as9 - ECON 331 Written Assignment 9 due in class Nov. 25 1....

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ECON 331 Written Assignment 9 due in class Nov. 25 1. Let y f K , L be a production function and suppose that the factors of production are paid according to their marginal value products. That is if p is the price of the output y , r is the price of capital K and w is the price of labour L then pf K rp f L w Suppose also that the firm’s employment of capital and labour are both growing at a continuous rate of a % per year. That is K t K 0 e at L t L 0 e at Then letting y t f K t , L t  show that dy / dt is also a constant times e at . 2. Given the function f x , y x 3 xy 2 x 4 find an expression for the slope of the tangent line to a level curve of f . Then find the slope of the tangent line to the level curve which passes through the point
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