Price Elasticity of Supply - Microeconomics

1. Which of the following scenarios best illustrates a market with a perfectly inelastic supply?
   Answer: The market for admission tickets to a specific, sold-out concert at a venue with a fixed number of seats. Perfectly inelastic supply (Es = 0) occurs when the quantity supplied does not change regardless of the price. This happens when the quantity of a good is fixed. For a specific, sold-out concert, the number of seats in the venue is fixed. Even if prices in the resale market skyrocket, no more seats can be created for that event. The other options describe markets with varying degrees of positive elasticity: smartphones have elastic supply, wheat has supply that is elastic in the long run, and freelance services have a highly elastic supply due to low barriers to entry.
2. A linear supply curve for a product is given by the equation $Q_s = -50 + 10P$. What is the price elasticity of supply at a market price of $15?
   Answer: 1.5 To calculate point elasticity, we use the formula $E_s = \frac{dQ_s}{dP} \cdot \frac{P}{Q_s}$. First, find the quantity supplied at P=$15: $Q_s = -50 + 10(15) = -50 + 150 = 100$. The derivative $\frac{dQ_s}{dP}$ is the coefficient on P, which is 10. Now, substitute these values into the formula: $E_s = 10 \cdot \frac{15}{100} = \frac{150}{100} = 1.5$. This supply curve has a positive price-axis intercept (at P=5), so elasticity will be greater than 1. Distractor A is incorrect; unit elasticity would occur if the curve passed through the origin. Distractor B is the inverse of the correct answer (1/1.5). Distractor D incorrectly uses the slope coefficient as the elasticity.
3. If the price elasticity of supply for a good is 1.0, and the price of the good increases by 20%, what will be the resulting percentage change in total revenue for the producers?
   Answer: Total revenue will increase by 44%. When you encounter questions combining price elasticity of supply with total revenue, you need to work through two separate steps: first calculate the quantity change, then determine how both price and quantity changes affect total revenue. Given that price elasticity of supply equals 1.0 and price increases by 20%, you can find the quantity change using the elasticity formula: $\text{Price Elasticity of Supply} = \frac{\% \text{ Change in Quantity Supplied}}{\% \text{ Change in Price}}$ Substituting the known values: $1.0 = \frac{\% \text{ Change in Quantity Supplied}}{20\%}$ This means quantity supplied increases by 20%. Now for total revenue calculation. Since $\text{Total Revenue} = \text{Price} \times \text{Quantity}$, when both price and quantity increase by 20%, the total revenue change is: $(1.20) \times (1.20) = 1.44$, representing a 44% increase. Answer A (20% increase) incorrectly assumes only the price change matters, ignoring the quantity response. Answer B (unchanged) would only be correct if the supply curve were perfectly inelastic (elasticity = 0), where quantity doesn't respond to price changes. Answer C (10% increase) might result from incorrectly averaging the price and quantity changes, but this isn't how revenue calculations work. The key insight is that when supply is unit elastic (elasticity = 1.0), price and quantity move proportionally in the same direction, creating a multiplicative effect on total revenue rather than just an additive one. Always remember to calculate both the quantity response and then the combined revenue impact.
4. Firm A has a price elasticity of supply of 1.8. Firm B operates in the same competitive market and has a price elasticity of supply of 0.6. Both firms are currently producing the same quantity. If the market price increases by 15%, which of the following statements about the change in producer surplus is true?
   Answer: The producer surplus of Firm A will increase by a larger absolute amount than that of Firm B. Producer surplus is the area above the supply curve and below the market price. When price increases, this area grows. The increase consists of a rectangle (the price increase on the original quantity) and a triangle (the surplus on the new quantity produced). Since both firms produce the same initial quantity and face the same price increase, the rectangular portion of the increase is the same for both. However, Firm A has a more elastic supply, meaning its supply curve is flatter and it will increase its quantity supplied by a much larger amount in response to the price increase. This larger quantity response creates a larger triangular area of new surplus. Therefore, Firm A's total producer surplus will increase by a larger absolute amount.
