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Price Elasticity of Demand - Microeconomics

  1. A company's demand curve is given by P=50−2QP = 50 - 2Q, where P is price and Q is quantity. At what output level is the price elasticity of demand equal to -2, and what is the significance of this point for revenue management?
    Answer: Q = 8.33, P = $33.33; this point shows moderately elastic demand where the firm should consider price reductions to increase revenue From P = 50 - 2Q, we get Q = (50-P)/2, so dQ/dP = -1/2. Elasticity = (dQ/dP) × (P/Q) = (-1/2) × (P/Q) = -2. This gives us P/Q = 4, so P = 4Q. Substituting into the demand equation: 4Q = 50 - 2Q, so 6Q = 50, Q = 8.33, P = 33.33. At elasticity of -2, demand is elastic, so price reductions would increase revenue. Choice A gives the unit elastic point. Choice B incorrectly identifies this as unit elastic. Choice C has wrong calculations.
  2. A retailer observes that when the price of Product X increases from $20 to $24, the quantity demanded of Product Y increases from 100 units to 130 units, while the quantity demanded of Product X decreases from 150 units to 120 units. What can be concluded about these products and their market relationships?
    Answer: Products X and Y are substitutes with a cross-price elasticity of +1.5, and Product X has unit elastic demand with own-price elasticity of -1.0 When you encounter a question involving price changes and quantity responses for multiple products, you're dealing with elasticity concepts - specifically cross-price elasticity (how one product's demand responds to another's price change) and own-price elasticity (how a product's demand responds to its own price change). Let's calculate both elasticities using the midpoint method. For cross-price elasticity of X and Y: the percentage change in Y's quantity is (130−100)(130+100)/2=30115=26.1%\frac{(130-100)}{(130+100)/2} = \frac{30}{115} = 26.1\%. The percentage change in X's price is (24−20)(24+20)/2=422=18.2%\frac{(24-20)}{(24+20)/2} = \frac{4}{22} = 18.2\%. Cross-price elasticity = 26.1%18.2%=+1.4\frac{26.1\%}{18.2\%} = +1.4 (approximately +1.5). For X's own-price elasticity: percentage change in X's quantity is (120−150)(120+150)/2=−30135=−22.2%\frac{(120-150)}{(120+150)/2} = \frac{-30}{135} = -22.2\%. Own-price elasticity = −22.2%18.2%=−1.2\frac{-22.2\%}{18.2\%} = -1.2 (approximately -1.0). The positive cross-price elasticity confirms X and Y are substitutes - when X becomes more expensive, consumers buy more Y instead. Answer A has the wrong own-price elasticity (-0.6 instead of -1.0) and incorrectly classifies X's demand as elastic when it's actually unit elastic. Answer C drastically overstates the cross-price elasticity as +6.0. Answer D misidentifies the relationship entirely - these products are substitutes, not complements, since their cross-price elasticity is positive. Remember: positive cross-price elasticity = substitutes, negative = complements. Own-price elasticity of -1.0 indicates unit elastic demand.
  3. A student's demand for coffee from a campus cafe is known to be price inelastic. If the cafe lowers the price of coffee, what will be the effect on the student's total expenditure on coffee and the quantity of coffee they purchase?
    Answer: Total expenditure will decrease, and quantity purchased will increase. According to the law of demand, a lower price will always lead to an increase in the quantity purchased. The effect on total expenditure depends on price elasticity. Total expenditure (from the buyer's side) is equivalent to total revenue (from the seller's side). When demand is price inelastic, price and total expenditure move in the same direction. Since the price falls, the student's total expenditure on coffee will also decrease. Therefore, quantity purchased increases, and total expenditure decreases.
