Price Elasticity of Demand

1. Which of the following statements is true regarding a downward-sloping linear demand curve?
   A) The price elasticity of demand is constant along the entire curve and is equal to the slope of the curve.
   B) Demand is price elastic at high prices and price inelastic at low prices.
   C) Demand is price inelastic at high prices and price elastic at low prices.
   D) Price elasticity is zero at the vertical intercept and infinite at the horizontal intercept.

2. A local theater company finds that when it charges $10 per ticket, it sells 1,200 tickets per show. When it raises the ticket price to $14, it sells 800 tickets. Using the midpoint method, what is the absolute value of the price elasticity of demand?
   A) 0.83
   B) 1.20
   C) 1.00
   D) 1.50

3. Which of the following goods is expected to exhibit the most price elastic demand?
   A) Insulin prescribed for a diabetic patient
   B) Electricity used for residential heating
   C) A specific brand of premium organic whole milk
   D) All dairy beverages combined

4. If the price elasticity of demand for a consulting service is 0.60, a 15% increase in the hourly rate charged by the consultant will cause the quantity of services demanded to:
   A) decrease by 9% and the consultant's total revenue to increase.
   B) decrease by 9% and the consultant's total revenue to decrease.
   C) decrease by 25% and the consultant's total revenue to increase.
   D) decrease by 25% and the consultant's total revenue to decrease.

5. A local bookstore estimates that the price elasticity of demand for course textbooks is 0.30, while the price elasticity of demand for mystery novels is 1.80. If the bookstore wants to increase its total revenue across both departments, how should it adjust its prices?
   A) Decrease textbook prices and increase mystery novel prices.
   B) Increase prices for both textbooks and mystery novels.
   C) Decrease prices for both textbooks and mystery novels.
   D) Increase textbook prices and decrease mystery novel prices.

6. A metropolitan transit authority increases the price of a single bus ride from $2.00 to $2.50. Consequently, weekly ridership falls from 50,000 riders to 45,000 riders.
   Part A: Use the midpoint method to calculate the percentage change in quantity demanded and the percentage change in price.
   Part B: Calculate the price elasticity of demand (absolute value).
   Part C: Based on your calculation, determine whether the transit authority succeeded in increasing its total weekly revenue. Show your calculations for revenue before and after the price change.

7. Reflect on your notes, reading, prior practice, or personal observation of a real-world price change you have experienced or analyzed (for example, subscription streaming services, coffee, gasoline, or textbooks). Choose one specific product, describe the price change, and analyze consumer responsiveness based on at least two key determinants of elasticity (such as availability of substitutes, budget share, or time horizon).

8. Suppose a freeze in Florida destroys half of the orange crop, causing the supply of oranges to shift to the left. If the price elasticity of demand for oranges is highly inelastic:
   Part A: Explain what happens to the equilibrium price and equilibrium quantity of oranges.
   Part B: Explain what happens to the total expenditure of consumers on oranges. Use the relationship between elasticity and total revenue to support your answer.

9. In microeconomic theory, the relationship between marginal revenue (MR), price (P), and the absolute value of the price elasticity of demand (Ed) is given by the formula:
   MR = P × (1 - 1/Ed)
   Part A: Use this formula to show why marginal revenue is equal to zero when demand is unit-elastic (Ed = 1).
   Part B: Explain what this mathematical relationship implies about the level of total revenue when demand is unit-elastic.

10. Compare a perfectly inelastic demand curve (Ed = 0) with a standard linear demand curve.
    Part A: Describe how the elasticity coefficient changes as you move down a linear demand curve.
    Part B: Explain why the price elasticity of demand remains constant at zero along a perfectly inelastic demand curve, regardless of the price. Provide the economic intuition behind this constant relationship.

Answers and Explanations

1. B) Demand is price elastic at high prices and price inelastic at low prices.
   Explanation: Along a downward-sloping linear demand curve, the price elasticity of demand varies from elastic at high prices to inelastic at low prices, with unit elasticity occurring at the midpoint. Slope is constant, but elasticity is not.

