Excel problem

The parameters for the benchmark case are: z = 1, s = 0.45, = 0.08, = 0.3.

1. Define the steady state value of capital and denote it by k . Show k in a graph that has Capital in the x-axis and Output, Depreciation, and Investment in the y-axis (you can use the Policy Rules sheet for the Excel file we worked on in class, but must update the parameters). What is the value of k in the benchmark case?

2. Define the golden rule value of capital, and denote it by kg. What is the difference between k and kg? (explain intuitively, feel free to use graphs). Compute kg for the benchmark case.

3. What happens with k when s increases to 0.5? Show how the graph changes and explain why k changes (you can use your Excel sheet to re-compute this value and to make the plots). What happens with kg? Explain.

4. How do k and kg change when z = 1.1 (assuming all other parameters are the same as in the benchmark case)?

5. Let's go back to our initial example with parameters z = 1, s = 0.45, = 0.08, = 0.3. Suppose that the initial value of capital is k = 4. How long does capital take to reach k = 11? What is the value of consumption, investment and output at this level? (use the Evolution sheet that we worked on in class for this).