1. Suppose that the aggregate production function in the Solow-Swan model has the Cobb-Douglas form, y = ka. Also, assume a = 0.35, saving rate s = 15%, population growthn = 5%, technology growth g = 10%, and no depreciation ổ = 0%.(a) Show that f'(k) > 0, f"(k) < 0, and the Inada conditions limp-of"(k) = o andlimz f'(k) = 0 are satisfied.(b) What are the numerical steady-state values of y* and e*? Show your workings.(c) Why is the steady state unique?(d) Assume labour and capital are paid their marginal products and the economy is on abalanced growth path at time t = 0:i) What is the real wage w(0) if A(0) = 1?ii) What is the growth rate of wages w/w along the balanced growth path?iii) What is the return to "working" capital r?iv) What are the shares of income going to capital and to labour?v) If the depreciation rate were positive (e.g., 6 = 10%), explain what would hap-pen to the return to "working" capital r and the shares of income going to (both"working" and "dead/depreciated") capital and to labour compared to the no de-preciation case?(e) Draw the transition path given a change in the saving rate from s = 15% to s' = 25%in the basic diagram for the Solow model.(f) Again assuming no depreciation 8 = 0%, what are the growth rates of real wages,i /w, and the return on working capital, ř/r at the beginning of the transition whenk = 1? What do these results predict about real wage growth and the return on work-ing capital as an economy with a high saving rate such as China gets closer to the newsteady state?(g) Can the economy achieve a higher c* than for s' = 25%? Why or why not?Nou oogideRomag model ith th e gomoobh Douglog ngmproduation fung

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1. Suppose that the aggregate production function in the Solow-Swan model has the Cobb- Douglas form, y = n = 5%, technology growth g = 10%, and no depreciation 6 = 0%. k. Also, asSume a = 0.35, saving rate s = 15%, population growth (a) Show that f"(k) > 0, f"(k) < 0, and the Inada conditions limof"(k) = x and lim- f" (k) = 0 are satisfied. (b) What are the numerical steady-state values of y* and e? Show your workings. (c) Why is the steady state unique?

1. Suppose that the aggregate production function in the Solow-Swan model has the Cobb- Douglas form, y = n = 5%, technology growth g = 10%, and no depreciation 6 = 0%. k. Also, asSume a = 0.35, saving rate s = 15%, population growth (a) Show that f"(k) > 0, f"(k) < 0, and the Inada conditions limof"(k) = x and lim- f" (k) = 0 are satisfied. (b) What are the numerical steady-state values of y* and e? Show your workings. (c) Why is the steady state unique?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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