9. If demand had the same elasticity for a price decline from $1.00 to $0.50 as it does for the decline from $1.50 to $1.00, would cutting the price from $1.00 to $0.50 increase or decrease Danny’s total revenue?

a. increase

b. decrease

Question

9.  If demand had the same elasticity for a price decline from $1.00 to $0.50 as it does for the decline from $1.50 to $1.00, would cutting the price from $1.00 to $0.50 increase or decrease Danny’s total revenue?

a. increase

b. decrease

BlackTom AI · Accepted Answer

Price elasticity of demand (in absolute value) greater than 1 means quantity responds proportionally more than price, so a price cut raises total revenue. 1) Relevant knowledge points and concepts - Price elasticity of demand, ε = (% change in quantity demanded) / (% change in price). For convenience use absolute values: |ε|. - Total revenue (TR) = P × Q. For small percent changes, %ΔTR ≈ %ΔP + %ΔQ. A price decrease (negative %ΔP) raises TR when the percent increase in Q exceeds the percent decrease in P, i.e., |%ΔQ| > |%ΔP|. - If demand is elastic (|ε| > 1), a price decrease increases TR; if inelastic (|ε| < 1), a price decrease decreases TR. 2) Step-by-step reasoning - Compute the percent price changes: - From $1.50 to $1.00: %ΔP = (1.00 − 1.50)/1.50 = −0.3333 = −33.33%. - From $1.00 to $0.50: %ΔP = (0.50 − 1.00)/1.00 = −0.50 = −50.00%. - The question states “demand had the same elasticity for a price decline from $1.50 to $1.00,” and we are told to assume that same elasticity applies to the $1.00→$0.50 decline. Implicitly, the decline from $1.50 to $1.00 produced the revenue outcome that characterizes an elastic response (the context of the textbook problem indicates that the price cut led to higher revenue), so |ε| > 1 on that interval. - Using the elasticity relationship for the second cut: |%ΔQ| = |ε| × |%ΔP|. Because |ε| > 1 and |%ΔP| for $1.00→$0.50 is 50%, the percent increase in quantity will exceed 50%, so the percent increase in Q is larger than the percent decrease in P. Hence %ΔTR = %ΔQ + %ΔP > 0, so TR rises. 3) Intermediate calculation illustration (symbolic) - Let p = |%ΔP|. For a price fall, %ΔP = −p, %ΔQ = +|ε| p. - %ΔTR ≈ −p + |ε| p = p(|ε| − 1). If |ε| > 1, %ΔTR > 0. 4) Why the correct answer is correct - Because the demand elasticity on the earlier interval was elastic (|ε| > 1) and the elasticity is the same for the later, larger percentage price cut, the percentage increase in quantity will exceed the percentage decrease in price; total revenue therefore increases when price falls from $1.00 to $0.50. 5) Why the other option is incorrect - Option b (decrease) would be correct only if demand were inelastic (|ε| < 1) on that interval. That contradicts the given that elasticity is the same as for the $1.50→$1.00 decline, which implies an elastic response. 6) Conclusion - Therefore, cutting the price from $1.00 to $0.50 would increase Danny’s total revenue. This matches the provided answer: a.

9. If demand had the same elasticity for a price decline from $1.00 to $0.50 as it does for the decline from $1.50 to $1.00, would cutting the price from $1.00 to $0.50 increase or decrease Danny’s total revenue? a. increase b. decrease 单项选择题

类似问题

Which of the following is correct regarding the "elasticity of demand with respect to price"?

If ƐD = 1.6 then a 10% decrease in price causes a:

Which is true regarding price elasticity of demand?

If demand is elastic then:

2. When the percentage change in price is greater than the resulting percentage change in quantity demanded: A. a decrease in price will increase total revenue. B. demand may be either elastic or inelastic. C. an increase in price will increase total revenue. D. demand is elastic.

2. Using the determinants of price elasticity of demand, for which the following products is demand probably elastic: a. bottled water b. toothpaste c. Crest toothpaste d. ketchup e. diamond bracelets f. Microsoft’s Windows operating system.

If the price of IPads rises by 20 per cent and quantity demanded for IPads decreases by 30 per cent, the price elasticity of demand would be:

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单