The budget constraints for the low-wage individuals and high-wage individuals are, respectively, Cz + (1-tz) . WL . LL = (1-tz) . WI and CH + (1-TH) . WH. H = (1-TH) . WH, in which the "L" and "H' subscripts indicate, respectively, low-wage individuals and high-wage individuals. The Lagrange function for low-wage individuals is L,(C1, ],, ) = Inc, + Inl, + 2, . [(1-51) . WL -cz -(1-zz). W. Iz], and the Lagrange function for high-wage individuals is LH (CH,H, AH) = Inc# +Ing + AH . [(1-TH) . WH - CH -(1-TH) . WH . H]a. Based on the Lagrange function above for low-wage individuals, compute the first-order conditions (FOCs) for consumption and leisure. Display the two FOCs clearly. b. Based on the Lagrange function above for high-wage individuals, compute the first-order conditions (FOCs) for consumption and leisure. Display the two FOCs clearly. c. Based on the results obtained in part a, construct the consumption-leisure optimality condition for low-wage individuals, which should be written as ...= (1-1)WI, in which the term in ellipses ("...") is for you to determine. Display the final expression clearly. Clearly and carefully provide important algebraic steps. (Note: The final expression, even if correct, will be awarded ZERO points if there is no or very little clearly-written algebraic support behind it.) d. Based on the results obtained in part b, construct the consumption-leisure optimality condition for the high-wage individuals, which should be written as ... = (1-TH ) WH, in which the term in ellipses ("...") is for you to determine. Display the final expression clearly. Clearly and carefully provide important algebraic steps. (Note: The final expression, even if correct, will be awarded ZERO points if there is no or very little clearly-written algebraic support behind it.)