ECON 1002 Week 6 Price Elasticity Write-up Example

Price Elasticity of Demand for Short-Term Stays in Port Ellery on an Ordinary Weeknight and During the River Festival: Two Midpoint Calculations, the Determinants Behind the Gap and the Total Revenue Test

Student Name

Walden University

ECON 1002: Microeconomics

Instructor Name

Month Day, Year

Price Elasticity of Demand for Short-Term Stays in Port Ellery on an Ordinary Weeknight and During the River Festival: Two Midpoint Calculations, the Determinants Behind the Gap and the Total Revenue Test

The Question

Everyone expects bookings to fall when nightly rates rise. The useful question for a host or a city planner is by how much, and whether the answer changes with the night. This write-up measures the price elasticity of demand for short-term stays in Port Ellery, a composite riverside city, in two situations: an ordinary Tuesday night in May and the Saturday night of the city's three-day river festival in July. All figures are illustrative.

The Data

Table 1

Illustrative Nightly Rates and Nights Booked Across the City

Figures are illustrative and represent nights booked across all listed units in the city on the given night.

Why the Midpoint Method

Price elasticity of demand, a measure Marshall (1890) introduced, compares two percentages: how far quantity demanded moves relative to how far the price moved. The difficulty is that a percentage change depends on the starting point: a rise from $90 to $110 is 22 percent, but a fall from $110 to $90 is 18 percent. The midpoint method solves this by dividing each change by the average of its two endpoints, which gives one answer whichever direction the price moves (Greenlaw et al., 2022).

Ordinary Weeknight

Change in quantity: 160 − 240 = -80. Midpoint quantity: (240 + 160) / 2 = 200. Percentage change in quantity: -80 / 200 = -40 percent.

Change in price: 110 − 90 = 20. Midpoint price: (90 + 110) / 2 = 100. Percentage change in price: 20 / 100 = 20 percent.

Elasticity: -40 / 20 = -2.0, or 2.0 in absolute value.

Demand on an ordinary weeknight is elastic. A 20 percent rise in rates cuts bookings by twice that share.

Festival Saturday

Change in quantity: 390 − 410 = -20. Midpoint quantity: (410 + 390) / 2 = 400. Percentage change in quantity: -20 / 400 = -5 percent.

Change in price: 250 − 150 = 100. Midpoint price: (150 + 250) / 2 = 200. Percentage change in price: 100 / 200 = 50 percent.

Elasticity: -5 / 50 = -0.1, or 0.1 in absolute value.

Festival demand is strongly inelastic. Rates rise by half and bookings barely move.

Why the Two Answers Differ

The main determinant is the availability of substitutes. A visitor planning a weeknight stay in May has many alternatives: a hotel room, a stay in a nearby town, a different week or no trip at all. When short-term rental rates rise, those alternatives are attractive, so many visitors switch. On festival Saturday, the alternatives mostly disappear. Hotels are full, the festival happens on one weekend only and visitors who have bought tickets and planned travel cannot easily move the date. With few substitutes, demand becomes insensitive to price (Mankiw, 2021).

Two other determinants point the same way. Time to adjust matters: festival visitors often book late, after ticket purchases are fixed, leaving little time to search for alternatives. And the share of the trip's total cost matters. For a festival visitor who has paid for tickets, travel and meals, a higher rate is a smaller part of a large budget, whereas for a weeknight visitor the room may be the main cost.

The Total Revenue Test

When demand is elastic, raising the price lowers total revenue; when demand is inelastic, raising it increases total revenue.

On the weeknight, revenue at $90 is $90 x 240 = $21,600, and at $110 it is $110 x 160 = $17,600. Revenue falls by $4,000, consistent with elastic demand.

On festival Saturday, revenue at $150 is $150 x 410 = $61,500, and at $250 it is $250 x 390 = $97,500. Revenue rises by $36,000, consistent with inelastic demand.

What This Means for Hosts and the City

For hosts, the results support low weeknight rates and high festival rates, which is what most already do. For the city, the festival result explains why visitors complain about festival prices: demand that does not respond to price lets rates climb far above their ordinary level. It also warns that a cap on festival rates would create a large shortage, since bookings would barely change at a lower price while some hosts would withdraw their units. These figures are illustrative, and real elasticities would need booking data across many nights.

References

Greenlaw, S. A., Shapiro, D., & MacDonald, D. (2022). Principles of microeconomics (3rd ed.). OpenStax. https://openstax.org/details/books/principles-microeconomics-3e

Mankiw, N. G. (2021). Principles of microeconomics (9th ed.). Cengage Learning.

Marshall, A. (1890). Principles of economics. Macmillan.