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Chap004

Chap004 - Chapter 4 Answers to Questions and Problems 1 a...

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Chapter 4: Answers to Questions and Problems 1. a. The market rate of substitution is 25 . 0 40 10 - = - = - y x P P . b. See Figure 4-1. c. Increasing income to \$800 (by \$400) expands the budget set, as shown in Figure 4-1. Since the slope is unchanged, so is the market rate of substitution. Budget Set 0 5 10 15 20 25 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 X Y Increase in income Figure 4-1 4-1

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2. a. The consumer’s budget line is Y X 10 \$ 5 \$ 250 \$ + = . Rearranging terms and solving for Y results in X Y 5 . 0 25 - = . b. See in Figure 4-2. c. When the price of X increases to \$10, the budget line becomes Y X 10 \$ 10 \$ 250 \$ + = , which is equivalent to X Y - = 25 (after rearranging and simplifying terms). This is shown in Figure 4-2. The market rate of substitution changes from 5 1 10 2 x y P P - = - = - to 10 1 10 x y P P - = - = - . Budget Set 0 5 10 15 20 25 30 0 5 10 15 20 25 30 35 40 45 50 X Y Figure 4-2 3. a. Since the slope of the line through point A is 20 1 20 - = - and the price of good X is \$5, it follows that 5 y P = . b. If the consumer spends all her income on good X she can purchase 20 units. Since these units cost \$5 each, her income must be \$100. c. At point A, the consumer spends (\$5)(10) = \$50 on good Y, which means that the remaining \$100 - \$50 = \$50 is being spent on good X. Since good X costs \$5 per unit, point A corresponds to 10 units of good X. d. The price of good Y decreased to \$2.50. The consumer achieves a higher level of satisfaction at point B. 4. This is not always the case. For instance, if the consumer was initially consuming more of the inferior good than a gift certificate would purchase, then less of the inferior good will be consumed when given a gift certificate. 4-2
5. 6. A half-price sale cuts the price of each and every unit in half. In contrast, a buy-one, get-one-free deal does not change the relative price of any units between 0 and 1 unit. Furthermore, it makes the price of units purchased between 1 and 2 units purchased zero. 7. a. 50 \$ = x P , 100 \$ = y P and M = \$300. b. 300 3 100 y M P = = units. c. 300 6 50 x M P = = units. d. 1 unit (since the \$50 gift certificate will purchase exactly one unit of good X). e. \$50 350 7 50 x M P + = = units. f. D , B, C, A. g. Normal. 8. a. Consumption of good X will decrease and consumption of good Y will increase. b.

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Chap004 - Chapter 4 Answers to Questions and Problems 1 a...

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