  4. The price elasticity of demand for a particular brand of smartphone is estimated to be -1.5. In order to increase the quantity sold by 30%, the company must implement an approximate price change of:
    Answer: a 20% decrease. When you encounter price elasticity of demand questions, you're working with the relationship between percentage changes in price and quantity demanded. The formula is: Price Elasticity=% Change in Quantity Demanded% Change in Price\text{Price Elasticity} = \frac{\% \text{ Change in Quantity Demanded}}{\% \text{ Change in Price}} Given that the price elasticity is -1.5 and you want to increase quantity sold by 30%, you can solve for the required price change. Substituting into the formula: −1.5=30%% Change in Price-1.5 = \frac{30\%}{\% \text{ Change in Price}} Solving for the price change: % Change in Price=30%−1.5=−20%\% \text{ Change in Price} = \frac{30\%}{-1.5} = -20\% The negative sign indicates a price decrease, so the company must decrease price by 20%. This confirms answer A is correct. Let's examine why the other options are wrong. Answer B (20% increase) gets the magnitude right but the direction wrong—a price increase would decrease quantity demanded, not increase it. Answer C (45% decrease) results from incorrectly multiplying 30% by 1.5 instead of dividing, showing a misunderstanding of the elasticity formula. Answer D (30% decrease) assumes elasticity equals -1 (unit elastic), ignoring the given elasticity of -1.5. Remember this key strategy: when demand is elastic (absolute value greater than 1), as in this case with |-1.5| > 1, small price changes create proportionally larger quantity changes. Always pay attention to the sign—negative elasticity means price and quantity move in opposite directions, which is the normal case for demand curves.
  5. A university aims to increase total revenue from campus parking by raising the price of parking permits. This strategy will succeed only if demand is inelastic. Which of the following independent events would make it more likely that this strategy will succeed?
    Answer: The university eliminates most online course options, requiring more students to attend classes in person. When analyzing pricing strategies and revenue, you need to understand the relationship between price elasticity of demand and total revenue. If demand is inelastic (price elasticity less than 1), consumers are relatively unresponsive to price changes, so raising prices will increase total revenue. The key is identifying what makes demand more inelastic. Option A is correct because eliminating online courses forces more students to come to campus physically. This removes a substitute for in-person attendance, making campus parking more of a necessity rather than a choice. When consumers have fewer alternatives and the good becomes more essential, demand becomes more inelastic. Option B is wrong because moving departments to a satellite campus reduces the need for parking at the main campus, decreasing demand overall and potentially making remaining users more price-sensitive. Option C is incorrect because introducing efficient public transportation provides students with a substitute for driving and parking on campus. More substitutes make demand more elastic, not less. Option D is wrong because a new private parking garage gives students an alternative to university parking, creating more substitutes and making demand more elastic. Remember this pattern: demand becomes more inelastic when consumers have fewer substitutes and the good becomes more necessary. Look for factors that eliminate alternatives or increase the essential nature of the product. Conversely, anything that provides more choices or substitutes will make demand more elastic, making price increases counterproductive for revenue goals.
  6. A firm faces a linear, downward-sloping demand curve. As the firm lowers its price from the vertical intercept (where quantity is zero) down to the price where total revenue is maximized, which of the following occurs?
    Answer: Total revenue increases, and the absolute value of price elasticity of demand falls toward 1. The upper half of a linear demand curve (from the price intercept down to the midpoint) is the elastic region. The midpoint is where demand is unit elastic and total revenue is maximized. The lower half is the inelastic region. When the firm lowers its price starting from the highest possible price, it is moving down along the elastic portion of the demand curve. In this region, a price decrease leads to an increase in total revenue. As the price falls, the point on the demand curve moves closer to the midpoint, so the price elasticity of demand, while still elastic, is decreasing in absolute value towards 1.
  7. The market demand for a product is given by the equation QD=200−4PQ_D = 200 - 4P. At what price is the absolute value of the price elasticity of demand equal to 1 (unit elastic)?
    Answer: $25 For a linear demand curve, unit elasticity occurs at the midpoint. First, find the intercepts. The quantity intercept (where P=0) is Q=200. The price intercept (where Q=0) is 0=200−4P⇒4P=200⇒P=500 = 200 - 4P \Rightarrow 4P = 200 \Rightarrow P = 50. The midpoint of the demand curve occurs at half the price intercept and half the quantity intercept. Therefore, the unit-elastic price is $50/2=$25\$50 / 2 = \$25. At this price, the quantity would be 200−4(25)=100200 - 4(25) = 100, which is half the quantity intercept.
