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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1) The depreciation rate of capital in the US is 8 = 0.043 and the population growth rate is g₁ = 0.007. Moreover, Y/K is around 0.35 on average over the last 60 years in the US (see the graph below). If the saving rate is s = 0.2 in the US, then find the long-run growth rate of average income in the US according to the Solow's model. (Note: To cross-check Compare your theoretical result with the actual growth rate of average income in the US which is 2%.) 0,43 0,41 0,39 0,37 0,35 0,33 0,31 0,29 0,27 0,25 1950 1953 1956 1959 1962 1965 Y/K in the US 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010
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