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micro-fall2007-25

micro-fall2007-25 - Demand for Insurance The optimal...

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Unformatted text preview: Demand for Insurance The optimal insurance plan Choose y 1 and y 2 so as to maximize EU [( y 1 ; π 1 ; y 2 ; π 2 = 1 & π 1 )] = π 1 ¡ u ( y 1 ) + ( 1 & π 1 ) ¡ u ( y 2 ) under the constraints: y 1 : = W & L + ( 1 & ρ ) ¡ D , y 2 : = W & ρ ¡ D y 1 , y 2 ¢ Conditions for an optimum: ρ y 1 + y 2 ( 1 & ρ ) = ( W & L ) ρ + W ( 1 & ρ ) MRS = π 1 ¡ u ( y 1 ) ( 1 & π 1 ) ¡ u ( y 2 ) = ρ 1 & ρ Ani Guerdjikova ECON 313 Fall 2007 263 / 267 Demand for Insurance Example u ( y ) = ln y u ( y ) = 1 y In the optimum, MRS = π 1 & y 2 ( 1 ¡ π 1 ) & y 1 = ρ 1 ¡ ρ y ¢ 1 = π 1 [( W ¡ L ) ρ + W ( 1 ¡ ρ )] ρ y ¢ 2 = π 2 [( W ¡ L ) ρ + W ( 1 ¡ ρ )] 1 ¡ ρ Ani Guerdjikova ECON 313 Fall 2007 264 / 267 Demand for Insurance The optimal insurance plan 6- r ........... . . . . . . . . . . . . . . . . . . . . . . . . . . . . W W & L y 1 y 2 @ @ @ @ @ @ @ @ @ @ @ @ ρ 1 & ρ . ....
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micro-fall2007-25 - Demand for Insurance The optimal...

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