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HomeworkAssignment1(fall2009) - Homework Assignment 1 Econ...

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Homework Assignment 1 Econ 7130 Instructions : Please provide your answers to the following questions in the spaces beneath each question. Make sure to clearly show your work and explain your answers for full credit. There are a total of 50 points possible. 1. (5 points) Please do Problem 1.8 from Varian’s text. (Hint : First, recall that a homothetic function can be expressed as g(h(x 1 ,x 2 )) , where h(x 1 ,x 2 ) is homogeneous in x 1 and x 2 and g is a positive monotonic transformation of h . Given this, derive the TRS for g being careful to use the chain rule. You’ll then have an expression that shows the equivalence of the TRSs for g and h . Finally, apply the third property of homogeneity that we proved in class to the TRS for h to show that the family of h 's isoquants are indeed parallel transformations of one another). 1
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2. (5 points) Show that the production function y = 2x represents a technology satisfying the convex-cone definition provided on page 134 of Mas-Colell, et al. Also show that the production function ݕ ൌ √ݔ does not satisfy this definition.
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