AK6.3 - Answer Key for Problem Set 6 ECON 211, Fall 2009...

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Answer Key for Problem Set 6 ECON 211, Fall 2009 Due on Friday, October 16 Part 1: Graded Questions Problem 1: 30 points Ralph and Lauren are talking about how much they like going to the gym and how much they like eating out at their favorite restaurant and they regularly do some of each. A session at the gym costs the same as a meal at the restaurant. Ralph says that, for his current consumption of gym sessions and restaurant meals, he values 1 more meal twice as much as he values 1 more session at the gym. Lauren is studying economics, and she tells him that his current consumption bundle cannot be optimal. a. (10 points) Draw a diagram of Ralph’s budget line and the indifference curve that he is on by making his current consumption choice. Place restaurant meals on the horizontal axis and gym sessions on the vertical axis. b. (10 points) Is Lauren right? Why or why not? c. (10 points) How should Ralph adjust his consumption so that it is optimal? Illustrate an optimal choice in your diagram. a. b. Lauren is right. Since Ralph values one more meal twice as much as he values one more session at the gym, his marginal utility for meals is twice as much as his marginal
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utility for gym sessions. That is, his marginal rate of substitution of meals in place of gym sessions is MUmeal/MUgym 2. However, the relative price of a meal is Pmeal/Pgym 1 (they both cost the same). A in the accompanying diagram illustrates this bundle. Since his marginal rate of substitution is different from the relative price, this cannot be his optimal consumption bundle. c. Since Ralph’s marginal rate of substitution is greater than the relative price of a meal, he should consume more meals and fewer gym visits to make himself better off. In the diagram, bundle B is the bundle that is optimal: the relative price is equal to Ralph’s marginal rate of substitution. Problem 2: 35 points Sabine can’t tell the difference between Coke and Pepsi—the two taste exactly the same to her. a.
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AK6.3 - Answer Key for Problem Set 6 ECON 211, Fall 2009...

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