Determinants and uses of price elasticity of demand – Elasticity (Senior 4 Economics) | Ganzaa

Elasticity

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Senior 4 · Economics

Elasticity

4 lessons

Lesson 2 of 4

Determinants and uses of price elasticity of demand

35 min

Why tax beer, cigarettes and fuel?

The Rwanda Revenue Authority (RRA) lists the excise duty rates now in force: 65% on most beer (40% where at least 70% of the raw materials, excluding water, are local), 36% of the retail price plus Frw 230 on a pack of 20 cigarettes, Frw 183 on each litre of premium petrol and Frw 150 on each litre of gas oil (diesel). It is no accident that governments everywhere tax these particular goods. People keep buying them when their prices rise, so a tax brings in a reliable revenue. This lesson explains what makes demand elastic or inelastic, and then puts PED to work for firms, farmers and the government.

1. What makes demand elastic or inelastic?

Determinant	More elastic when…	More inelastic when…
Substitutes	There are many close substitutes (one brand of soap)	There are few or none (salt, electricity)
Necessity or luxury	The good is a luxury that can be done without	The good is a necessity (basic food, medicine)
Share of income	It takes a large share of income (a motorcycle)	It takes a tiny share (a box of matches)
Time	Buyers have time to find alternatives (the long run)	The period is short; habits and equipment are fixed
Habit and addiction	The good is bought casually	The good is habit-forming (cigarettes, alcohol)
Number of uses	The good has many uses, some of which can be dropped	It has only one use
Durability	Purchase can be postponed (a new television)	It must be bought now (perishable food)
Definition of the market	The market is narrow (one company's buses)	The market is broad (all transport)
Complements	—	It is a small, needed part of a costly whole (a spark plug for a car)
Position on the curve	The price is high relative to the quantity	The price is low relative to the quantity

Definition

Tax incidence: how the burden of a tax is shared between buyers and sellers. It does not depend on who hands the money to the RRA; it depends on the elasticities of demand and supply.

Near the original equilibrium, the share paid by buyers is approximately

\text{Buyers' share} = \frac{\text{PES}}{\text{PES} + |\text{PED}|}

so the more inelastic the demand, the more of the tax falls on buyers.

2. Uses of PED

Pricing by firms: raise the price where demand is inelastic, cut it where demand is elastic, to increase total revenue.
Taxation: the government raises most revenue, with the least fall in sales, by taxing goods with inelastic demand. The same fact means a tax on a demerit good such as cigarettes raises money but reduces smoking only a little, so it is combined with bans on advertising and on smoking in public places.
Price discrimination: a firm that can separate its buyers charges a higher price in the market where demand is less elastic, for example business travellers as against students.
Farm incomes: because demand for food is inelastic, a big harvest can lower farmers' total revenue (Worked example 2).
Devaluation: a cheaper franc raises export earnings only if foreign demand for the exports is elastic enough.
Wage bargaining: a trade union can win higher wages with fewer job losses when demand for the product its members make is inelastic.
Public utilities and transport: fare and tariff setting, such as off-peak prices to fill empty buses.

Worked example 1: who really pays a fuel tax? (illustrative market)

Demand for fuel at one depot is $Q_d = 2\,000 - 0.5P$ and supply is $Q_{s} = - 400 + 2 P$ (Q in thousand litres a day, P in Frw per litre). A tax of Frw 183 per litre, the RRA's rate on premium petrol, is charged to sellers.

Before the tax: $2\,000 - 0.5P = -400 + 2P \Rightarrow 2.5P = 2\,400 \Rightarrow P_0 = 960,\ Q_0 = 1\,520$ .

After the tax: sellers keep $P - 183$ , so supply becomes $Q_{s} = - 400 + 2 (P - 183) = - 766 + 2 P$ :

2\,000 - 0.5P = -766 + 2P \Rightarrow 2.5P = 2\,766 \Rightarrow P_1 = 1\,106.4,\ Q_1 = 1\,446.8

Who pays: buyers pay $1\,106.4 - 960 = 146.4$ more per litre; sellers keep $1\,106.4 - 183 = 923.4$ , which is $36.6$ less than before.

\text{Buyers' share} = \frac{146.4}{183} = 0.80 = 80\%

Check with elasticities at the old equilibrium: $|\text{PED}| = 0.5 \times \frac{960}{1\,520} \approx 0.32$ and $\text{PES} = 2 \times \frac{960}{1\,520} \approx 1.26$ , so $\frac{1.26}{1.26 + 0.32} \approx 0.80$ . Demand is inelastic, so buyers carry most of the tax.

