Consider the Solow growth model. Recall that upper-case variables denote aggregate variables and lower-case variables denote...
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Consider the Solow growth model. Recall that upper-case variables denote aggregate variables and lower-case variables denote per worker (or per capita) variables. Capital is assumed to evolve according to the following equation: K'=1+(1-d)K, (1) where K' denotes aggregate capital in the future period and K is capital in the current period. There is a closedeconomy model without a government, so in a competitive equilibrium the income-expenditure identity is Y = C +1. (a) Use the income-expenditure identity and equation (1) to find an expression for the evolution of per-worker capital. In other words, show that equation (1) can be re-written as follows: k' szf(k) (1-d)k + (2) 1+n (b) Denote the steady-state level of capital per worker as k". Show that in the steady state, equation (2) implies the following equilibrium equation: szf(k) = (n+d)k". (3) For the rest of this question, suppose there are two countries with an aggregate production function Y = zK0.3 No.7. Further suppose the following values for the model's parameters: s = 0.25, d=0.1 and n = 0.02 in both countries. (c) Suppose z = 1 in country A. Use equation (3) and the given values for the model's parameters and production function to calculate the steady-state level of income per capita, y^, and the steady-state level of capital per worker, kj, in country A. (d) Suppose z = 2 in country B. Use equation (3) and the given values for the model's parameters and production function to calculate the steady-state level of income per capita, y, and the steady-state level of capital per worker, kg, in country B. (e) As measured by the steady-state level of income per capita, how much richer is country B relative to country A? (f) Will country A converge with country B in terms of per capita income? Explain your answer. Consider the Solow growth model. Recall that upper-case variables denote aggregate variables and lower-case variables denote per worker (or per capita) variables. Capital is assumed to evolve according to the following equation: K'=1+(1-d)K, (1) where K' denotes aggregate capital in the future period and K is capital in the current period. There is a closedeconomy model without a government, so in a competitive equilibrium the income-expenditure identity is Y = C +1. (a) Use the income-expenditure identity and equation (1) to find an expression for the evolution of per-worker capital. In other words, show that equation (1) can be re-written as follows: k' szf(k) (1-d)k + (2) 1+n (b) Denote the steady-state level of capital per worker as k". Show that in the steady state, equation (2) implies the following equilibrium equation: szf(k) = (n+d)k". (3) For the rest of this question, suppose there are two countries with an aggregate production function Y = zK0.3 No.7. Further suppose the following values for the model's parameters: s = 0.25, d=0.1 and n = 0.02 in both countries. (c) Suppose z = 1 in country A. Use equation (3) and the given values for the model's parameters and production function to calculate the steady-state level of income per capita, y^, and the steady-state level of capital per worker, kj, in country A. (d) Suppose z = 2 in country B. Use equation (3) and the given values for the model's parameters and production function to calculate the steady-state level of income per capita, y, and the steady-state level of capital per worker, kg, in country B. (e) As measured by the steady-state level of income per capita, how much richer is country B relative to country A? (f) Will country A converge with country B in terms of per capita income? Explain your answer.
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a To find an expression for the evolution of perworker capital we start with the incomeexpenditure identity Y C I Dividing both sides by the population N we get y c i where y is output per worker c is ... View the full answer
Related Book For
Accounting Information Systems
ISBN: 978-1133935940
10th edition
Authors: Ulric J. Gelinas, Richard B. Dull
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