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Unformatted text preview: 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 v [ c ( t )] e & t dt subject to the preceding two equations and _ k = y & c & &k; where v ( c ) = (1 & & 1 ) c 1 & & 1 and is the intertemporal substitution elasticity. (a) Show via the Maximum Principle that the intertemporal Euler equation for the households consumption is _ c c = h Au 1 & & !...
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This note was uploaded on 02/28/2012 for the course ECON 202A taught by Professor Akerlof during the Fall '07 term at University of California, Berkeley.
- Fall '07