Suppose we have the Neoclassical Growth model that we have developed in class. 311 3 Jose A rows at the rate . Assume a reneraI ieriod utility function. u c . I I t g I? I: I .. . t b. d. . 'Write down the Social Planners problem in terms of per capita consumption and capital stock. Set up the Lagrangian1 solve, and give the equations that for every time period are necessary for a solution (Euler equation and resource constraint}. Using the resource constraint. show why along a BGP per capita consumption and capital stock are growing at the rate of technological progress. gr. . Using the Euler Equation explain what restriction we must make on our period utility function in order for a BGP to exist. write the Euler equation with this restriction. i.e. so it is independent of time. Solve for the initial capital stock per capita. k, and output per capita, y. \"-rrite down the expressions for the capital stock per capita at time t. fat. and output per capita at time t. 31:. . Suppose capital fully depreciates each period. 1Iii-"hat is the savings rate1 i along a BGP? Discuss hos.r the savings rate changes with o and 55'. explain the intuition. Hovi.r does the savings rate change with 9? Explain why the effect of g on s differs as or changes