: This part considers a modified version of the Solow growth model. Suppose the production function is given by F(K,bN) = Kª(bN)!-a where b is the labour augmenting technology, which grows at a rate f, i.e., bị+1 = (1+ f)b.. For simplicity, assume that the total %3D factor productivity z = 1, and the population is constant, i.e., Ng = N for all t. The rest of the model is the same as in the standard Solow model in the textbook. Especially, the aggregate capital stock evolves according to Kt+1 = I; + (1 – d)Kt. And assume that the economy is still closed, and there is no government. For any aggregate variable X, let the lower case letter r be the variable per effective unit of worker; that is a = . ; Show that the production technology specified above satisfies the assumption of con- stant returns to scale.

: This part considers a modified version of the Solow growth model. Suppose the production function is given by F(K,bN) = Kª(bN)!-a where b is the labour augmenting technology, which grows at a rate f, i.e., bị+1 = (1+ f)b.. For simplicity, assume that the total %3D factor productivity z = 1, and the population is constant, i.e., Ng = N for all t. The rest of the model is the same as in the standard Solow model in the textbook. Especially, the aggregate capital stock evolves according to Kt+1 = I; + (1 – d)Kt. And assume that the economy is still closed, and there is no government. For any aggregate variable X, let the lower case letter r be the variable per effective unit of worker; that is a = . ; Show that the production technology specified above satisfies the assumption of con- stant returns to scale.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

Consider an economy described by the Solow model with the following production function: Y = F(K, L) = K“ (L)'-« L grows at the rate n, the depreciation rate is 8, and the country saves a constant fraction s of its income. The change in capital per-worker is given by Ak = sy – (n+ 8)k. (a) Derive the per-worker production function. (b) Assuming population growth equals n and the depreciation rate equals 8, find the steady state level of capital per worker. It will depend on a, s, n and 8. Imagine the economy begins at the steady state you found in part b. Then there is a war that destroys a substantial amount of the economy's capital. The war does not affect the size of the labor force, population growth, the depreciation rate, or the saving rate. c) What is the immediate effect of the war on output per worker? Explain. d) After the war, is the growth rate of output per worker higher or lower than it was in steady state? Explain. e) How does the war affect steady state output per…
Suppose the per-worker production function is: y = A(1-gA) Where ga is the fraction of all workers that produce technologies. Further, suppose the growth of technology is given by the following equation growth of A = (g//m)(L) Suppose L = 1 and m = 7, and that initially ga = 0.7. If ga fell to 0.8 the level of output per %3D worker would: fall Impossible to say rise stay the same
Consider the Solow model extended with human capital. Suppose the production function is Cobb Douglas. Find the levels of physical and human capital in the steady state. Describe the joint dynamics of the two forms of capital if the economy is not at the steady state.
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
9. Consider a numerical example using the Solow growth model. Suppose that F(K, N) KO.5N0.5, with d = z = 1, and take a period to be a year. (a) Determine capital per worker, income per capita, and consumption per capita in the steady state. 0.1, s = 0.2, n = 0.01, and
i need Question 6 solution
Consider our graph of the basic Solow growth model. On the graph above: y represents real output (or income) per worker; y=F(k) is the production function; k is the capital stock per worker; s is the savings rate; δ is the rate of depreciation of capital; ‘i’ represents business investment (purchases of capital) per worker); ‘LF’ stands for Loanable Funds. (For purposed of intuition, think of capital as ‘machines.’) If we started out with a capital (per worker) stock lower than the steady-state stock ( , above), we would expect to see which of the following happen over time? Group of answer choices A) Positive growth rates while the capital stock increases. B) Negative growth rates while the capital stock increases. C) Negative growth rates while the capital stock decreases. D) Positive growth rates while the capital stock stays less than the steady-state level. E) Positive growth rates while the capital stock decreases.