5. A new government subsidy is provided to all firms in a market with a price elasticity of supply of 2.5. How will this subsidy affect the market supply curve?
   Answer: The supply curve will shift to the right, and its elasticity at any given price will decrease. A per-unit subsidy is equivalent to a decrease in production costs, which shifts the supply curve to the right (or downward). Let's analyze the effect on point elasticity, $E_s = (dQ/dP) \cdot (P/Q)$. A subsidy that shifts the supply curve parallelly does not change the slope term $dQ/dP$. However, after the shift, at any given market price P, the quantity supplied Q is now higher. Because Q is in the denominator of the P/Q ratio, a larger Q means a smaller P/Q ratio. Therefore, the elasticity at that specific price P will decrease. For example, if supply is $Q = 10P$, Es=1. A subsidy of $2 per unit means firms receive P+2, so new supply is $Q = 10(P+2) = 10P+20$. This curve is inelastic at low prices and approaches 1.
6. In the market for aged artisanal cheese, which requires a minimum of three years of aging, a sudden and permanent increase in consumer demand occurs. How will the price elasticity of supply for this cheese most likely change over time, moving from the short run to the long run?
   Answer: It will increase, as producers have more time to adjust production levels and new firms can enter the market. The primary determinant of price elasticity of supply that applies here is the time horizon. In the short run, supply is highly inelastic because the quantity of cheese that is already aged or in the process of aging is largely fixed. In the long run, however, producers can respond to sustained higher prices by building new aging facilities, increasing their herds, or having new firms enter the market. This flexibility means that the quantity supplied is more responsive to price changes in the long run. Therefore, the elasticity of supply will increase over time.
7. A manufacturer of a product is able to keep a large inventory at a very low cost. How does this capability affect the firm's short-run price elasticity of supply for its product?
   Answer: It makes supply highly elastic because quantity can be adjusted rapidly by selling from inventory. Price elasticity of supply measures how responsive quantity supplied is to price changes. The key insight is that anything allowing a firm to quickly adjust quantity supplied will make supply more elastic. When a manufacturer can maintain large inventories at low cost, they gain tremendous flexibility in responding to price changes. If market prices rise, they can immediately increase quantity supplied by drawing from their existing stock without waiting for new production. If prices fall, they can reduce quantity supplied by storing more goods rather than selling them. This ability to rapidly adjust quantity through inventory management makes their supply curve highly elastic. Answer D correctly identifies this relationship: low-cost inventory storage makes supply highly elastic because quantity can be adjusted rapidly. The firm isn't constrained by production capacity in the short run since they can tap into stored goods. Answer A misunderstands the scenario by focusing only on production levels while ignoring inventory. Even if production is fixed, total quantity supplied (production plus inventory drawdown) remains flexible. Answer B incorrectly suggests elasticity could be negative. Price elasticity of supply is virtually always positive since firms supply more at higher prices. Inventory being a "fixed asset" doesn't create a negative relationship between price and quantity supplied. Answer C wrongly claims only the production function matters for elasticity. In reality, anything affecting a firm's ability to adjust quantity supplied—including inventory management, storage capacity, or distribution networks—influences supply elasticity. Remember: supply elasticity depends on all factors that affect quantity adjustment speed, not just production constraints.
8. A bakery's daily bread supply follows the function $Q_s = 50 + 10P - 2P^2$ where $Q_s$ is loaves per day and P is price per loaf in dollars. At what price is the supply elasticity equal to zero?
   Answer: $2.50 When you encounter supply elasticity problems, you need to understand that elasticity measures how responsive quantity supplied is to price changes. Supply elasticity equals zero when the supply curve has zero slope - meaning quantity supplied doesn't change with small price changes at that point. To find where supply elasticity equals zero, you need to find where the derivative of the supply function equals zero. Taking the derivative of $Q_s = 50 + 10P - 2P^2$: $\frac{dQ_s}{dP} = 10 - 4P$ Setting this equal to zero: $10 - 4P = 0$, which gives us $P = 2.50$. At this price, the supply curve has zero slope, making elasticity zero. Choice A ($2.50) is correct because this is exactly where the derivative equals zero. Choice B ($2.00) represents a common calculation error - students might forget the coefficient 4 in front of P when taking the derivative. Choice C ($3.00) might result from incorrectly setting up the elasticity formula or making arithmetic mistakes. Choice D (supply elasticity is never zero) reflects a misunderstanding of how supply curves work - many students think supply always slopes upward, but this quadratic function actually peaks and then slopes downward. Remember that for any quadratic supply function $Q_s = a + bP - cP^2$ (where c > 0), there will always be a point where elasticity equals zero. Look for the derivative equaling zero to find this critical point where the supplier is momentarily unresponsive to price changes.
