The Ramsey economic growth model is a social planner problem which is to maximize the utility subject to resource constraints. Formally, >B'U(c) subject to + k1 = (1 8)kt + f(k) max Ct,kt+1 t=0 where B is a discount parameter, U is the utility function, 8 is the depreciation rate and f is the production function. Use the Lagrangian multiplier method to write down the first order condition.