1. Consider the SolowSwan model in continuous time with the Cobb-Douglas aggregate pro- duction function, y = k\

1. Consider the Solow-Swan model in continuous time with the Cobb-Douglas aggregate pro- duction function, y kea , constant savings rate s, depreciation rate 5, productivity growth g and population growth n. (a) Show that f'(k) > O, f" (k) < O, and the Inada conditions c and O are satisfied. (b) What are the steady-state values of k* , y* and c* ? Show your workings. (c) Why is the steady state unique? 15%, population growth n 3%, Now consider country A with a 0.3, saving rate s technology growth g 2%, and depreciation 10%. Assume labour and capital are paid their marginal products and that the country is on its balanced growth path at t O. (d) (e) (f) (g) Solve for the numerical vales of k*A, and c*A? Show your workings. What is the growth rate of capital R A (KA in country A at t O? What are the growth rates of wages ti'A/wA and return to capital i A/rn in country A at t O? Can country A achieve a higher c* than for s 15%? Why or why not?