Business Calculus Quiz: Elastic Vs Inelastic Demand
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Elastic Vs Inelastic DemandQuestion 1 of 17

The demand for a specialized electronic component is given by the function D(p)=200(40−p)1.5D(p) = 200(40-p)^{1.5}, where pp is the price in dollars. The component is currently priced at p = \24$. If the company implements a small price increase, what will be the effect on total revenue?

Total revenue will decrease because demand is elastic.
Total revenue will increase because demand is inelastic.
Total revenue will decrease because demand is inelastic.
Total revenue will increase because demand is elastic.
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Business Calculus Quiz

Business Calculus Quiz: Elastic Vs Inelastic Demand

Practice Elastic Vs Inelastic Demand in Business Calculus with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Elastic Vs Inelastic Demand, giving you a quick way to practice the rules, question types, and explanations that matter most for Business Calculus.

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Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

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Question 1

The demand for a specialized electronic component is given by the function D(p)=200(40−p)1.5D(p) = 200(40-p)^{1.5}, where pp is the price in dollars. The component is currently priced at p = \24$. If the company implements a small price increase, what will be the effect on total revenue?

  1. Total revenue will decrease because demand is elastic. (correct answer)
  2. Total revenue will increase because demand is inelastic.
  3. Total revenue will decrease because demand is inelastic.
  4. Total revenue will increase because demand is elastic.
Explanation: First, calculate the elasticity of demand, E(p)=−p⋅D′(p)D(p)E(p) = -\frac{p \cdot D'(p)}{D(p)}. The derivative of the demand function is D′(p)=200⋅1.5(40−p)0.5(−1)=−30040−pD'(p) = 200 \cdot 1.5(40-p)^{0.5}(-1) = -300\sqrt{40-p}. At p=24p=24, we have D(24)=200(16)1.5=200(64)=12800D(24) = 200(16)^{1.5} = 200(64) = 12800 and D′(24)=−30016=−300(4)=−1200D'(24) = -300\sqrt{16} = -300(4) = -1200. Plugging these into the elasticity formula: E(24)=−24⋅(−1200)12800=2880012800=2.25E(24) = -\frac{24 \cdot (-1200)}{12800} = \frac{28800}{12800} = 2.25. Since E=2.25>1E = 2.25 > 1, demand is elastic. When demand is elastic, a price increase leads to a decrease in total revenue.

Question 2

A company finds that its revenue is maximized when it prices its product at p = \50.Basedontherelationshipbetweenrevenueandelasticity,whatcanbeconcludedabouttheelasticityofdemandatpricesof. Based on the relationship between revenue and elasticity, what can be concluded about the elasticity of demand at prices of p = $49andandp = $51$?

  1. Demand is elastic at p = \49andinelasticatand inelastic atp = $51$.
  2. Demand is inelastic at p = \49andelasticatand elastic atp = $51$. (correct answer)
  3. Demand is inelastic at both p = \49andandp = $51$.
  4. Demand is elastic at both p = \49andandp = $51$.
Explanation: Revenue is maximized at the price where demand is unit elastic (E=1E=1). For typical demand curves, at prices below the revenue-maximizing price, demand is inelastic (E<1E<1). At prices above the revenue-maximizing price, demand is elastic (E>1E>1). Therefore, at p = \49 (which is less than $50), demand is inelastic, and at $p = \51$ (which is greater than $50), demand is elastic.

Question 3

A coffee shop lowers the price of its signature latte by 3% and observes that its total revenue from the latte increases by approximately 1%. Which of the following statements about the demand for the latte at its original price is most accurate?

  1. Demand is inelastic, as the percentage increase in revenue is less than the percentage decrease in price.
  2. Demand is unit elastic, as both price and revenue changed.
  3. Demand is elastic, as a decrease in price led to an increase in total revenue. (correct answer)
  4. The elasticity cannot be determined without knowing the initial price and quantity sold.
Explanation: The relationship between revenue and elasticity dictates that if a price decrease leads to a revenue increase, the demand must be elastic (E>1E>1). The percentage change in quantity demanded must have been positive and greater in magnitude than the percentage change in price. Specifically, since %ΔR≈%Δp+%Δq\%\Delta R \approx \%\Delta p + \%\Delta q, we have 1%≈−3%+%Δq1\% \approx -3\% + \%\Delta q, which implies %Δq≈4%\%\Delta q \approx 4\%. The elasticity is E≈−%Δq%Δp=−4%−3%≈1.33E \approx -\frac{\%\Delta q}{\%\Delta p} = -\frac{4\%}{-3\%} \approx 1.33, which is greater than 1.

Question 4

The demand for a product is modeled by the equation p=100e−0.02qp = 100e^{-0.02q}, where pp is the price per unit and qq is the quantity demanded. At a production level of q=40q=40 units, is the demand elastic or inelastic, and what is the revenue implication of increasing production?

  1. Inelastic; increasing production will decrease total revenue.
  2. Elastic; increasing production will decrease total revenue.
  3. Elastic; increasing production will increase total revenue. (correct answer)
  4. Inelastic; increasing production will increase total revenue.
Explanation: Since price is given as a function of quantity, we can use the elasticity formula E(q)=−p/qdp/dqE(q) = -\frac{p/q}{dp/dq}. First, find dp/dq=100e−0.02q(−0.02)=−2e−0.02qdp/dq = 100e^{-0.02q}(-0.02) = -2e^{-0.02q}. Then E(q)=−100e−0.02q/q−2e−0.02q=50qE(q) = -\frac{100e^{-0.02q}/q}{-2e^{-0.02q}} = \frac{50}{q}. At q=40q=40, the elasticity is E(40)=5040=1.25E(40) = \frac{50}{40} = 1.25. Since E>1E > 1, demand is elastic. Increasing production (qq) requires a decrease in price (pp). When demand is elastic, a price decrease leads to an increase in total revenue. Therefore, increasing production will increase revenue.

Question 5

A company sells a product with a linear demand function p=80−0.5qp = 80 - 0.5q, where pp is the price in dollars and qq is the number of units. For what range of prices is the demand for this product elastic?

  1. For prices between $0 and $40.
  2. For prices between $40 and $80. (correct answer)
  3. Only at the price of $40.
  4. For all prices greater than $80.
Explanation: For a linear demand curve, demand is unit elastic at the price that maximizes revenue. Revenue is R(q)=p⋅q=(80−0.5q)q=80q−0.5q2R(q) = p \cdot q = (80 - 0.5q)q = 80q - 0.5q^2. To maximize revenue, find where R′(q)=0R'(q)=0: R′(q)=80−q=0R'(q) = 80 - q = 0, which gives q=80q=80. The price corresponding to this quantity is p = 80 - 0.5(80) = 80 - 40 = \40.Demandisunitelasticat. Demand is unit elastic at p=$40.Thedemandcurveintersectsthepriceaxisat. The demand curve intersects the price axis at p=$80(when(whenq=0). Demand is elastic on the upper half of the price range of the demand curve. Therefore, demand is elastic for prices between \40 and $80.

Question 6

A company's demand function is p=120−0.5qp = 120 - 0.5q, where pp is the price per unit and qq is the quantity demanded. At what price level does the demand transition from elastic to inelastic, and what strategic pricing decision should the company make if their current price is $45?

  1. The transition occurs at $60; since current demand is elastic, the company should increase price to maximize revenue (correct answer)
  2. The transition occurs at $60; since current demand is inelastic, the company should decrease price to maximize revenue
  3. The transition occurs at $75; since current demand is elastic, the company should decrease price to maximize revenue
  4. The transition occurs at $75; since current demand is inelastic, the company should increase price to maximize revenue
Explanation: First, find the elasticity transition point where |E| = 1. For linear demand p = a - bq, this occurs at p = a/2 = 120/2 = $60. At the current price of $45 (below $60), demand is elastic (|E| > 1), so revenue increases when price increases toward the unit elastic point. Choice B incorrectly states current demand is inelastic. Choices C and D incorrectly calculate the transition point as $75.

Question 7

A subscription service has a demand function q=500e−0.02pq = 500e^{-0.02p} where qq is the number of subscribers and pp is the monthly price. If the company's current price yields an elasticity of demand of -0.8, what pricing adjustment should the company make to maximize revenue?

  1. Maintain the current price because demand elasticity of -0.8 indicates revenue is already maximized
  2. Decrease the price because demand is elastic and lower prices will increase revenue until elasticity reaches -1
  3. Increase the price because demand is inelastic and higher prices will increase revenue until elasticity reaches -1 (correct answer)
  4. The elasticity value is impossible for this demand function, so no pricing decision can be made
Explanation: When you encounter price elasticity and revenue optimization problems, remember that revenue is maximized when the price elasticity of demand equals exactly -1. This is because elasticity measures how responsive quantity demanded is to price changes, and at elasticity = -1, the percentage change in quantity exactly offsets the percentage change in price. Since the current elasticity is -0.8, demand is inelastic (absolute value less than 1). This means subscribers are relatively unresponsive to price changes. When demand is inelastic, increasing price will increase total revenue because the price increase more than compensates for the small decrease in quantity demanded. The company should increase price until the elasticity reaches -1, at which point revenue will be maximized. Answer C correctly identifies this strategy. Answer A is wrong because -0.8 indicates the company hasn't reached the revenue-maximizing point yet. Revenue is only maximized when elasticity equals -1, not -0.8. Answer B incorrectly classifies -0.8 as elastic demand. Demand is only elastic when the absolute value exceeds 1. Additionally, it suggests decreasing price, which would move further away from the revenue-maximizing elasticity of -1. Answer D is incorrect because an elasticity of -0.8 is perfectly reasonable for an exponential demand function. Elasticity values between 0 and -1 indicate inelastic demand, which is common for many products and services. Study tip: Remember the revenue rule: if |elasticity| < 1 (inelastic), raise prices; if |elasticity| > 1 (elastic), lower prices. Stop when you reach |elasticity| = 1.

