practice midterm 1

# practice midterm 1 - Econ3101 Section 003 Intermediate...

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Econ3101 - Section 003 Intermediate Microeconomics Xavier Vinyals-Mirabent * Department of Economics University of Minnesota. Midterm 1 will be on Friday, October 15th, 2010. Practice Midterm 1. (*note: this list of exercises is not exhaustive and it may be the case that I ask about topics not covered here but seen in class.) * Borrowed from Erick Sager with permission. 1

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1. Theory of Choice Consider a consumer who has the following utility function: u ( x, y ) = 3 x + 2 y (a) Draw the indifference curve through the bundle ( x 0 , y 0 ) = (10 , 10), and indicate the direction of preferences. 0 5 10 15 20 25 0 5 10 15 20 25 (b) Do these preferences satisfy convexity (Axiom 4)? Justify your answer. You may use the above graph to illustrate your answer. If the preferences do in fact satisfy Axiom 4, relate your answer to the law of diminishing marginal utility. (c) Do these preferences satisfy non-satiation (Axiom 3)? Justify your answer. 2
2. Consmuer Optimization and Demand A (a) For P x > 0, P y > 0 and M > 0, can one find an interior solution (e.g. x * > 0 and y * > 0) to this consumer’s maximization problem? Justify your answer. (b) What is the direction of preferences for this consumer? Justify your answer. Also, indicate the direction on the graph below. (c) Given P x = 10, P y = 20 and M = 200, draw the budget constraint. 0 5 10 15 20 25 0 5 10 15 20 25 3

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3. Consumer Optimization and Demand B Again, consider a consumer who has the utility function: u ( x, y ) = 30 x 2 3 y 1 3 (a) Write down the consumer’s maximization problem.
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