as11 - satisfied(c WITHOUT solving the first order...

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ECON 331 Written Assignment 11 - not to be handed in - 1. Find all the extreme points for the problem of choosing x and y to optimize f x , y 2 x 2 y subject to the constraint x 2 y 2 1 Determine which of these points are local maxima and which are local minima. Do a sketch of the consraint curve and then add to your sketch a sketch of a level curves of f which passes through one of the extreme points of this problem. 2. A consumer has a utility function given by u x , y xy x y (a) Using the method of Lagrange, write down the first order necessary conditions which describe the solution of the problem of maximizing the consumer’s utility subject to her budget constraint which is px qy m (b) Check that the second order sufficient condition for a global maximum is
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Unformatted text preview: satisfied. (c) WITHOUT solving the first order conditions, find an expression for the slope of this consumer’s demand function for the first good. That is find an expression for x / p Is it possible to say what the sign of this derivative is? A model answer to this assignment will be posted on the 331 web page by Dec. 9. The reason for the WITHOUT is this. On exams, I sometimes give instructions like this on purpose to try and keep you from trying to solve a problem by a method that involves a long and time consuming calculation Not following such instructions can cost you a lot of marks....
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