Question 8

A concert venue has estimated its demand function as p=150−0.25qp = 150 - 0.25q where pp is the ticket price and qq is the number of tickets sold. The venue manager observes that when they reduced the price from $90 to $80, total revenue increased. However, when they further reduced the price from $80 to $70, total revenue decreased. What explains this pattern?

  1. The demand curve parameters were incorrectly estimated since revenue should always increase when moving from inelastic to elastic demand
  2. The venue crossed the unit elastic point (where revenue is maximized) between the $90-$80 and $80-$70 price reductions
  3. Consumer behavior changed between the two price reductions, invalidating the original demand function
  4. The venue moved from the elastic region to the inelastic region, passing through the revenue-maximizing point (correct answer)
Explanation: For p = 150 - 0.25q, revenue is maximized where MR = 0. Since MR = 150 - 0.5q and setting this to zero gives q = 300, so p* = $75. At $90 (above $75), demand is elastic, so reducing price increases revenue. At $80 (above $75), demand is still elastic. At $70 (below $75), demand is inelastic, so reducing price decreases revenue. The venue moved from elastic to inelastic demand, passing through the maximum at $75. Choice B incorrectly suggests the unit elastic point was between $90 and $80.

Question 9

The price elasticity of demand for a product is given by the function E(p)=p200−pE(p) = \frac{p}{200-p}. The product is currently selling for p = \120$. To increase total revenue, which of the following actions should the company take?

  1. Decrease the price. (correct answer)
  2. Increase the price.
  3. Keep the price the same, as revenue is already at its maximum.
  4. Increase production, which is independent of the pricing decision for revenue.
Explanation: When you encounter price elasticity of demand problems, remember that elasticity measures how responsive quantity demanded is to price changes, and it directly impacts revenue decisions. The key insight is that revenue increases when you move toward unit elasticity (where ∣E∣=1|E| = 1). First, let's calculate the current elasticity: E(120)=120200−120=12080=1.5E(120) = \frac{120}{200-120} = \frac{120}{80} = 1.5. Since the elasticity is greater than 1 in absolute value, demand is elastic at this price point. When demand is elastic (∣E∣>1|E| > 1), a price decrease will increase total revenue because the percentage increase in quantity demanded exceeds the percentage decrease in price. Conversely, when demand is inelastic (∣E∣<1|E| < 1), price increases boost revenue. Revenue is maximized when ∣E∣=1|E| = 1. Looking at each option: A) is correct because decreasing price when demand is elastic increases revenue. B) is wrong because increasing price when demand is elastic would decrease revenue - the large drop in quantity would outweigh the price gain. C) is incorrect because revenue isn't maximized; that would occur when E=1E = 1, which happens when p=100p = 100 (solving p200−p=1\frac{p}{200-p} = 1). D) is wrong because production changes don't directly affect the price-revenue relationship that elasticity governs. Study tip: Remember the elasticity rule of thumb: when ∣E∣>1|E| > 1 (elastic), move price in the opposite direction of where you want revenue to go. When ∣E∣<1|E| < 1 (inelastic), move price in the same direction as your revenue goal.

Question 10

The demand function for a digital subscription service is given by D(p)=5000p−1.5D(p) = 5000p^{-1.5}, where pp is the monthly price. Which statement accurately describes the relationship between price and revenue for this service?

  1. The effect of a price change on revenue depends on whether the current price is high or low.
  2. Any price increase will always lead to an increase in revenue.
  3. Revenue is maximized when the price is set to p = \1.50$.
  4. Any price decrease will always lead to an increase in revenue. (correct answer)
Explanation: For a demand function of the form D(p)=kp−nD(p) = kp^{-n}, the elasticity of demand is constant and equal to nn. Here, n=1.5n=1.5. The elasticity of demand is E(p)=−p⋅D′(p)D(p)=−p⋅(5000(−1.5)p−2.5)5000p−1.5=1.5E(p) = -\frac{p \cdot D'(p)}{D(p)} = -\frac{p \cdot (5000(-1.5)p^{-2.5})}{5000p^{-1.5}} = 1.5. Since E=1.5E=1.5 for all prices p>0p > 0, demand is always elastic. When demand is elastic, a decrease in price leads to an increase in revenue.

