Please show your full work on question (a) to question (d).

Part A: Consumption Suppose that a household lives for two periods and has a utility function and intertemporal budget constraint as follows: U(c1,c2)=1(c10.5+c20.5)1ITBC:c1+1+rc2=y1+1+ry2 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. b) Find a solution for optimal consumption in both period 1 and 2 as a function of the parameter as well as the variables r,y1 and y2. c) What is the ceteris paribus effect on consumption today (c1) and tomorrow (c2) of the following shocks: (i) An increase in . (ii) A decrease in lifetime income. (iii) An increase in . d) Is there a condition where c1=c2 ? If so, what value must assume