You are the chief economic advisor to the President of a country with an aggregate (per capita)production function of y= 2√k. The savings rate is 8% of output, the rate of depreciation is 10%, and population growth is 2%. There is no technological progress. a) On one graph, show the output, break-even investment (depreciation plus population growth), and savings functions for this economy (as a function of capital per worker). Denote steady state capital per worker k∗.
b) What is the numerical value of this economy’s steady state level of capital per worker? Output per worker?
c) If the economy’s original level of capital per worker is 4 units, describe how the economy works its way toward the steady state. Specifically, what is the numerical value of investment at k = 4? What is the numerical value of investment necessary to break even at k = 4? What do these variables tell you about what is happening to the capital stock?
d) If this country’s population growth rate increases to 8%, what would the new (numerical) value of capital per worker be? Output per worker?
e) How fast is this country growing in the steady state?
f) If technological progress (the growth rate of technology) increased to 3%, how fast would this country grow in the steady state?