ufp_ps3_12_sol

# Income in community 1 is uniformly distributed over

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Income in community 1 is uniformly distributed over the interval [0 , y * ] which implies that the density is equal to 1 y * . The mean income levels in community in community 1 is, therefore, given by the following expression: ¯ y 1 = Z y * 0 1 y * x dx = y * 2 (13)

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Similarly, the mean income levels in community in community 2 is: ¯ y 2 = Z 1 y * 1 1 - y * x dx = 1 + y * 2 (14) Moreover, y * must be indifferent between community 1 and community 2, and hence we have: (1 + y * )(1 + y * 2 ) - c 1 = (1 + y * )(1 + 1 + y * 2 ) - c 1 - Δ (15) Hence (1 + y * ) 1 2 - Δ = 0 (16) and hence y * = 2Δ - 1. Problem 3: Poverty (20 percent) a) Early childhood education such as the Perry Preschool Program improve school readiness and increase cognitive and non-cognitive skills. Career academies keep students engaged in high school by teaching around career themes and partnering with local employers to give kids work experience. b) The Philadelphia Youth Networks provides a variety of summer internship programs that provide valuable work experience and improve job readiness of disadvantaged youth.
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