Consider the following model based on Banerjee and Mullianathan (American Economic Review, 2008), where the utility function is

Q2. Consider the following utility function that individuals maximise U 2f\" p(166)(B c), 0 <: a c: e subject to income y="c+f." wherey="h(16)+," u. fand c are respectively food and comfort goods is the attention paid home p probability of error happening at home. h human capital individuals endowed with. decide on then level b. find optimal value c. show that will high mll always choose step write objective function interms this way budget constraint being included in too there no need for lagrange u="(y" now take first derivative with respect au ac="(-1)-" lp several things note:0 positive we can assume directly thay> a 1 - a Lp(1-80). To ensure this is indeed the maximum we need to check the second order condition azu a. (1 - a) do2 = (-1) ( y - c ) 2 - a 50 The negative second order condition ensures the sufficiency condition for the maximisation.(b) E} is chosen once optimal value of c is decided. Now put the optimal value of c in the utility function a: 1 [I m or E U 2 [10(1 66)] _ \"(1 _ 56) [B _ 3" + [p(1 56)] ] We replace 5! by the equation given in the question Thus, Bh(l)a+[]] U = []% p(1 as) Collecting terms we can write {I II U = (1 or) (BE (1 am pea 66) + p(1 66){h(1 6) + 5} Assume that Be{0,1}. Therefore i U09 2 D) = (1 or) [Era +133 +ph+ps $ me = 1) = (1 or) [an (1 mm + pB(1 a) + p(1 53.5 As can be seen, 6:0, level of h plays a role, that we don't see when 6:1. U = fa - p(1 - 80)(B -c), , 0