_sol - EC314-Fall 2010 Solutions Problem Set 4 Matt...

This preview shows pages 1–3. Sign up to view the full content.

EC314-Fall 2010 Solutions – Problem Set 4 Matt Turner (updated: 18 August 2010) . 1. 2. (a.) 0 n l f = 1 f = 2 k = wn + lk (isocost) 2 a a 2 b b 0 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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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 0 + δ 20 + ... ) = δ 9 tr ( x )( 1 + α + α 2 + ... ) = δ 9 tr ( x ) Σ t = 0 α t 2
= δ 9 tr ( x ) 1 1 - α = δ 9 tr ( x ) 1 - δ 10 We need Tr ( x ) such that V ( x ) = Σ t = 0 δ t Tr ( x ) = V ( x ) = 1 1 - δ Tr ( x ) = ( 1 - δ ) V ( x ) = Tr ( x ) (c.) The after tax rent gradient R ( x ) = ( 1 + T ) r ( x ) , where r is what landlords keep.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern