Other Elasticities: Practice Questions (Microeconomics 2.5)

Answer: (A). % change in quantity = −2 ÷ 9 × 100 = −22.22%. % change in income = 10,000 ÷ 45,000 × 100 = 22.22%. YED = −22.22 ÷ 22.22 = −1.00. It is negative, so the coats are an inferior good for this group.

• (B) drops the minus sign. For YED the sign is the answer: a positive value would mean a normal good.
• (C) divides by the starting values (−20% ÷ 25%) instead of using the midpoint method.
• (D) uses starting values and puts income on top (25% ÷ −20%). Quantity always goes in the numerator.

Answer: (A). A negative XED means the price of Y and the quantity demanded of X move in opposite directions. That is the pattern for complements: when Y costs more, people buy less Y and so need less X. The demand curve for X shifts left.

• (B) uses the size instead of the sign. Whether goods are substitutes or complements depends on the sign; the size only shows how strong the link is.
• (C) mixes up cross-price and income elasticity. Only YED tells you whether a good is inferior.
• (D) mixes up cross-price and own-price elasticity. XED says nothing about how X’s quantity responds to X’s own price.

Answer: (A). The percentages are given, so divide directly: XED = 12 ÷ 8 = +1.5. Rail’s price and the quantity of coach tickets move in the same direction, so XED is positive and the goods are substitutes.

• (B) gives a negative sign although both changes are increases.
• (C) puts the price change on top (8 ÷ 12). The quantity change belongs in the numerator.
• (D) has the right number but the wrong conclusion. Positive XED means substitutes, not complements.

(a) % change in income = 500 ÷ 2,250 × 100 = 22.22%.

(b) Gym memberships: normal (positive). Bus passes: inferior (negative). Rice: normal (positive, but small). Gym memberships respond most: 1.29 is the largest value in size.

(c) % change in Q = YED × % change in income = 1.29 × 10 = about 12.9% more gym memberships.

Suggested mark points (3): 1 for the 22.22% income change and all three YEDs with signs; 1 for all three classifications based on the sign; 1 for about 12.9%.

Common error: comparing size and sign together. Bus passes (−0.78) are more responsive than rice (+0.20) even though −0.78 is the smaller number. Compare sizes to judge strength.

(a) Electric bicycles: 0.4 × 15 = +6%, so 800 × 1.06 = 848 per month. Large cars: −0.8 × 15 = −12%, so 300 × 0.88 = 264 per month.

(b) Each graph has “Price” on the vertical axis and “Quantity” (electric bicycles per month, or cars per month) on the horizontal axis, with a downward-sloping demand curve D₁. For electric bicycles, draw D₂ to the right of D₁. For large cars, draw D₂ to the left of D₁. Arrows show the direction of each shift. At the original price, D₂ should be at 848 bicycles and 264 cars.

(c) Electric bicycles have a positive XED: they are substitutes for driving a petrol car, so dearer petrol sends some travellers to electric bicycles and demand increases. Large cars have a negative XED: they are complements to petrol, because they cannot be used without it. Dearer petrol makes running one more expensive, so demand decreases.

Do not award the second point for a movement along the demand curve: the own price of each good has not changed.

(a) New price = $120 × 0.9 = $108. Quantity rises by 0.5 × 10 = 5%, to 21,000. Revenue goes from $120 × 20,000 = $2,400,000 to $108 × 21,000 = $2,268,000: a fall of $132,000. Demand for printers is inelastic, so the price cut lowers printer revenue.

(b) % change in cartridges = −1.2 × (−10) = +12%, so 50,000 × 1.12 = 56,000 cartridges. Cartridge revenue goes from $30 × 50,000 = $1,500,000 to $30 × 56,000 = $1,680,000: a rise of $180,000.

(c) Printers and cartridges are complements (negative XED). Cheaper printers mean more printers in use, which raises demand for cartridges. The extra cartridge revenue ($180,000) is larger than the lost printer revenue ($132,000), so total revenue rises by $48,000 per month.

(d) Positive. If the rival’s printers get cheaper, some buyers choose them instead of Inkwell printers. Fewer Inkwell printers in use means fewer Inkwell cartridges are needed. So the rival’s price falls and the quantity of Inkwell cartridges falls: they move in the same direction, giving a positive XED. The rival’s printers are substitutes for Inkwell printers, and that link passes through to the cartridges.

(a) % change in sales = 400 ÷ 4,200 × 100 = 9.52%. % change in advertising = 10,000 ÷ 25,000 × 100 = 40%. Elasticity = 9.52 ÷ 40 = 0.24. A 1% rise in advertising spending raises sales by about 0.24% at the same price. Demand responds, but by a much smaller percentage than the change in spending. Any determinant of demand can be measured this way.

(b) The law of demand means price elasticity of demand is always negative, so the sign adds no information and people often report the size only. Income and cross-price elasticities can be either positive or negative, and the sign carries the meaning: normal or inferior, substitutes or complements. Dropping it would turn one answer into its opposite.

(c) The claim is too strong. YED is measured over a range of incomes, and it can change sign as income changes. For example, a household on a very low income may buy more bus travel as its income rises (YED positive: normal), but once it is well off it may buy a car and use the bus less (YED negative: inferior). So a good can be normal over one income range and inferior over another, or for one group of buyers and not another. Over any one measured range, though, the sign gives one classification.