2. Consider the Solow growth model without population growth or technological change. The savings rate is 20% (s = 0.2) and depreciation rate is 5% (8 = 0.05). Let k denote capital per worker; y output per worker; c consumption per worker; i investment per worker. (a) Rewrite production function Y = K1/3 L2/3 in per-worker term. (b) Find the steady-state level of the capital stock, k*.

2. Consider the Solow growth model without population growth or technological change. The savings rate is 20% (s = 0.2) and depreciation rate is 5% (8 = 0.05). Let k denote capital per worker; y output per worker; c consumption per worker; i investment per worker. (a) Rewrite production function Y = K1/3 L2/3 in per-worker term. (b) Find the steady-state level of the capital stock, k*.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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9. Suppose there is no population or technological growth. Define k as the capital-to-labor ratio. If the per worker production function is given by y = ¹/2, the saving ratio is 0.3, and the depreciation rate is 0.1, then the steady state capital per worker ratio is (a) 1 (b) 2 (c) 4 (d) 6 9
1) In the steady state of the Solow model with technological progress, which of the following variables is not constant? (a) capital per effective worker (b) the real rental price of capital (c) the real wage (d) the capital-output ratio
Let 0 be the saving rate, n the population growth rate and d the depreciation rate. Which of the following conditions is consistent with steady state in the Solow-Swan model? Y = 0K K = (n + d)Y O OY/L = (n+ d)K/L о өК — (п +d)Y
Question 2Assume production function is given by:Y= K(1/2) L(1/2)a. Write the production function in per worker terms (y=f(k))b. Assume that the per worker level of capital in the steady state is 4, the depreciation rate is 5% per year, and population growth is 5% per year. Does this economy have “too much” or “too little” capital? How do you know? [Show your work].
In this problem, we distinguish between labor and population in the Solow growth model. A proportion of the population, a, between zero and one, works. The production function is now written as Y = A(K^1/3)[(aL)^2/3] (a) How does an increase in a from 0.3 to 0.6 change steady state GDP? (b) Does it change the steady-state capital? Explain. (c) Suppose a rises steadily over time. How do you think would affect the growth rate of GDP?
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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.
Consider the Solow model with a production function Y(t) = A*K(t)αL(t)1-α, Where A is a fixed technological parameter. Explicitly solve for the steady-state value of the per capita capital stock and per capita income. How do these values change in response to a rise in (a) the technological parameter A, (b) the rate of saving s, (c) α , (d) δ, the depreciation rate, and the population growth rate n?
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
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The convergence to a steady-state capital-labour ratio k* is ensured by the fact that if k is at a level Multiple Choice lower than k*, saving will exceed the investment required to maintain constant k, causing k to rise lower than k*, investment will exceed saving, leading to an increase in the capital stock lower than k*, saving will exceed the investment required to maintain a constant k, causing output per capita to decline higher than k*, the rate of depreciation will be higher than the savings rate, causing k to decrease higher than K*, output per capita will continue to increase until a new steady-state equilibrium is reached