Suppose the income elasticity of demand for food is 0.40 and the price elasticit

Question

Suppose the income elasticity of demand for food is 0.40 and the price elasticity of demand is -2.00. Suppose also that Felicia spends $10,000 a year on food, the price of food is $2, and that her income is $25,000. 14000- If a sales tax on food caused the price of food to increase to $2.50, what would happen to her consumption of food? Because a large price change is involved, use the arc elasticity to measure the price elasticity of demand rather than a point elasticity C1 8000 | 6000 O 4000- consumption of food would decrease by 1818.18 units. (Enter your response rounded to two decimal places.) Suppose that Felicia gets a tax rebate of $2,500 to ease the effect of the sales tax. What would her consumption of food be now? (Again, use an arc income elasticity to answer this question instead of a point income elasticity.) Felicia's consumption of food would now beunits. (Enter your response rounded to two decimal places.) F1 0 2000 4000 6000 8000 10000 12000 14000 Food

Explanation / Answer

(1) Quantity of food = Spending / Price = $10,000 / $2 = 5,000. If new quantity of food be Q, then

Price elasticity of demand = (Change in Quantity / Average quantity) / (Change in price / Average price)

- 2 = [(Q - 5,000) / (Q + 5,000)] / [$(2.5 - 2) ] $(2.5 + 2)]

- 2 = [(Q - 5,000) / (Q + 5,000)] / (0.5 / 4.5)

- 2 = [(Q - 5,000) / (Q + 5,000)] / (1/9)

- 2 = 9 x [(Q - 5,000) / (Q + 5,000)]

- 2Q - 10,000 = 9Q - 45,000

11Q = 35,000

Q = 3,181.82

Decrease in consumption = 5,000 - 2,181.82 = 1,818.18

(2) After sales tax rebate, income rises by $2,500 to $(25,000 + 2,500) = $27,500.

Income elasticity = (Change in Quantity / Average quantity) / (Change in income / Average income)

0.4 = [(Q - 5,000) / (Q + 5,000)] / [$2,500 / $(25,000 + 27,500)]

0.4 = [(Q - 5,000) / (Q + 5,000)] / (2,500 / 52,500)

0.4 = [(Q - 5,000) / (Q + 5,000)] / (1/21)

0.4 = 21 x [(Q - 5,000) / (Q + 5,000)]

0.4Q + 2,000 = 21Q - 105,000

20.6Q = 107,000

Q = 5,194.17

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