# 3 a if your income is 10000 your price elasticity of

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3. a. If your income is \$10,000, your price elasticity of demand as the price of compact discs rises from \$8 to \$10 is [(40 - 32)/36]/[(10 - 8)/9] =0.22/0.22 = 1. If your income is \$12,000, the elasticity is [(50 - 45)/47.5]/[(10 - 8)/9] = 0.11/0.22 = 0.5. b. If the price is \$12, your income elasticity of demand as your income increases from \$10,000 to \$12,000 is [(30 - 24)/27] / [(12,000 - 10,000)/11,000] = 0.22/0.18 = 1.22. If the price is \$16, your income elasticity of demand as your income increases from \$10,000 to \$12,000 is [(12 - 8)/10] / [(12,000 - 10,000)/11,000] = 0.40/0.18 = 2.2. 4. a. If Emily always spends one-third of her income on clothing, then her income elasticity of demand is one, since maintaining her clothing expenditures as a constant fraction of her income means the percentage change in her quantity of clothing must equal her percentage change in income. For example, suppose the price of clothing is \$30, her income is \$9,000, and she purchases 100 clothing items. If her income rose 10 percent to \$9,900, she'd spend a total of \$3,300 on clothing, which is 110 clothing items, a 10 percent increase. b. Emily's price elasticity of clothing demand is also one, since every percentage point increase in the price of clothing would lead her to reduce her quantity purchased by the same percentage. Again, suppose the price of clothing is \$30, her income is \$9,000, and she purchases 100 clothing items. If the price of clothing rose 1 percent to \$30.30, she would purchase 99 clothing items, a 1 41

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percent reduction. [Note: This part of the problem can be confusing to students if they have an example with a larger percentage change and they use the point elasticity. Only for a small percentage change will the answer work with an elasticity of one. Alternatively, they can get the second part if they use the midpoint method for any size change.] c. Since Emily spends a smaller proportion of her income on clothing, then for any given price, her quantity demanded will be lower. Thus her demand curve has shifted to the left. But because she'll again spend a constant fraction of her income on clothing, her income and price elasticities of demand remain one. 5. a. With a 4.3 percent decline in quantity following a 20 percent increase in price, the price elasticity of demand is only 4.3/20 = 0.215, which is fairly inelastic. b. With inelastic demand, the Transit Authority's revenue rises when the fare rises. c. The elasticity estimate might be unreliable because it is only the first month after the fare increase. As time goes by, people may switch to other means of transportation in response to the price increase. So the elasticity may be larger in the long run than it is in the short run. 6. Tom's price elasticity of demand is zero, since he wants the same quantity regardless of the price. Jerry's price elasticity of demand is one, since he spends the same amount on gas, no matter what the price, which means his percentage change in quantity is equal to the percentage change in price. 7. To explain the fact that spending on restaurant meals declines more during economic downturns than does spending on food to be eaten at home, economists look at the income elasticity of demand. In economic downturns, people have lower income. To explain the fact, the income elasticity of restaurant meals must be larger than the income elasticity of spending on food to be eaten at home.
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