Suppose that a household lives for two periods and has a utility function and intertemporal budget constraint as follows: U (C1, C2) = ( c 1.5 + Bc2.5) 1- Y 1 -y ITBC: C1 + C2 = y1 + 2 1+r 1+r a) Derive step by step the Euler equation faced by this consumer (define the Lagrangian and then obtain first order conditions as we did it in the lecture). Explain the intuition of the Euler equation.Page No. Date; h = ( c 0. 5 + ( 2 0.5 ) " - 1( c, 4 / ( x ) - y - 943 1 - Y 2 1 = 1 2 8 ( c , 0 5 + ( , 015 ) J-. 05 61- 05 - 1 20 aci 1 - X - 1 20 -0 C, 0.5 + 6 2 0.5 0.5c, 6.5 - 0 .5 2 C 2 1- Y 0 5 +(, 0- 575 0.5 6 20.5 1+ 7 = 0 - G From 0 & 0 5 c , 05 C . 0.5 + 2 20 15 ) ) 0-5 6 2 10.5 cos ( ity ) = c , 0.5 G) using in B 4+ 9 yz . co5 2 0 C 20.5