9. A firm's supply curve is linear and intersects the quantity axis at a positive value (e.g., 200 units). As the price increases and the firm moves upward along this supply curve, what happens to the price elasticity of supply?
   Answer: It increases and approaches one. The point elasticity formula is $E_s = (dQ/dP) \cdot (P/Q)$. For a linear supply curve $Q = a + bP$, the slope term $dQ/dP = b$ is constant. A positive quantity-axis intercept means $a > 0$. So, $E_s = b \cdot (P / (a + bP))$. As price P increases, the fraction $P / (a + bP))$ also increases, but it is always less than 1. As P becomes very large, this fraction approaches $bP/bP = 1$. Therefore, the elasticity starts at a value less than 1 and increases, approaching 1 as a limit. Students often incorrectly assume constant slope means constant elasticity.
10. Consider a perfectly competitive industry where each firm has the same supply function: $q = 2p - 10$ (where q is individual firm output and p is price). If there are currently 50 firms in the market, and the market price increases from $15 to $18, what is the short-run market elasticity of supply?
    Answer: 1.5 Individual firm supply: q = 2p - 10. Market supply: Q = 50q = 50(2p - 10) = 100p - 500. At p = $15: Q = 1000. At p = $18: Q = 1300. Using midpoint method: %ΔQ = (300/1150) × 100 = 26.09%. %ΔP = (3/16.5) × 100 = 18.18%. Elasticity = 26.09/18.18 = 1.43 ≈ 1.5. Choice A uses simple percentage change. Choice C assumes unit slope equals unit elasticity. Choice D incorrectly calculates the midpoint.
11. A firm's production process is characterized by a marginal cost that rises very rapidly as output increases. What does this imply about the firm's price elasticity of supply?
    Answer: Supply is highly inelastic because a large price increase is needed to justify a small increase in production. When you encounter questions about price elasticity of supply, focus on the relationship between price changes and quantity changes along the supply curve. The key insight is that marginal cost directly determines a firm's willingness to produce additional units. If marginal cost rises very rapidly, the firm faces steeply increasing costs for each additional unit produced. This means the firm will only produce more output if prices rise substantially to cover these higher costs. When a large price increase generates only a small quantity increase, supply is inelastic. The firm essentially says, "I'll only make a little bit more, even if you pay me much more, because my costs skyrocket." Answer D correctly captures this relationship: supply is highly inelastic because large price increases are needed to justify small production increases. Answer A misunderstands the concept entirely. High elasticity would mean the firm eagerly increases production with small price increases, but rapidly rising marginal costs make this impossible. Answer B confuses elasticity with profitability. Zero elasticity (perfectly inelastic) would mean quantity never changes regardless of price, which isn't what rapidly rising marginal costs implies. Answer C makes an incorrect connection between marginal cost and unit elasticity. While marginal cost does relate to supply curves, unit elasticity (where percentage price change equals percentage quantity change) isn't automatically created by this relationship. Remember: steep marginal cost curves create inelastic supply. When costs rise rapidly, firms need big price incentives to produce just a little bit more. Think "expensive to expand" equals "inelastic supply."
12. Which of the following goods is likely to have the most price-elastic supply?
    Answer: Digital copies of a software application. Elasticity of supply depends on how easily producers can change the quantity they produce. For digital goods like software, the marginal cost of producing an additional copy is virtually zero. The quantity can be increased almost infinitely and instantaneously in response to demand. Therefore, its supply is nearly perfectly elastic. In contrast, Rembrandt paintings have a perfectly inelastic supply (the quantity is fixed). The supply of surgeons and handmade barrels is inelastic in the short run due to long training periods and time-consuming production processes, respectively.
