1. Suppose the aggregate production function in the SolowSwan model is CobbDouglas, y = k\

1. Suppose the aggregate production function in the Solow-Swan model is Cobb-Douglas, y ,lcQ, with a 0.3. Assume population growth n 2%, technology growth g 3%, and depreciation 10%. (a) Derive k* , y* , and c* as functions of the model parameters and determine their values when the saving rate s 15%. (b) Assume both labour and capital are paid their marginal products and the economy is on a balanced growth path at time t 0: i) What is the real wage w(0) if A(O) 1? ii) What is the growth rate of wages qi'/w? iii) What is the return to "working" capital r? (working refers to capital minus depre- ciation) iv) What are the shares of income going to (both "working" and "dead/depreciated") capital and to labour? (c) How would your answers to part (b) change if the saving rate were s' 30% and the economy was on the balanced growth path? (d) Draw the transition given a change in the saving rate from s 15% to s' = 30% in the basic diagram for the Solow model (You may use MATLAB to make this diagram if you like). (e) What are the growth rates of real wages, qi'/w, and the return on working capital, i/r at the beginning of the transition when k 1? What do these results predict about real wage growth and the return on working capital as an economy with a high saving rate such as China gets closer to the new steady state? (f) Can the economy achieve a higher c* than for s = 30%? Why or why not?