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# PS4 - Economics 202A Problem Set#4 1 An endogenous growth...

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Economics 202A Problem Set #4 1. An endogenous growth model based on human capital. Consider an economy with a °xed labor force. Output per worker is given by y = Ak ° ( uh ) 1 ° ° where k is physical capital (per worker), h is human capital (per worker), and u 2 [0 ; 1] is the fraction of the human capital stock allocated to production of output. The rest of the human capital is used to produce new human capital, which depreciates at rate ° : _ h = B (1 ° u ) h ° °h: Here, A and B are constant. The stocks k and h are predetermined state variables as, therefore, is their ratio, ! ± k=h: The representative household maximizes Z 1 0 v [ c ( t )] e ° ±t dt subject to the preceding two equations and _ k = y ° c ° °k; where v ( c ) = (1 ° ± ° 1 ) c 1 ° ² ° 1 and ± is the intertemporal substitution elasticity. (a) Show via the Maximum Principle that the intertemporal Euler equation for the household±s consumption is _ c c = ± h ²Au 1 ° ° !

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PS4 - Economics 202A Problem Set#4 1 An endogenous growth...

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