PROBLEMS (50 points) 1. (30 points) Consider the Solow model with technological growth. Assume the production func- tion is ye = 10ke-4, where output per efficiency unit of work ye = TT, is a function of capital per efficiency unit of work, ke = T.I. M. The saving rate in this economy is 30% of output, the yearly population growth rate is 1%, the yearly depreciation rate is 6%, and the growth rate of technology is 2%. (a) (12.5 points) Draw a diagram of the model, with ke, on the x-axis and ye, on the y-axis. Your diagram should have three curves; identify them. Identify the steady-state capital per efficiency unit of work, ke's, and output per unit worker, yes, in your diagram and calculate them. Suppose now that the depreciation rate increases to 8%. (b) (12.5 points) Calculate the new steady-state, ke's' and yes', and show the change in your diagram by redoing it. (c) (5 points) At what rate do aggregate output Y, output per worker y, and output per efficiency unit of labor ye, grow in the new steady-state? How does that compare to the original steady-state