Exercises: Elasticity

Explain what the price elasticity of demand measures and write its formula using percentage changes: $E_p = \frac{\%\ \Delta Q_d}{\%\ \Delta P}$. What is the difference between elastic and inelastic demand?

The price of a music app rises by $10\ \%$ and subscriptions fall by $20\ \%$.

1. a) Calculate the price elasticity of demand in absolute value.
2. b) Classify the demand (elastic, unit elastic, or inelastic) and interpret the result.

The figure shows two demand curves, D1 and D2, intersecting at point P: one very steep and the other very flat.

1. a) Which of the two curves corresponds to a more elastic demand? Explain your answer by looking at the slope.
2. b) Give an example of a good that could have each curve and justify it.

When the price of sandwiches in the cafeteria rises from $\$80$ to $\$100$, daily sales fall from $100$ to $90$.

1. a) Calculate the percentage change in price and quantity.
2. b) Calculate the price elasticity in absolute value and interpret the result for the cafeteria.

Classify these demands as more elastic or more inelastic and justify each one considering substitutes and how necessary the good is: gas for a truck driver, movie tickets, a drug without a generic alternative, and a specific brand of cookies.

A cinema lowers the ticket price from $\$180$ to $\$140$ and weekend revenue changes from $\$90\,000$ to $\$112\,000$.

1. a) Calculate how many spectators there were before and after the price cut.
2. b) With these data, what can you say about the elasticity of demand in that price range? Reason the relationship between elasticity and total revenue.

A public metropolitan transport company operates at a loss. It currently charges $\$1.50$ per ticket and records $120,000$ daily trips. A technical report estimates that the price elasticity of demand in this range is $0.3$ in absolute value.

The Councillor for the Treasury proposes raising the ticket price by $20\ \%$ (up to $\$1.80$), stating: "Since the metro is an essential service, our daily revenue will increase by exactly $20\ \%$, which will allow us to restore the company to financial health while hardly losing any passengers." At the same time, a passenger association maintains that any price increase will lead to a drop in total revenue because people will stop using public transport.

1. a) Prove mathematically that both parties are mistaken: calculate the new quantity of daily trips, the percentage change in demand, and the final total revenue. Determine by what exact percentage revenue changes, and explain why the increase in revenue does not match the $20\ \%$ fare hike.
2. b) Imagine that the company operated in a coastal tourist city during the summer, where the price elasticity of the metro was $1.4$ due to an abundance of alternatives (rental bicycles, walking routes, scooters). Predict what would happen to revenue if the same $20\ \%$ price increase were applied, and justify what pricing policy the company should adopt in this second scenario if its goal were to increase revenue.

A sudden tourism boom generates a $40\ \%$ increase in demand for two goods in a coastal region: locally produced strawberries (for restaurants) and residential rental housing. In the first month after the shock, prices of both goods double ($+100\ \%$).

Eighteen months later, the market shows two opposite realities:

• The price of strawberries has returned practically to its original level and marketed production has tripled.

• The price of residential rent remains $80\ \%$ above the initial level and the number of rental flats has barely increased by $4\ \%$.

1. a) Interpret these data using the concept of price elasticity of supply. Explain how the elasticity of supply changes in the very short run (momentary run), the short run, and the long run in each of the two sectors, justifying the structural causes (production cycle, product perishability, planning permissions, and capital stock) that prevent housing from responding with the same agility as strawberries.
2. b) In the face of citizen protests, the city council plans to grant direct subsidies to construction companies, demanding that "within a maximum of six months, they double the supply of rental flats". Predict the real effectiveness of this measure based on the short-run elasticity of supply, and propose two alternative supply-oriented measures that would be viable over a five-year horizon.

The Ministry of Finance is considering two tax measures to increase public revenue and address health problems:

• Measure 1: A $30\ \%$ tax on a specific brand of sugary soft drink ("Choco-Cola").

• Measure 2: A $30\ \%$ tax on all tobacco products in general.

A junior adviser writes in their report: "Since the percentage tax rate is identical in both cases ($30\ \%$), we can expect an equivalent revenue and a similar $15\ \%$ reduction in the consumption of both harmful goods".

1. a) Refute the adviser's report by analysing how the breadth of the market definition (specific brand versus general category) and the availability of substitute goods influence the price elasticity of demand for each good. Predict, with reasoned arguments, in which of the two cases the drop in consumption will be drastic and in which it will be very small.
2. b) The public sector usually pursues two objectives with these taxes: a revenue-raising objective (generating income) and a corrective objective (reducing the consumption of goods with negative externalities). Explain the conflict or trade-off that arises between both objectives when taxing goods with elastic demand versus inelastic demand, and redesign the tax in Measure 1 so that it effectively reduces total consumption of sugary drinks rather than merely diverting buyers to competing brands.