# Homework 3 Answers - ECO 301 Intermediate Microeconomics...

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ECO 301: Intermediate Microeconomics Marco A Castaneda Homework 3: Answers 1. ANSWER The consumer maximizes her preferences, and therefore the optimal consumption vector must solve the necessary conditions for the utility maximization problem. Therefore, we have I Y P X P P P MU MU Y X Y X Y X = + = 500 ) 30 ( P ) 10 ( P P P 1 2 Y X Y X = + = This is a simple system of equations, where P X and P Y are the unknowns, and can be solved by the substitution method. Therefore, we must have P X = 20 and P Y = 10 2. ANSWER We have the utility function U = min{X,Y} The commodities are perfect complements. Therefore, the conditions for utility maximization are X = Y P X X + P Y Y = I [ P X = 5 ] In this situation, we have 300 Y 10 X 5 Y X = + = 20 * Y and 20 * X = = [ P X = 10 ] In this situation, we have 300 Y 10 X 10 Y X = + = 15 * Y and 15 * X = = [ P X = 15 ] In this situation, we have 300 Y 10 X 15 Y X = + = 12 * Y and 12 * X = = 1

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[ P X = 20 ] In this situation, we have 300 Y 10 X 20 Y X = + = 10 * Y and 10 * X = = Therefore, we obtain the values in the table P X X* 5 20 10 15 15 12 20 10 P X 20 15 10 5 X 25 30 5 10 15 20 25 30 Demand 3. ANSWER The consumer has preferences represented by the utility function U = XY For this utility function, we have X Y MU MU MRS Y X XY = = 2
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