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Midterm1_2005 - Introduction to Economic Analysis Fall 2005...

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Introduction to Economic Analysis Fall 2005 Mid-term Exam: September 21 Time: 1 hour and 15 minutes. Try to answer all questions. Good luck! Question 1 (30 points) Let the utility function be: u ( x 1 , x 2 ) = x 1 + x 2 (If you think there is something strange here because the utility is linear in x 2 , you are right! but trust me, do not worry and proceed as usual). 1. Write down the budget constraint: call income m and normalize the price p 1 , that is, p 1 = 1. Determine the demanded bundle as a function of price p 2 and income, m . (substitution works; Lagrange too; whatever is easier for you). 2. Extra Points Draw the demand for good x 2 and the demand for x 1 as a function of price p 2 . (Now is the moment to think about the fact that the utility function is linear in x 2 . Does your solution generate always non-negative quantities x 1 and x 2 ?). Question 2 (30 points). Consider the preference relation on X = 2 + defined as follows: for any element x = x 1 x 2 and y = y 1 y 2 of X : x y if and only if Max { x 1 , x 2 } ≥ Max { y 1 , y 2 } 1. Is this preference relationship complete ?
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