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191ps6sol - Therefore the change in rule does not affect...

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1 ECON191 Spring 2010 Outline of suggested solutions to Problem Set 6 Point E is initial endowment: 0 hours of music time for Ada and 10 units of other goods For Ada, A forA MRS y dx dy = - = * * * For Bill, B forB MRS y y dx dy = - - = - = ) 12 ( * Along the contract curve, MRS A = MRS B , therefore * * 12 y y - = Contract curve: 6 * = y . The contract curve is a horizontal line with 6 * = y The slopes of the indifference curves at the tangency are 6 * - = y . The slopes do not change along the contract curve Competitive equilibrium before Ada is allowed to play music is at M. Ada has 6 hours of music and 9 units of other goods. After the change in rule, the new endowment point is F (Ada has the right to play music). Competitive equilibrium is at N. Ada has 6 hours of music time and 11 units of other goods.
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Unformatted text preview: Therefore, the change in rule does not affect the length of music for Ada The above results are true only because music/quietness is independent of any income effect, given the utility functions (the contract cure is horizontal). This is not a general result. If we do not have this very special kind of utility function, there is no guarantee that the competitive equilibrium noise level remains at 6 hours. So with different utility functions, once the dorm rule changes, the noise level also changes. (the competitive equilibrium will move along contract curve that is not horizontal) 0A Y A * = Y A ’ = 6 Y B = 12 X B = 10 X A = 10 U A1 U B1 Contract Curve Slope = -6 0B M E F N X A ’ = 11 X A * = 9...
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