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# ch04 - Chapter 4 Consumer Choice Solutions to Review...

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Chapter 4 Consumer Choice Solutions to Review Questions 1. Relative to any point on the budget line, when the consumer has a positive marginal utility for all goods she could increase her utility by consuming some basket outside the budget line. However, baskets outside the budget line are unaffordable to her, so she is constrained (as in “constrained optimization”) to choosing the most preferred basket that lies along the budget line. 2. An increase in income will shift the budget line away from the origin in a parallel fashion expanding the set of possible baskets from which a consumer may choose. A decrease in income will shift the budget line in toward the origin in a parallel fashion, reducing the set of possible baskets from which a consumer may choose. 3. If the price of one of the goods increases, the budget line will rotate inward on the axis for the good with the price increase. The budget line will continue to have the same intercept on the other axis. For example, suppose someone buys two goods, cups of coffee and doughnuts, and suppose the price of a cup of coffee increases. Then the budget line will rotate as in the following diagram: Coffee Doughnuts BL 1 BL 2 4. With an interior optimum the consumer is choosing a basket that contains positive quantities of all goods, while with a corner point optimum the consumer is choosing a basket with a zero quantity for one of the goods. The tangency condition usually does not apply at corner optima. 5. If the optimum is an interior solution, the slope of the budget line must equal the slope of the indifference curve. If these slopes are not equal at the chosen interior Page 4 - 1

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basket then the “bang for the buck” condition will not hold. This condition states that at the optimum the extra utility gained per dollar spent on good x must be equal to the extra utility gained per dollar spent on good y . If this condition does not hold at the chosen basket, then the consumer could reallocate his income to purchase more of the good with the higher “bang for the buck” and increase his total utility while remaining within the given budget. Thus, if these slopes are not equal the basket cannot be optimal assuming an interior solution. 6. At an interior optimum, the slope of the budget line must equal the slope of the indifference curve. This implies y x y x y x P P MU MU MRS = = , This can be rewritten as y y x x P MU P MU = which is known as the “bang for the buck” condition. If this condition does not hold at the chosen interior basket, then the consumer can increase total utility by reallocating his spending to purchase more of the good with the higher “bang for the buck” and less of the other good. 7. The “bang for the buck” condition will not necessarily hold at a corner solution optimum. The consumer could theoretically increase total utility by reallocating his spending to purchase more of the good with the higher “bang for the buck” and less of the other good. Since the basket is a corner point, however, he is already purchasing zero of one of the goods.
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ch04 - Chapter 4 Consumer Choice Solutions to Review...

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