2. B) 1.20
   Explanation: Using the midpoint method, the percentage change in quantity is (800 - 1200) / 1000 = -40%. The percentage change in price is (14 - 10) / 12 = 33.33%. Price elasticity of demand is |-40% / 33.33%| = 1.20.

3. C) A specific brand of premium organic whole milk
   Explanation: A specific brand of a good has many close substitutes (other brands of milk), which makes its demand highly elastic. In contrast, broad categories (all dairy beverages) or necessities with no close substitutes (insulin, residential electricity) have highly inelastic demand.

4. A) decrease by 9% and the consultant's total revenue to increase.
   Explanation: Percentage change in quantity demanded = Elasticity * Percentage change in price = 0.60 * 15% = 9% decrease. Since demand is inelastic (Ed < 1), an increase in price leads to an increase in total revenue.

5. D) Increase textbook prices and decrease mystery novel prices.
   Explanation: For inelastic goods (textbooks, Ed = 0.30 < 1), increasing prices increases total revenue. For elastic goods (mystery novels, Ed = 1.80 > 1), decreasing prices increases total revenue.

6. Part A: Percentage change in quantity demanded is -10.53%; percentage change in price is 22.22%. Part B: Price elasticity of demand is 0.47. Part C: Yes, the transit authority succeeded in increasing revenue. Revenue increased from $100,000 to $112,500.
   Explanation: Using midpoints: % change Q = (45,000 - 50,000) / 47,500 = -10.526%. % change P = (2.50 - 2.00) / 2.25 = 22.222%. Elasticity = 10.526 / 22.222 = 0.474 (inelastic). Initial Revenue = $2.00 * 50,000 = $100,000. Final Revenue = $2.50 * 45,000 = $112,500. Since demand is inelastic, price and revenue move in the same direction.

7. Answers will vary. Students must select a specific real-world product and describe a price change. They must then analyze consumer responsiveness using at least two determinants of elasticity. For example, for a price increase in Netflix streaming plans, a student might argue demand is relatively inelastic because there are few perfect substitutes and the subscription represents a small share of the consumer's monthly budget, or they might note that over a longer time horizon, more consumers will cancel as alternatives emerge.
   Explanation: This is an open-ended reflection question. Responses should be graded based on whether they correctly name a real product, identify a price change, and apply at least two determinants of elasticity (e.g., availability of substitutes, share of budget, luxury vs. necessity, or time horizon) logically to characterize the elasticity of demand.

8. Part A: Equilibrium price increases and equilibrium quantity decreases. Part B: Total expenditure of consumers increases. Since demand is price inelastic, the percentage increase in price is larger than the percentage decrease in quantity, resulting in a net increase in total consumer spending.
   Explanation: A leftward shift in supply reduces quantity and raises price. Because demand is inelastic, consumers do not reduce their purchases much in response to the price increase, which causes total expenditure (Price * Quantity) to rise.

9. Part A: Substituting Ed = 1 into the formula yields MR = P * (1 - 11) = P * (1 - 1) = P * 0 = 0. Part B: When marginal revenue is zero, total revenue is at its maximum and does not change with small changes in quantity or price.
   Explanation: Mathematically, the derivative of total revenue with respect to quantity is marginal revenue. When MR = 0, the total revenue curve is at its peak (mathematical maximum).

10. Part A: On a downward-sloping linear demand curve, elasticity decreases as you move down and to the right along the curve. Part B: Along a perfectly inelastic demand curve, elasticity is zero at every price because the quantity demanded does not change at all in response to a change in price. Consumers purchase the exact same quantity regardless of the price.
    Explanation: For a linear demand curve, slope is constant but the ratio of price to quantity decreases as you move down, driving elasticity down. For a perfectly inelastic curve (vertical line), the percentage change in quantity is always zero for any price change, keeping the elasticity coefficient constant at zero.