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Question 2 (30 points) A simple economy is represented by the Cobb-Douglas production function, Y = K0.25 N 0.75. Labour is growing at an annual
Question 2 (30 points) A simple economy is represented by the Cobb-Douglas production function, Y = K0.25 N 0.75. Labour is growing at an annual rate of 1% and the depreciation rate is 4%. A. If the saving rate as a fraction of income is 40%, what are the steady-state levels of the capital-labour ratio, per capita income, and per capita consumption? (15 points) B. Define the golden rule capital-labour ratio. At the steady-state value of the capital-labour ratio in part A, is there more or less capital than at the golden rule level? (Hint: Calculate the golden-rule capital-labour ratio and compare it to your answer for the steady-state capital-labour ratio in part A. Round your responses to two decimal places.) (8 points) C. Is the economy's saving rate too high, too low, or just right? Draw an accurate diagram to justify your answer. Include your numerical calculations for the capital-labour ratio from parts A and B in the diagram. (Hint: Add a tangent to your diagram.) (7 points) Question 2 (30 points) A simple economy is represented by the Cobb-Douglas production function, Y = K0.25 N 0.75. Labour is growing at an annual rate of 1% and the depreciation rate is 4%. A. If the saving rate as a fraction of income is 40%, what are the steady-state levels of the capital-labour ratio, per capita income, and per capita consumption? (15 points) B. Define the golden rule capital-labour ratio. At the steady-state value of the capital-labour ratio in part A, is there more or less capital than at the golden rule level? (Hint: Calculate the golden-rule capital-labour ratio and compare it to your answer for the steady-state capital-labour ratio in part A. Round your responses to two decimal places.) (8 points) C. Is the economy's saving rate too high, too low, or just right? Draw an accurate diagram to justify your answer. Include your numerical calculations for the capital-labour ratio from parts A and B in the diagram. (Hint: Add a tangent to your diagram.) (7 points)
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