problemset9

problemset9 - Problem set 9 (Inspired by a paper by Craig...

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Problem set 9 (Inspired by a paper by Craig Bond and Hossein Farzin) Consider the following linear-quadratic control problem: N is a n dimensional vector of stocks of nutrients and F is the f ow of fertilizer application. The f ow of nutrients available to a plant is y = F + γ 0 N , and the output (revenue) is π = ay b 2 y 2 . The unit cost of nutrients in cF and the equation of motion for nutrients is ˙ N = AN + BF. Note that by including the constant 1 in the vector N ,th isequat iono f motion includes a constant term. The constant discount rate is r .T h e farmer wants to maximize the present value of the f ow of pro F ts over an in F nite horizon. Suppose that F is unconstrained. Assume that b> 0 (so that pro F ts are concave in nutrients, B> 0 (so that an increase in fertilizer increases the stock of nutrients) and A<
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problemset9 - Problem set 9 (Inspired by a paper by Craig...

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