We want to explore the role of infrastructure in economic growth by modeling infrastructure as productive...
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We want to explore the role of infrastructure in economic growth by modeling infrastructure as productive public capital in a Solow-style model. The key departure from the textbook version is that public capital, G₁, enhances total factor productivity (TFP). In particular, start with simple aggregate production technology Y₁ = AKON- A₁ = G 0<7<1-a Additionally, suppose that i aggregate employment is constant at N = 1 for all t = 0, 1,...; ii private capital, K,, and public capital, G₁, have a common depreciation rate = 1; iii the government finances public capital by imposing a constant tax rate 7 € [0, 1] on all national income, Y. This means that... G,=? iv the private sector saves a constant fraction, & € (0, 1) of after-tax income, (1-T)Y,, which is invested in private capital, K. a) Once you figure out the expressions for G, and K, from iii. and iv. above, show how the ratio G₁/K, depends on the choice of the fiscal parameter 7. Use this result to write out GDP as a function of private capital alone. b) Describe the law of motion for this economy and depict it in a diagram. c) Compute the capital stock K* > 0) in the positive steady state and describe how it depends on the tax rate T. Explain the intuition behind it. d) Compute GDP Y> 0 in the positive steady state and describe how it depends on the tax rater. Explain the intuition behind it. e) What tax rate * should the government choose if it wants to maximize GDP in the positive steady state? Explain the intuition behind it. We want to explore the role of infrastructure in economic growth by modeling infrastructure as productive public capital in a Solow-style model. The key departure from the textbook version is that public capital, G₁, enhances total factor productivity (TFP). In particular, start with simple aggregate production technology Y₁ = AKON- A₁ = G 0<7<1-a Additionally, suppose that i aggregate employment is constant at N = 1 for all t = 0, 1,...; ii private capital, K,, and public capital, G₁, have a common depreciation rate = 1; iii the government finances public capital by imposing a constant tax rate 7 € [0, 1] on all national income, Y. This means that... G,=? iv the private sector saves a constant fraction, & € (0, 1) of after-tax income, (1-T)Y,, which is invested in private capital, K. a) Once you figure out the expressions for G, and K, from iii. and iv. above, show how the ratio G₁/K, depends on the choice of the fiscal parameter 7. Use this result to write out GDP as a function of private capital alone. b) Describe the law of motion for this economy and depict it in a diagram. c) Compute the capital stock K* > 0) in the positive steady state and describe how it depends on the tax rate T. Explain the intuition behind it. d) Compute GDP Y> 0 in the positive steady state and describe how it depends on the tax rater. Explain the intuition behind it. e) What tax rate * should the government choose if it wants to maximize GDP in the positive steady state? Explain the intuition behind it.
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a The private capital is equal to the private savings and given as Kt It 1T Yt The government spend... View the full answer
Related Book For
Management Accounting Information for Decision-Making and Strategy Execution
ISBN: 978-0137024971
6th Edition
Authors: Anthony A. Atkinson, Robert S. Kaplan, Ella Mae Matsumura, S. Mark Young
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