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2 3. Consider the following Solow model. Total output is given by Y = ZK3 N³ where K is the aggregate capital stock, N denotes the workforce, and z denotes total factor productivity. Assume that z = 1. Saving/investment is equal to 10% of output. Capital depreciates at a rate of 8% per year, while the work force grows at a rate of 2% a year. In the Solow model, the steady-state capital per capita, y*, satisfies the following equation: s.z(k) = (n + d)k* where s denotes the saving rate, n denotes the growth rate of the labor force, and d denotes the depreciation rate. • • Prove the equation above using the equation 7.18 in the textbook. Give a brief interpretation of the left-hand side and the right-side of the equation above. Calculate the steady state quantities k* and y*. *We could also say that we focus on what happens in the labour market in one period of time t, and we ignore what happened in the past t - 1, or what will happen in the future t + 1. OR, we could assume that all processes are repetitive, and it is enough to look at one period in order to understand the history and predict the future.

2 3. Consider the following Solow model. Total output is given by Y = ZK3 N³ where K is the aggregate capital stock, N denotes the workforce, and z denotes total factor productivity. Assume that z = 1. Saving/investment is equal to 10% of output. Capital depreciates at a rate of 8% per year, while the work force grows at a rate of 2% a year. In the Solow model, the steady-state capital per capita, y*, satisfies the following equation: s.z(k) = (n + d)k* where s denotes the saving rate, n denotes the growth rate of the labor force, and d denotes the depreciation rate. • • Prove the equation above using the equation 7.18 in the textbook. Give a brief interpretation of the left-hand side and the right-side of the equation above. Calculate the steady state quantities k* and y*. *We could also say that we focus on what happens in the labour market in one period of time t, and we ignore what happened in the past t - 1, or what will happen in the future t + 1. OR, we could assume that all processes are repetitive, and it is enough to look at one period in order to understand the history and predict the future.

Economics (MindTap Course List)
Economics (MindTap Course List)
13th Edition
ISBN:9781337617383
Author:Roger A. Arnold
Publisher:Roger A. Arnold
Chapter17: Economic Growth: Resources, Technology, Ideas And Institutions
Section: Chapter Questions
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2 3. Consider the following Solow model. Total output is given by Y = ZK3 N³ where K is the aggregate capital stock, N denotes the workforce, and z denotes total factor productivity. Assume that z = 1. Saving/investment is equal to 10% of output. Capital depreciates at a rate of 8% per year, while the work force grows at a rate of 2% a year. In the Solow model, the steady-state capital per capita, y*, satisfies the following equation: s.z(k) = (n + d)k* where s denotes the saving rate, n denotes the growth rate of the labor force, and d denotes the depreciation rate. • • Prove the equation above using the equation 7.18 in the textbook. Give a brief interpretation of the left-hand side and the right-side of the equation above. Calculate the steady state quantities k* and y*. *We could also say that we focus on what happens in the labour market in one period of time t, and we ignore what happened in the past t - 1, or what will happen in the future t + 1. OR, we could assume that all processes are repetitive, and it is enough to look at one period in order to understand the history and predict the future.
Transcribed Image Text:2 3. Consider the following Solow model. Total output is given by Y = ZK3 N³ where K is the aggregate capital stock, N denotes the workforce, and z denotes total factor productivity. Assume that z = 1. Saving/investment is equal to 10% of output. Capital depreciates at a rate of 8% per year, while the work force grows at a rate of 2% a year. In the Solow model, the steady-state capital per capita, y*, satisfies the following equation: s.z(k) = (n + d)k* where s denotes the saving rate, n denotes the growth rate of the labor force, and d denotes the depreciation rate. • • Prove the equation above using the equation 7.18 in the textbook. Give a brief interpretation of the left-hand side and the right-side of the equation above. Calculate the steady state quantities k* and y*. *We could also say that we focus on what happens in the labour market in one period of time t, and we ignore what happened in the past t - 1, or what will happen in the future t + 1. OR, we could assume that all processes are repetitive, and it is enough to look at one period in order to understand the history and predict the future.
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