13. Consider a competitive market where supply is relatively elastic (e.g., $E_s = 1.8$) and demand is relatively inelastic (e.g., $|E_d| = 0.5$). If the government imposes a per-unit tax on producers, which outcome is most likely?
    Answer: Consumers bear most of the tax burden, and the equilibrium quantity decreases substantially. The burden of a per-unit tax falls more heavily on the side of the market that is less elastic. In this case, demand is inelastic (0.5) while supply is elastic (1.8), so consumers will bear the larger share of the tax burden. The change in equilibrium quantity depends on the elasticities of both supply and demand. Because supply is elastic, producers are very responsive to price changes. The tax effectively lowers the price they receive, causing them to reduce their quantity supplied by a large amount. Therefore, the equilibrium quantity will decrease substantially.
14. The price elasticity of supply for beachfront properties is estimated to be 0.2. If a new zoning law that restricts future coastal development unexpectedly causes the market price for existing properties to increase by 50%, what is the most likely impact on the total revenue received by sellers?
    Answer: Total revenue will increase by more than 50%. Total revenue is Price × Quantity (P×Q). The price increases by 50%. The price elasticity of supply (Es) is 0.2, which is inelastic. The percentage change in quantity supplied is $\%\Delta Q_s = E_s \cdot \%\Delta P = 0.2 \cdot 50\% = 10\%$. So, the quantity supplied increases by 10%. Since both price and quantity supplied increase, total revenue must increase. The new total revenue will be $(1.5 \cdot P_{old}) \cdot (1.1 \cdot Q_{old}) = 1.65 \cdot (P_{old} \cdot Q_{old})$. This is a 65% increase, which is more than 50%. Distractor A incorrectly applies the total revenue rule for price elasticity of demand. For supply, when price increases, quantity supplied also increases, so total revenue always increases. Distractor B only states the change in quantity, not revenue. Distractor D is incorrect because even with highly inelastic supply, there is still some quantity response unless it is perfectly inelastic.
15. The supply of a product is perfectly elastic. If the demand for this product increases, what will be the effect on the equilibrium price and quantity?
    Answer: Price will remain the same, and quantity will increase. When you encounter questions about perfectly elastic supply, remember that this describes a horizontal supply curve where producers are willing to supply any quantity at a fixed price, but none at any lower price. With perfectly elastic supply, the price is completely determined by the supply curve and cannot change regardless of demand shifts. When demand increases, the demand curve shifts rightward. At the intersection with the horizontal supply curve, the equilibrium moves to a higher quantity while the price remains exactly the same. Think of this like a perfectly competitive market where producers have constant marginal costs and can easily expand production without any price increases. Answer choice A is incorrect because while quantity does change with perfectly elastic supply, it increases rather than remaining the same. The horizontal supply curve allows for unlimited quantity expansion at the same price. Answer choice B is wrong because the effect on quantity is completely certain, not uncertain. With perfectly elastic supply, any increase in demand must result in higher quantity since price cannot adjust. Answer choice C represents the most common error students make. This would be correct for normal upward-sloping supply curves, but with perfectly elastic supply, the horizontal curve prevents any price increases regardless of demand changes. Answer choice D correctly identifies that price stays constant while quantity increases, which is the defining characteristic of perfectly elastic supply. Remember this pattern: perfectly elastic supply means horizontal supply curves, which always keep price fixed while allowing quantity to adjust freely to demand changes.
