Consider an economy whose production can be characterized by the following production function: Yt = 2K^5 N^5
Suppose that individuals in this economy invest 30% (use .30 in the graph) of what they produce; the labor force in this economy grows at 5% (use .05) per year; and 10% (use .1) of the capital stock wears out each year.
a. Write the production function in per worker terms. Draw a graph of this production function. Introduce a curve that shows the level of investment in the economy for each value of k. Add a segment that shows the required rate of investment for a steady state capital labor ratio. What is the slope of this last line? Show the steady state equilibrium points. Label carefully.
b. Suppose that the capital labor ratio equals 9. Calculate the value of investment in the economy. Calculate the required rate of investment for k = 9 to be a steady state. Is 9 a steady state capital labor ratio? Why or why not.