HW3-solution - Econ 501 Homework Assignment 3 Due January...

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Econ 501 Homework Assignment 3 Due January 29, Tuesday 1. BB 4.3 This question cannot be solved using the usual tangency condition. However, you can see from the graph below that the optimum basket will necessarily lie on the “elbow” of some indifference curve, such as (5, 3), (10, 6) etc. If the consumer were at some other point, he could always move to such a point, keeping utility constant and decreasing his expenditure. The equation of all these “elbow” points is 3 x = 5 y , or y = 0.6 x . Therefore the optimum point must be such that 3 x = 5 y. The usual budget constraint must hold of course. That is, 220 10 5 = + y x . Combining these two conditions, we get ( x , y ) = (20, 12). 2. BB 4.7 See the graph below. The fact that Helen’s indifference curves touch the axes should immediately make you want to check for a corner point solution. To see the corner point optimum algebraically, notice if there was an interior solution, the tangency condition implies ( S + 10)/( C +10) = 3, or S = 3 C + 20. Combining this with the budget constraint, 9 C + 3 S = 30, we find that the optimal number of CDs would be given by 30 18 = C which implies a negative number of CDs. Since it’s impossible to purchase a negative amount of something, our (5,3) (10,6) y x (20,12)
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assumption that there was an interior solution must be false. Instead, the optimum
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This note was uploaded on 07/17/2008 for the course ECON 501.02 taught by Professor Yang during the Winter '08 term at Ohio State.

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HW3-solution - Econ 501 Homework Assignment 3 Due January...

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