1. Consider the BelowSwan model in continuous time with the CobbDouglas aggregate pro duction function, y = k\

1. Consider the Solow Swan model in continuous time with the Cobb-Douglas aggregate pro- duction function, y = ku , constant savings rate s, depreciation rate (5, productivity growth g and population growth n. (a) Show that f' (k) > O, f < O, and the Inada conditions = and = O are satisfied. (b) What are the steady state values of and ? Show your workings. (c) Why is the steady state unique? Now consider country A with = 0.3, saving rate s = 15%, population growth n techn010ky growth g = 2%, and depreciation (5 10%. Assume labour and capital are paid their marginal products and that the country is on its balanced growth path at t = O. (d) Solve for the numerical vales of yi and cA? Show your workings. (e) What is the growth rate of capital in country A at t = O? (f) What are the growth rates of wages li'A/WA and return to capital iA/rA in country A at t = O? (g) Can country A achieve a higher c' than for s 15%? Why or why not? Now consider country B characterised by the same capital share a, saving rate s, population growth n, technology growth g, and depreciation (5 as in country A. Labour and capital are also paid their marginal products. Suppose, however, that country B begins with kB(O) = 0.5 att = O. (h) What is the growth rate of capital R B/ KB in country B at t = O? (i) What are the growth rates of wages li.'B/u.'B and return to capital iB/rB in country B at t = O? (j) Compare the growth rates of capital, wages, and returns to capital between countries A and B. What do the results predict about conditional convergence or catch-up effect?