  8. A local cinema raises the price of a movie ticket from $10 to $15. As a result, the number of tickets sold per screening drops from 200 to 100. According to the midpoint method, the absolute value of the price elasticity of demand for these movie tickets is approximately:
    Answer: 1.67 The midpoint method for price elasticity of demand is calculated as ∣(Q2−Q1(Q1+Q2)/2)/(P2−P1(P1+P2)/2)∣| (\frac{Q_2 - Q_1}{(Q_1+Q_2)/2}) / (\frac{P_2 - P_1}{(P_1+P_2)/2}) |. Percentage change in quantity = 100−200(100+200)/2=−100150≈−0.667\frac{100 - 200}{(100+200)/2} = \frac{-100}{150} \approx -0.667. Percentage change in price = 15−10(15+10)/2=512.5=0.4\frac{15 - 10}{(15+10)/2} = \frac{5}{12.5} = 0.4. Price elasticity of demand = ∣−0.6670.4∣≈1.67| \frac{-0.667}{0.4} | \approx 1.67. Distractor A (1.00) results from using the simple percentage change from the initial point. Distractor D (3.00) results from using the simple percentage change from the final point. Distractor C (2.00) results from incorrectly averaging the simple initial point elasticity (1.0) and final point elasticity (3.0).
  9. A government wishes to impose an excise tax on a product to raise revenue while minimizing the tax's deadweight loss. It is considering two goods: Good A has a price elasticity of demand of -0.4, and Good B has a price elasticity of demand of -1.8. Assuming supply elasticities are similar, which good should be taxed and why?
    Answer: Good A, because its inelastic demand will result in a smaller reduction in the quantity traded. Deadweight loss from a tax is greater when demand (or supply) is more elastic, because the tax causes a larger distortion in the market outcome (i.e., a larger reduction in quantity traded). Good A has inelastic demand (|-0.4| < 1), while Good B has elastic demand (|-1.8| > 1). To minimize deadweight loss, the government should tax the good with the more inelastic demand, which is Good A. The quantity sold of Good A will decrease by less than that of Good B, leading to a smaller deadweight loss. Also, tax revenue is typically higher when taxing goods with inelastic demand.
  10. An agricultural economist studies corn demand and finds that a 10% increase in corn prices leads to a 15% increase in quantity demanded for wheat, while corn consumption decreases by 4%. If wheat prices simultaneously increase by 5%, what is the net effect on wheat demand, assuming wheat's own-price elasticity is -0.8?
    Answer: Net increase of 11% in wheat quantity demanded due to the stronger substitution effect overwhelming the own-price effect When analyzing demand changes with multiple price shifts, you need to calculate each elasticity effect separately and then combine them. This question tests your understanding of cross-price elasticity (how one good's price affects another's demand) and own-price elasticity (how a good's price affects its own demand). First, calculate the cross-price effect: When corn prices rise 10%, wheat demand increases 15%. This gives us a cross-price elasticity of +1.5, confirming wheat and corn are substitutes. Next, calculate the own-price effect: Wheat prices increase 5% with an own-price elasticity of -0.8. Using the elasticity formula: \text{% change in quantity} = \text{elasticity} \times \text{% change in price}, we get: −0.8×5%=−4%-0.8 \times 5\% = -4\% The net effect combines both: +15% (from corn price increase) + (-4%) (from wheat price increase) = +11% increase in wheat quantity demanded. Choice A incorrectly claims a 19% increase, apparently adding 15% + 4% without recognizing that the own-price effect reduces demand. Choice C shows only a 4% increase, which appears to subtract the full 15% cross-price effect from some other calculation. Choice D incorrectly concludes the own-price effect dominates, leading to decreased demand, when the substitution effect (+15%) clearly outweighs the own-price effect (-4%). Remember: When multiple price changes affect demand simultaneously, calculate each elasticity effect separately using the appropriate elasticity coefficient, then add the percentage changes algebraically to find the net effect.