16. Based on the passage above, what can be concluded about the price elasticity of supply for wireless earbuds?
    Answer: The price elasticity of supply cannot be accurately calculated without controlling for the technology change effects. When analyzing supply elasticity, you need to isolate the effect of price changes from other factors that might shift the supply curve. Price elasticity of supply measures how responsive quantity supplied is to price changes alone, holding all other factors constant. The standard formula for price elasticity of supply is: $\frac{\% \text{ change in quantity supplied}}{\% \text{ change in price}}$. Using the given data, this would yield $\frac{20\%}{50\%} = 0.4$. However, this calculation is fundamentally flawed because it ignores the technological improvement that occurred simultaneously. The technology change that reduced marginal costs by $8 per unit represents a positive supply shock—it shifts the entire supply curve rightward, making producers willing to supply more at any given price. This means some of the observed quantity increase came from the technology improvement, not from the price increase. Without separating these effects, any elasticity calculation will be misleading. Answer D is correct because you cannot accurately measure price elasticity when multiple factors affecting supply change simultaneously. Answer A calculates a different elasticity value but still suffers from the same methodological problem of not controlling for technology changes. Answer B acknowledges the technology issue but incorrectly assumes you can still calculate a meaningful elasticity figure. Answer C attempts to "adjust" for cost reductions but provides no valid methodology for doing so with the given information. Study tip: When calculating any elasticity, always check whether "all else equal" conditions are met. If other demand or supply determinants changed during the period, the elasticity calculation will be contaminated and unreliable.
17. A breakthrough in 3D-printing technology makes it possible to manufacture complex industrial parts on-demand, significantly reducing the need for large, specialized factories. What is the likely effect of this innovation on the price elasticity of supply for these parts?
    Answer: It will increase because firms can more rapidly and flexibly respond to price changes by adjusting output. Price elasticity of supply is determined by factors that affect producers' ability to change output in response to price changes. The new technology increases flexibility and reduces the time and fixed investment needed to scale production. This enhanced ability to adjust output means that supply becomes more responsive to price signals, which is the definition of a higher price elasticity of supply.
18. In response to a 10% increase in the price of copper, a mining company increases its output by 6%. Over the next five years, with the price of copper remaining high, the company opens a new mine and its output increases by a total of 25% from its original level. This indicates that:
    Answer: The short-run elasticity of supply is 0.6 and the long-run elasticity is 2.5. Price elasticity of supply is $\%\Delta Q_s / \%\Delta P$. The short-run response is a 6% increase in quantity for a 10% price increase, so the short-run elasticity is $6\% / 10\% = 0.6$. The long-run response is a 25% increase in quantity for the same 10% price increase, so the long-run elasticity is $25\% / 10\% = 2.5$. This demonstrates the principle that supply is typically more elastic in the long run (2.5) than in the short run (0.6) because producers have more time to make significant adjustments to capacity.
19. If the price elasticity of supply for a particular agricultural good is calculated to be 0.75, what does this value imply?
    Answer: A 1% increase in price will lead to a 0.75% increase in quantity supplied. The price elasticity of supply measures the responsiveness of quantity supplied to a change in price. A value of 0.75 means that for every 1 percent change in price, the quantity supplied will change in the same direction by 0.75 percent. Since 0.75 is less than 1, supply is characterized as inelastic. Distractor A has the incorrect sign; this would describe price elasticity of demand. Distractor C confuses elasticity with the slope of the supply curve. Distractor D is a possible reason for inelastic supply, but it is not a direct implication of the numerical value itself; the value is simply a measurement of responsiveness.
20. The inverse supply function for a product is $P = 40 + 2Q_s$. At an equilibrium where 50 units are sold, what is the price elasticity of supply?
    Answer: 1.40 This problem requires multiple steps. First, find the price at the equilibrium quantity: $P = 40 + 2(50) = 40 + 100 = 140$. Second, find the supply function in terms of Q. The given function is the inverse supply function. We solve for $Q_s$: $P - 40 = 2Q_s \Rightarrow Q_s = 0.5P - 20$. Third, find the slope term for the elasticity formula, $dQ_s/dP$, which is 0.5. Finally, use the point elasticity formula $E_s = (dQ_s/dP) \cdot (P/Q_s)$: $E_s = 0.5 \cdot (140/50) = 0.5 \cdot 2.8 = 1.40$. Distractor A incorrectly uses the slope of the inverse supply function (2) and its inverse (0.5). Distractor C incorrectly uses just the slope of the inverse supply function (2). Distractor D is the P/Q ratio, not the full elasticity calculation.

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