ufp_ps3_12_sol

The utility in community 2 will be u =(1 1(1 1 c 2 =

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Unformatted text preview: the utility in community 2 will be: U = (1 + 1) (1 + 1)- c 2 = 4- c 1- Δ (3) The pay-off in community 2 is higher if Δ < 1. (b) Suppose all individuals live in community 2, then we know that ¯ y 2 = 0 . 5 (4) Consider the poorest person with income equal to 0. His utility from staying in community 2 is U = (1 + 0) (1 + 0 . 5)- c 1 = 1 . 5- c 1- Δ (5) If he moves to community 1, mean income be equal to zero, i.e. ¯ y 1 = 0 and the utility in community 1 will be: U = (1 + 0) (1 + 0)- c 1 = 1- c 1 (6) The pay-off in community 1 is higher if Δ > . 5. (c) Consider two individuals with y l < y h . Assume y h lives in 1 and y l lives in 2 with ¯ y 1 < ¯ y 2 . We will show that this assumption will lead to a contradiction. Consider the individual with income y l . The utilities from living in community 1 and 2 are: U ( y l , ¯ y 2 ) = (1 + y l ) (1 + ¯ y 2 )- c 2 = 1 + y l + ¯ y 2 + y l ¯ y 2- c 1- Δ (7) U ( y l , ¯ y 1 ) = 1 + y l + ¯ y 1 + y l ¯ y 1- c 1 for this to be an equilibrium, we need U ( y l , ¯ y 2 ) > U ( y l , ¯ y 1 ) (8) which implies that ¯ y 2 + y l ¯ y 2- Δ > ¯ y 1 + y l ¯ y 1 (9) and similarly for individual h , we need U ( y h , ¯ y 2 ) < U ( y h , ¯ y 1 ) (10) which implies ¯ y 2 + y h ¯ y 2- Δ < ¯ y 1 + y h...
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the utility in community 2 will be U =(1 1(1 1 c 2 = 4 c 1...

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