Dynamic General Equilibrium model. Consider the basic dynamic general equilibrium model discussed in class and answer the following questions:

a. What is the objective of the Basic DGE model? What are some of the main simplifications?

b. Let the production function be given by F(k_t) = k_t^awhere 0 < < 1. Using the same notation as in class for the remaining variables, derive the resource constraint for this economy.

c. Define and compute the Golden Rule level of consumption and capital. Show the results in a graph. Why is the Golden Rule dynamically unstable? Continue assuming that the production function is given by F(k_t) = k_t^awhere 0 < < 1. Also, assume that the period utility function is given by U(c_t) = ln(c_t).

d. Find the Euler equation for an economy that maximizes the present value of current and future consumption subject to the resource constraint and transversality condition. (Set up and solve the intertemporal maximization problem, clearly show the constraint and transversality condition)

e. Interpret the Euler equation and depict the equilibrium of this economy in a simplified two period graph.

f. Is the optimal level of capital in the long run lower\higher than the Golden Rule level? Explain.

g. In a phase diagram, depict the dynamics of the optimal solution. Explain the direction of the arrows using the specific functions, the resource constraint and the Euler equation.

h. Using the phase diagram in part g, illustrate the effects of a permanent technology shock on the levels of capital, output and consumption. What about a temporary technology shock?