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Unformatted text preview: Economic Growth and Development MS&E 249 Professor Olivier de La Grandville Autumn 2008 Final Answer Keys 1. (40 points) y = aω = a ( y- ry ) → dy y = a- 1 a · dr r → Z dy y = a- 1 a Z dr r → ln y = a- 1 a ln r + ln C, where C is the positive constant of integration. → y = Cr a- 1 a → y = y ( r r ) a- 1 a , since C = y r a- 1 a from y ( r ) = y → Y/L = Y /L ( K/L K /L ) a- 1 a Finally we get, → Y = Y ( K/K ) 1- 1 a ( L/L ) 1 a ,which is the Cobb-Douglas production function. 2. (60 points) In the Solow model of economic growth, equilibrium implies sf ( r * ) = nr * . On the other hand, maximization of consumption per person implies sf ( r * ) = n . Therefore in this system of two equations we can eliminate n and obtain s = r * f ( r * ) /f ( r * ). As a consequence, the savings rate should be equal to the elasticity of production with respect to capital. Typically, this number is about 0.3, which is much too high to constitute a reasonable optimal savings rate (refer to Table 2 of Chapter 13). Especially, in case of the Cobb-Douglas production function,(refer to Table 2 of Chapter 13)....
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- Fall '08
- Calculus, Exogenous growth model, Cobb-Douglas production function, Robert Solow