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# Specifically n g j 1 h yp b j 1 i o = n g j h yp b j

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Unformatted text preview: Specifically,- n g j +1 + h yp- B j +1 i o =- n g j + h yp- B j i o (27) Collect terms containing y on the left-hand side: y h p- B j +1- p- B j i = h g j- g j +1 i (28) Solve for y y = h g j- g j +1 i h p- B j +1- p- B j i 1 (29) c) Households that indifferent between both communities are still characterized by the indifference condition as above. Since households also differ in , it is useful to rewrite this indifference condition as y = h g j- g j +1 i h p- B j +1- p- B j i (30) Rearranging and taking logs yields ln( )- ln( y ) = K j where K j = ln p- B j +1- p- B j g j- g j +1 The boundary indifference condition is thus a line in the (ln y, ln )-space. The slope is determined by , the intercept is given by K j . Note that &amp;lt; 0 so the slope is negative. Higher income households must have lower preferences for public goods to be indifferent. d) Consider an equilibrium in which two communities have different housing price, say p 1 &amp;lt; p 2 (31) We are interested in an equilibrium in which both cities have positive population. The level of public good in community 2 should be higher than that of community 1, g 1 &amp;lt; g 2 (32) Otherwise all people will choose community 1 because it is cheaper and better. The set of individuals that are indifferent between community 1 and 2 are given by the equation derived in problem (c). Plotting this line, the equilibrium sorting will then look as follows: Note that holding tastes for public goods fixed at some level we have perfect sorting of households by income. But since households differ in tastes, there will not be perfect sorting by income in equilibrium. Problem 4: Externalities and Cap &amp;amp; Trade a) The social optimum requires that Marginal Benefit = Marginal Cost for each firm....
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Specifically n g j 1 h yp B j 1 i o = n g j h yp B j i o(27...

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