Q3. Consider the following Cobb-Douglas production function: Y = AL K- where 0 = 0.25 Assuming settings of Neo-Classical theory of investment derive the following: a. Function representing the current value of desired stock of capital. b. Current value of desired stock of capital when output is 5 billion S while rental cost is 0.12. c. Now suppose output is expected to rise to 7 billion S, find corresponding value in desired stock of capital? d. How would you define value of investment in the given context of discussion?

Q3. Consider the following Cobb-Douglas production function: Y = AL K- where 0 = 0.25 Assuming settings of Neo-Classical theory of investment derive the following: a. Function representing the current value of desired stock of capital. b. Current value of desired stock of capital when output is 5 billion S while rental cost is 0.12. c. Now suppose output is expected to rise to 7 billion S, find corresponding value in desired stock of capital? d. How would you define value of investment in the given context of discussion?

Economics: Private and Public Choice (MindTap Course List)

16th Edition

ISBN:9781305506725

Author:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson

Publisher:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson

Chapter9: An Introduction To Basic Macroeconomic Markets

Section: Chapter Questions

Problem 9CQ

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Q3. Consider the following Cobb-Douglas production function: Y = AL K1-0 where 0 = 0.25 Assuming settings of Neo-Classical theory of investment derive the following: a. Function representing the current value of desired stock of capital. b. Current value of desired stock of capital when output is 5 billion $ while rental cost is 0.12. c. Now suppose output is expected to rise to 7 billion $, find corresponding value in desired stock of capital? d. How would you define value of investment in the given context of discussion?
a. List all the equilibrium conditions of this model and Using the equilibrium conditions listed, write down an expression that describes the evolution of the aggregate capital stock, Kt over time. Briefly explain why this expression is not particularly convenient for our analysis of the model? b.Using your answer to the above question, derive the equation that describes the evo- lution of the the capital stock per effective unit of worker, kt. ' Why is the analysis in terms of the variables per effective unit of worker more useful than the one with the aggregate capital stock? c. Assume that a E (0, 1). Draw a diagram that describes the evolution of kt, and show that there exists a unique steady state, k* > 0. Label properly. Find the expressions for the steady state variables k*, y*, and c* in terms of the parameters of the model. , Now, assume that α = 1. Draw a diagram that describes the evolution of kt, and show that income per worker can grow indefinitely in this case. Label…
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