This is 1 problem with several sub-parts. My main issue is that I'm not sure how to set up the lagrangian. I know that a0 and a2 should be set to 0.

Department of Applied Economics Johns Hopkins University Economics 602 Macroeconomic Theory and Policy Assignment 4 Professor Sanjay Chugh Spring 2021 Due: Monday, February 22, 2021 at 11:00am ET (Note: all submissions must be submitted via Blackboard in PDF) Durable Consumption. In the two-period consumption-savings framework, the representative consumer's utility function is u (G , C2, a, 2UR) = In(c ) +yr . In(cDUR ) + B[In(c2 ) + 4 . In(c202)]. in which the parameter S (the Greek lowercase letter "beta") is a fixed exogenous number between zero and one, w (the Greek lowercase letter "psi") is a fixed exogenous strictly positive number, c, is the period-1 flow of "nondurable" consumption, c, is the period-2 flow of "nondurable" consumption, and c DUR and COUR are "durable" goods in periods 1 and 2, respectively. The relative prices of durable goods are P, DUR and P2 in periods 1 and 2, respectively. As can be seen in Figure 1, durable consumption goods are stock variables, not flow variables. Due to "wear and tear" of durable goods, an exogenous fraction & (the Greek lowercase letter "delta") of durable goods depreciates between periods. The depreciation parameter lies between zero and one (i.e., 0