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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Given a saving rate of 6%, a depreciation rate of 1%, and a production function in which y = k0.5 where y is output per worker and k is capital per worker, calculate the steady state values for capital per worker, output per worker, consumption per worker, and Calculate the golden rule steady state level of capital Assuming an economy is at steady state, with the use of an appropriate diagram with descriptions illustrate the impact of a reduction in the saving rate on capital per worker and output per worker. In the context of the Solow model, illustrate with appropriate descriptions the impact of increased migrant workers on capital per worker and output per worker in an economy.
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W (2 bookr Suppose that the depreciation rate increases. In the Solow growth model, determine the effects of this on the quantity of capital per worker and on output per worker in the steady state. Explain the economic intuition behind your results.
Suppose that two countries share identical technology, depreciation rate, saving rate, and population growth. However, these two countries started off with different levels of capital stock. Which of the following is/are true? (i) The country with initially smaller capital stock grows more quickly to reach the steady state compared to the country with initially larger capital stock. (ii) The country with initially smaller capital stock will have a smaller capital stock in the steady state compared to the country with initially larger capital stock. (iii) Both countries will grow at the same rate in reaching the steady state. O a. Both (i) and (ii). O b. Only (iii). O c. Only (i). O d. Cannot tell. Need more information.
Consider a Solow-Swan model with saving rate s - 0.4, labour force growth g, - 0.05. constant productivity A = 1, and depreciation = 0.05. If output per worker is y = Y/L = 200 and capital per worker is k = K/L = 800, which of the following is true? O Efective depreciation per worker is 60, saving per worker is 80 and k will decrease towards the steady state Effective depreciation per worker is 80, saving per worker is 80 and k is at the steady state O Efective depreciation per worker is 60, saving per worker is 80 and k will increase towards the steady state O Effective depreciation per worker is 80, saving per worker is 60 and k will decrease towards the steady state
QUESTION 2 If Z = (XY)2, and we know that the annual growth rate of Z is 3%, and the annual growth rate of X is 2%, the annual growth rate of Y is а. - 1% b. - 0.5% C. 0.5% d. 1.0%
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