Assignment2 - ECO 610 Fall 2010 Assignment 2 The due date...

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ECO 610 Fall 2010 Assignment 2 The due date for this assignment is Tuesday March 22. 1. (Capital Utilization) Consider an economy in which each individual ranks consumption sequence according to the functional X t =0 β t u ( c t ) , 0 <β< 1 where the function u is increasing, di f erentiable and strictly concave. This economy imports investment goods. Assume that the international price of the investment good is p k 1 . Thus, the feasiblility constraint faced by the planner is c t + p k x t f ( k e t ) , where k e t denotes e f ective units of capital per worker (to be de f ned). The planner chooses that intensity of use of the capital stocks. Let intensity of use be denoted ν , where 0 ν 1 . If the economy has available k units of capital and it is used at intensity ν ,thee f ective supply of capital is k e = νk . In this case the depreciation rate is δ ( ν )= ν 1+ λ , λ> 0 and 0 ν 1 . In this economy there are installation costs. If x units of investment goods are allocated to the production of new capital, they produce G ( x, a ) units of new capital goods. Thus, the aggregate law of motion of capital is k t +1 =(1 δ ( ν t )) k t + G ( x t ,a ) , where a is a factor of f xed supply. . The function G is assumed increasing in each argument, di f erentiable and concave. One interpretation of G is that it represents installation costs that are necessary to make capital goods productive. Assume that the production function is given by
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Assignment2 - ECO 610 Fall 2010 Assignment 2 The due date...

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