Question 11

The demand equation for a product is given by q2+2p=600q^2 + 2p = 600, where pp is the price per unit and qq is the number of units demanded. The company plans to set the price at the level that maximizes its total revenue. At this specific price, what is the price elasticity of demand?

  1. It cannot be determined without calculating the revenue-maximizing price first.
  2. E=0E = 0
  3. E=1E = 1 (correct answer)
  4. E=2E = 2
Explanation: This is a conceptual question. Total revenue is maximized at the price (and corresponding quantity) where the price elasticity of demand is equal to 1. This condition is known as unit elasticity. No calculations are necessary to determine that E=1E=1 at the point of maximum revenue.

Question 12

A manufacturer's marketing department estimates that the price elasticity of demand for its flagship product is currently E=1.8E = 1.8. The company is considering a 5% price increase to improve its profit margins. What is the most likely immediate effect of this price increase on the company's total revenue?

  1. Total revenue will increase because the price increase outweighs the decrease in quantity sold.
  2. Total revenue will decrease because the percentage decrease in quantity demanded will be greater than 5%. (correct answer)
  3. Total revenue will remain unchanged because the price increase is small.
  4. The effect on total revenue cannot be predicted without knowing the product's cost structure.
Explanation: The elasticity of demand is E=1.8E=1.8, which is greater than 1. This means demand is elastic. For elastic demand, price and total revenue have an inverse relationship. An increase in price will lead to a decrease in total revenue. The definition of elasticity E=−%Δq%ΔpE = -\frac{\%\Delta q}{\%\Delta p} implies that %Δq=−E⋅%Δp=−1.8⋅(5%)=−9%\%\Delta q = -E \cdot \%\Delta p = -1.8 \cdot (5\%) = -9\%. Since the percentage decrease in quantity (9%) is larger in magnitude than the percentage increase in price (5%), total revenue will fall.

Question 13

Two firms compete in the same market with identical linear demand curves q=400−2pq = 400 - 2p. Firm A currently prices at $120 while Firm B prices at $80. Both firms are considering a 15% price reduction to gain market share. Based on elasticity analysis, which firm's strategy is more likely to succeed in increasing total revenue?

  1. Firm A's strategy is better because reducing price from the inelastic region yields larger revenue gains than from the elastic region
  2. Firm B's strategy is better because reducing price in the elastic region yields larger revenue gains than in the inelastic region (correct answer)
  3. Both strategies are equally effective since both firms face identical demand curves and percentage price reductions
  4. Neither strategy will increase revenue since 15% price reductions are too large for effective price discrimination
Explanation: For q = 400 - 2p, revenue is maximized at p = $100 (where MR = 400 - 4p = 0). Firm A at $120 is in the inelastic region (above $100), while Firm B at $80 is in the elastic region (below $100). When reducing price in the elastic region, revenue increases, but when reducing price in the inelastic region, revenue decreases. Therefore, Firm B's strategy will increase revenue while Firm A's will decrease it. Choice A incorrectly states that inelastic price reductions increase revenue.

Question 14

A software company's demand function is q=1000p1.5q = \frac{1000}{p^{1.5}} where qq is the number of licenses sold and pp is the price per license. The company wants to determine if increasing price from $100 to $110 will increase or decrease total revenue. What is the correct analysis?

  1. Revenue will increase because for this demand function, elasticity is constant at -1.5, making demand always elastic
  2. Revenue will decrease because for this demand function, elasticity is constant at -1.5, making demand always elastic (correct answer)
  3. Revenue will increase because the price increase moves the company closer to the revenue-maximizing price
  4. Revenue will decrease because the demand function shows that quantity falls faster than price rises
Explanation: For the demand function q = 1000p^(-1.5), the elasticity is constant: E_d = -(dq/dp)(p/q) = -(-1.5 × 1000p^(-2.5))(p/(1000p^(-1.5))) = -1.5. Since |E_d| = 1.5 > 1, demand is always elastic. When demand is elastic, price and revenue move in opposite directions, so increasing price decreases revenue. Choice A correctly identifies constant elasticity of -1.5 but incorrectly concludes revenue will increase. Choices C and D don't recognize the constant elasticity property.