  11. A typical consumer spends a very small fraction of their income on table salt but a significant portion of their income on housing. If the prices of both salt and housing were to increase by 20%, the percentage decrease in quantity demanded would likely be:
    Answer: greater for housing because it represents a larger proportion of a consumer's budget. One of the key determinants of price elasticity of demand is the proportion of income spent on the good. Goods that constitute a large share of a consumer's budget, like housing, tend to have more elastic demand because a price increase has a significant impact on the consumer's ability to purchase other goods. Goods that make up a very small budget share, like salt, tend to have very inelastic demand because the price change is almost unnoticeable in the consumer's overall budget. Therefore, a 20% price increase will cause a much larger percentage drop in quantity demanded for housing than for salt.
  12. A city government imposed a 5% tax on restaurant meals to raise revenue. A year later, it was found that total consumer spending on restaurant meals, including the tax, had decreased significantly, and tax revenues were far below projections. Which statement provides the best explanation for this outcome?
    Answer: The demand for restaurant meals was more price elastic than the government had estimated. When you encounter tax policy questions, focus on how price elasticity of demand determines consumer responses to price changes. Price elasticity measures how sensitive quantity demanded is to price changes - elastic demand means consumers are very responsive to price increases. The evidence points clearly to elastic demand: when the 5% tax raised meal prices, consumer spending fell significantly and tax revenues came in far below projections. This tells you that consumers dramatically reduced their restaurant visits in response to higher prices, indicating they viewed restaurant meals as easily substitutable with alternatives like home cooking or takeout. Let's examine why the other options don't fit. Option B suggests perfectly inelastic supply, meaning restaurants absorbed the entire tax without raising prices. But this contradicts the scenario - if prices hadn't increased, consumer spending wouldn't have dropped. Option C claims demand was more inelastic than estimated, but inelastic demand means consumers continue purchasing despite price increases, which would have generated the projected tax revenue. Option D refers to income elasticity (how demand responds to income changes), but this scenario involves a tax-induced price change, not an income change. The government clearly underestimated how price-sensitive restaurant customers are. When dining became more expensive, consumers found substitutes rather than paying the higher prices. Study tip: Remember that when tax revenues fall short of projections after a tax increase, it usually signals that demand was more elastic than policymakers anticipated. Consumers found alternatives rather than paying the higher price.
  13. When the price of Product X increases by 10%, the quantity demanded of Product X falls by 5%. In response to the price change of Product X, the quantity demanded of Product Y increases by 8%. Based on this information, the price elasticity of demand for Product X is:
    Answer: -0.5 The question specifically asks for the price elasticity of demand for Product X. This is calculated as the percentage change in the quantity demanded of X divided by the percentage change in the price of X. The information about Product Y is extraneous and relates to cross-price elasticity. PEDX=(%ΔQX)/(%ΔPX)=(−5%)/(+10%)=−0.5PED_X = (\%\Delta Q_X) / (\%\Delta P_X) = (-5\%) / (+10\%) = -0.5.
  14. A major city invests heavily in a new, extensive public transportation system, creating a convenient alternative to driving. At the same time, the price of gasoline rises significantly. How will the combination of these two events likely affect the price elasticity of demand for gasoline in this city?
    Answer: Both events will make the demand for gasoline more price elastic. Two determinants of price elasticity are at play. First, the new public transportation system is a substitute for driving, and therefore for gasoline. An increase in the availability of substitutes makes the demand for a good more elastic. Second, a significant price increase means consumers are operating on a higher portion of their demand curve. For a typical linear demand curve, demand is more elastic at higher prices than at lower prices. Therefore, both events work in the same direction to make the demand for gasoline more price elastic.
  15. A firm faces a linear demand curve for its product. At the current price of $20, it sells 100 units per week. The firm's marketing department provides a reliable estimate that the price elasticity of demand at this point is -2.5. To maximize its weekly total revenue, the firm should:
    Answer: lower the price, because demand is elastic. The price elasticity of demand is -2.5. The absolute value, 2.5, is greater than 1, which indicates that demand is price elastic at the current price. Total revenue is maximized when price elasticity of demand is unit elastic (equal to -1). When demand is elastic, a decrease in price leads to a proportionally larger increase in quantity demanded, thus increasing total revenue. Therefore, the firm should lower its price from $20 to move down the demand curve towards the unit-elastic point and increase its total revenue.
