Macroeconomic question

The Golden Rule and Optimization In this section, we will use tools of mathematical optimization to solve for the optimal consumption in the steady state, much like the golden rule. Suppose we have a version of the Solow Growth Model in which there is no technological progress, population grows at rate n and depreciation is 8. Denote per capita capital as k and per capita consumption as c. You will denote the savings rate as s, though we will be trying to find it in this section. 1. Show how the law of motion for capital per capita kt+1 = kt+s f(kt) - Skt implies the steady state for k* = kt+1 =kt 2. Set up the optimization problem as we did in class to maximize steady state consu c* choosing s and using the constraint that c* = (1 s)f(k*) and the fact that k* is in steady state. 3. Solve for the golden rule savings rate when f(k) = ka 4. Solve for the golden rule savings rate when f(k) = log k (where log is the natural log). The Golden Rule and Optimization In this section, we will use tools of mathematical optimization to solve for the optimal consumption in the steady state, much like the golden rule. Suppose we have a version of the Solow Growth Model in which there is no technological progress, population grows at rate n and depreciation is 8. Denote per capita capital as k and per capita consumption as c. You will denote the savings rate as s, though we will be trying to find it in this section. 1. Show how the law of motion for capital per capita kt+1 = kt+s f(kt) - Skt implies the steady state for k* = kt+1 =kt 2. Set up the optimization problem as we did in class to maximize steady state consu c* choosing s and using the constraint that c* = (1 s)f(k*) and the fact that k* is in steady state. 3. Solve for the golden rule savings rate when f(k) = ka 4. Solve for the golden rule savings rate when f(k) = log k (where log is the natural log)