Question 15

A firm's weekly revenue function is R(p)=p(100−2p)R(p) = p(100 - 2p) where pp is the price per unit. The marketing department reports that a 10% price increase from the current level resulted in a 12% decrease in total revenue. What does this indicate about the firm's current pricing strategy?

  1. The firm is currently at the revenue-maximizing price and should not change its pricing strategy
  2. The firm is currently pricing in the inelastic region and should decrease price to move toward revenue maximization
  3. The firm is currently pricing in the elastic region and should increase price to move toward revenue maximization (correct answer)
  4. The reported data is inconsistent with the given revenue function and cannot be used for pricing decisions
Explanation: When analyzing pricing strategy using revenue functions, you need to understand the relationship between price changes and revenue changes, which connects to the concept of price elasticity of demand. Let's verify the reported data first. The revenue function R(p)=p(100−2p)=100p−2p2R(p) = p(100 - 2p) = 100p - 2p^2 gives us R′(p)=100−4pR'(p) = 100 - 4p. To find the revenue-maximizing price, set R′(p)=0R'(p) = 0: 100−4p=0100 - 4p = 0, so p=25p = 25. At this optimal price, R(25)=25(100−50)=1250R(25) = 25(100 - 50) = 1250. Now, if a 10% price increase causes a 12% revenue decrease, this tells us the firm is currently pricing above the revenue-maximizing point. When you're in this region (called the elastic region), demand is highly responsive to price changes - a small price increase leads to a proportionally larger drop in quantity sold, reducing total revenue. To move toward revenue maximization, the firm should increase price until reaching p=25p = 25. Answer D is wrong because the reported data is actually consistent with the revenue function when the current price exceeds the optimal price. Answer A is incorrect because if the firm were at the revenue-maximizing price, a price increase wouldn't decrease revenue by 12%. Answer B misidentifies the pricing region - the firm is in the elastic region (above optimal price), not the inelastic region (below optimal price). Study tip: Remember that when price increases cause proportionally larger revenue decreases, you're in the elastic region above the revenue maximum. Counter-intuitively, you should continue increasing price to reach the peak.

Question 16

The price elasticity of demand for a product is Ed=−2p100−pE_d = -\frac{2p}{100-p}, where pp is the price. If the company currently charges $25 and is considering whether to raise or lower prices to increase revenue, which analysis is correct?

  1. At $25, |E_d| = 0.67 < 1, so demand is inelastic and the company should raise prices to increase revenue (correct answer)
  2. At $25, |E_d| = 0.67 < 1, so demand is elastic and the company should lower prices to increase revenue
  3. At $25, |E_d| = 1.5 > 1, so demand is elastic and the company should lower prices to increase revenue
  4. At $25, |E_d| = 1.5 > 1, so demand is inelastic and the company should raise prices to increase revenue
Explanation: Substituting p = 25: E_d = -2(25)/(100-25) = -50/75 = -2/3. So |E_d| = 2/3 ≈ 0.67 < 1, meaning demand is inelastic. When demand is inelastic, price and revenue move in the same direction, so raising prices increases revenue. Choice B correctly calculates elasticity but incorrectly identifies it as elastic. Choices C and D incorrectly calculate |E_d| = 1.5.

Question 17

The weekly demand for a luxury good is given by the demand function D(p)=800−10pD(p) = 800 - 10\sqrt{p}, where pp is the price in dollars. At what price is the demand for this good unit elastic?

  1. p = $6400.00
  2. p = $25600.00
  3. p = $53.33
  4. p = $2844.44 (correct answer)
Explanation: Demand is unit elastic when E(p)=1E(p)=1. The elasticity function is E(p)=−p⋅D′(p)D(p)E(p) = -\frac{p \cdot D'(p)}{D(p)}. First, find the derivative: D′(p)=−10⋅12p−1/2=−5p−1/2D'(p) = -10 \cdot \frac{1}{2}p^{-1/2} = -5p^{-1/2}. Now, substitute into the elasticity formula: E(p)=−p(−5p−1/2)800−10p=5p800−10pE(p) = -\frac{p(-5p^{-1/2})}{800-10\sqrt{p}} = \frac{5\sqrt{p}}{800-10\sqrt{p}}. Set E(p)=1E(p)=1: 1=5p800−10p1 = \frac{5\sqrt{p}}{800-10\sqrt{p}}. This gives 800−10p=5p800-10\sqrt{p} = 5\sqrt{p}, so 15p=80015\sqrt{p} = 800. Then p=80015=1603\sqrt{p} = \frac{800}{15} = \frac{160}{3}. Finally, p = (\frac{160}{3})^2 = \frac{25600}{9} \approx \2844.44$.