  16. For which of the following pairs of goods is the first good likely to have a significantly more price elastic demand than the second good, ceteris paribus?
    Answer: A round-trip airline ticket from New York to London vs. tap water from a local utility. Price elasticity of demand is determined by factors such as the availability of substitutes, whether the good is a necessity or luxury, the definition of the market, and the time horizon. An airline ticket is a non-essential service with substitutes (other airlines, other destinations, not traveling) and represents a significant budget item, making its demand relatively elastic. Tap water is a necessity with no substitutes and a small budget share, making its demand highly inelastic. Therefore, the airline ticket (first good) is more price elastic than tap water (second good). The other pairs have the relationship reversed.
  17. A concert promoter lowers the ticket price for a show from $60 to $50 and observes that the quantity of tickets sold increases from 2,000 to 2,500. Based solely on this information, which action should the promoter take to continue increasing total revenue?
    Answer: Lower the ticket price further, because demand is price elastic in this range. To determine the correct strategy, we use the total revenue test. Initial total revenue was $60 × 2,000 = $120,000. The new total revenue is $50 × 2,500 = $125,000. Since a decrease in price led to an increase in total revenue, the demand for tickets in this price range is price elastic. When demand is price elastic, a firm should continue to lower its price to increase total revenue, moving towards the unit-elastic point on the demand curve.
  18. An economist estimates that the price elasticity of demand for gasoline is -0.3 in the short run and -1.2 in the long run. If gasoline prices increase by 25%, what is the expected difference between short-run and long-run percentage changes in quantity demanded?
    Answer: The long-run decrease will be 22.5 percentage points greater than the short-run decrease in quantity demanded Short-run: % change in quantity = elasticity × % change in price = -0.3 × 25% = -7.5%. Long-run: % change in quantity = -1.2 × 25% = -30%. The difference is 30% - 7.5% = 22.5 percentage points. Choice B confuses the elasticity coefficients with the actual percentage changes. Choice C states the correct values but reverses the comparison. Choice D incorrectly calculates the relationship between the elasticities.
  19. A coffee shop notices that when it raises the price of its specialty latte from $4.50 to $5.50, daily sales decrease from 120 lattes to 96 lattes. However, when the shop raises the price of its basic coffee from $2.00 to $2.40, daily sales decrease from 200 cups to 180 cups. What can be concluded about the relative price elasticities of demand for these two products?
    Answer: The specialty latte has more elastic demand than basic coffee because its elasticity coefficient is approximately -1.0 compared to -0.5 for basic coffee For the specialty latte: % change in quantity = (96-120)/120 = -20%; % change in price = (5.50-4.50)/4.50 = 22.2%; elasticity = -20%/22.2% ≈ -0.9. For basic coffee: % change in quantity = (180-200)/200 = -10%; % change in price = (2.40-2.00)/2.00 = 20%; elasticity = -10%/20% = -0.5. The specialty latte is more elastic. Choice A makes an unsupported generalization. Choice B incorrectly compares absolute rather than percentage changes. Choice D ignores the percentage-based nature of elasticity calculations.
  20. A luxury car dealership notices that during economic recessions, a 20% decrease in consumer income leads to a 60% decrease in luxury car sales, while a 15% increase in the price of gasoline leads to a 45% decrease in luxury car sales. What do these elasticities suggest about the dealership's optimal pricing strategy during economic downturns?
    Answer: Focus on cost reduction rather than price changes because both income elasticity (+3.0) and gasoline cross-price elasticity (-3.0) indicate demand is driven by external factors Income elasticity = (-60%)/(-20%) = +3.0 (luxury good). Gasoline cross-price elasticity = (-45%)/(+15%) = -3.0 (complementary relationship). Both elasticities are high in absolute value, indicating that external factors (income and gas prices) have much larger effects on demand than the dealership's own pricing decisions would. Therefore, focusing on operational efficiency and cost control makes more sense than price manipulation. Choice A misunderstands how income elasticity works during recessions. Choice B ignores that both effects matter. Choice D contradicts economic logic about luxury goods during recessions.

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