Assume a production function is Cobb - Douglas in capital and labour. Y = ZF(K, N) = zK\alpha N1-\alpha (a) Derivethe per worker production function, y = zf (k) where y = Y/N, k = K/N (b) Use the Solow Model to derive the steadystate level of capital per worker, for given s, d and n. (c) Show diagrammatically the impact on the steady state solutionof i) a rise in z; ii) a rise in s, using both the Solow Model diagram and time path diagrams of Iny and Inc. (d)Showdiagrammatically (ideallysupplementedwithkeyequations)howtode rive the Golden Rule, and explain why thismatters for your answer to part c) ii) (e) Show diagrammatically the impact of a fall in n, in the short and long term

The objective of the question is to understand the Cobb-Douglas production function and its…

Answered: Assume a production function is Cobb -…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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A CES production function with physical and human capital Consider the CES production function in terms of physical capital, K, and human capital, H: where 0 a. Set up the Hamiltonian and find the first-order conditions. b. What is the optimal relation between K and H? Substitute this relation into the given production function to get a relation between Y and K. What does this “reduced-form” production function look like? c. What is the steady-state value of the ratio of physical to human capital, (K/H)∗? d. Describe the behavior of the economy over time if the initial condition is such that K(0)/H(0)? e. Suppose that the inequality restrictions IK ≥ 0 and IH ≥ 0 apply. How do these constraints affect the dynamics if the economy begins with K(0)/H(0)∗?
Consider the Solow model. Using suitable diagrams, compare the different dynamics for the levels and growth rates of capital per capita and output per capita following: (a) a new wave of immigration, (b) an increase in the saving rate, (c) a one-shot foreign investment which increase the size of the available stock of capital, (d) an important technological advance.
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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.
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Venezuela experienced a large outow of population. Choose one scenario for the subsequent Venezuelan economy that cannot be explained by Solow model. (a) Assume that productivity is constant. If those who subsequently leave return to Venezuela, then in the long run the amount of capital will return to what it was before the population outow. (b) According to the Solow model, the capital per worker should be above it's steady state. Assuming population and productivity are xed, thereafter, capital per worker will decline. (c) Assume that productivity is constant. The level of real GDP immediately after outows is lower than the original level because of the decline in population. (d) Assuming that the population remains unchanged permanently after the population outow, even in the short term, Venezuela's growth rate will be determined solely from the growth rate of productivity.
Given the following aggregate production function: Y = K0.25 (AL) 0.75, where technology A grows at a fixed rate: = g> 0 (a) Obtain the marginal product of capital algebraically, also discussing the second derivative. (b) Transform the production function into efficiency-worker terms, showing how =ỹ depends AL on =k. K AL
Given the following aggregate production function: Y = K0.25 (AL) 0.75, where technology A grows at a fixed rate: A=g>0 (f) Find the steady state solution algebraically for output per efficiency worker, ỹ, where (i = 1,2). Show all workings. (g) Outline and explain the behaviour of per worker variables along the model's balanced growth path.
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