Part A: Consumption Suppose that a household has a utility function and intertemporal budget constraint as follows: U(C 1, C2) = ( cp.5 + Bc2.5 ) 1 - Y 1 -y ITBC: C1 + C2= y1 + 2 1+r 1+r a) Determine the marginal rate of substitution for this utility function and derive 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. b) Find a solution for optimal consumption in both period 1 and 2 as a function of the parameter S as well as the variables r, y1 and y2