Tax revenue: $183 \times 1\,446.8$ thousand litres $\approx \text{Frw } 265$ million a day, while sales fall by under 5%.

Worked example 2: the farmers' paradox (illustrative)

National demand for beans is $P = 2\,400 - 20Q$ (P in Frw per kg, Q in thousand tonnes). Last season farmers harvested 90 thousand tonnes; this season the rains were good and they harvested 100 thousand tonnes.

P_0 = 2\,400 - 20(90) = 600 \qquad P_1 = 2\,400 - 20(100) = 400

\text{TR}_0 = 600 \times 90 \text{ million kg} = \text{Frw } 54 \text{ billion} \qquad \text{TR}_1 = 400 \times 100 \text{ million kg} = \text{Frw } 40 \text{ billion}

Output rose by about 11%, but the price fell by a third, so farmers' revenue fell by about 26%. The reason is inelastic demand: $|\text{PED}| = \frac{1}{20} \times \frac{600}{90} \approx 0.33$ at the old equilibrium. This is the fallacy of composition from Unit 1, now explained by elasticity, and it is why governments try to stabilise farm prices (Unit 4).

Warning

A tax is not always "paid by the seller". The law may tell the importer or the brewer to pay the RRA, but the price rises and buyers bear part of it. With very inelastic demand, almost all of it. Always say who bears the burden, not just who hands over the money.

Tip

"SPLAT" for determinants of PED: Substitutes, Proportion of income, Luxury or necessity, Addiction and habit, Time. Then add durability, number of uses and the breadth of the market.

Important

Discuss. RRA taxes locally made beer at 40% but other beer at 65%. Using elasticity and the idea of substitutes, explain how this difference might affect what Rwandan drinkers buy and what brewers produce.

EconplusDal, "PED and Total Revenue". Watch how he links the elasticity of demand to a firm's pricing decision, then apply the same reasoning to the farmers' paradox above.

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Practice

Explain five determinants of the price elasticity of demand.
Why is the demand for salt inelastic, while the demand for one particular brand of salt is elastic?
Explain why the government prefers to levy excise duty on goods with inelastic demand.
Demand is $Q_{d} = 300 - P$ and supply is $Q_{s} = 2 P$ . A tax of 30 per unit is imposed on sellers. Find the new equilibrium price paid by buyers, the price kept by sellers, and each side's share of the tax.
The harvest of Irish potatoes rises by 20% and, because demand is inelastic, the price falls by 40%. By what percentage does farmers' total revenue change?
Explain how a bus company could use PED to set peak and off-peak fares.
Why is the tax on cigarettes, on its own, a weak way to reduce smoking?
"Raising a tax on a good always raises the government's tax revenue." Discuss, using elasticity.

Show answersHide answers

Any five: availability of substitutes; necessity or luxury; proportion of income; time period; habit and addiction; number of uses; durability; breadth of the market; position on the demand curve.
Salt as a whole has no substitute and costs very little; one brand of salt has many close substitutes (other brands), so buyers switch when its price rises.
Sales fall little when the price rises, so the tax base stays large and revenue is high and predictable.
Before: $300 - P = 2P \Rightarrow P = 100,\ Q = 200$ . After: $Q_{s} = 2 (P - 30)$ : $300 - P = 2P - 60 \Rightarrow P = 120,\ Q = 180$ . Buyers pay 120 (20 more); sellers keep 90 (10 less). Buyers bear $\frac{20}{30} = \frac{2}{3}$ , sellers $\frac{1}{3}$ .
New TR $= 1.2 \times 0.6 = 0.72$ of the old: a fall of 28%.
Demand at peak hours (commuters) is inelastic, so a higher fare raises revenue; off-peak demand is elastic, so a lower fare attracts many more riders and fills empty seats.
Smokers are addicted, so demand is inelastic: a price rise reduces consumption only a little. Bans on advertising, public-smoking rules and health campaigns are also needed.
Not always. If demand is elastic, a higher tax raises the price, sales fall sharply and the tax base shrinks, so revenue can fall. Revenue rises with the tax only while demand stays fairly inelastic.

Quick check

Match each good to the main reason its demand is likely to be inelastic or elastic.

Tap one on the left, then its partner on the right.

Key points

Demand is more elastic with more substitutes, for luxuries, for goods taking a big share of income, over longer periods and for narrowly defined markets.
Firms use PED to price; governments to choose what to tax; farmers' incomes depend on it.
The more inelastic the demand, the larger the share of a tax borne by buyers: about $\frac{\text{PES}}{\text{PES} + |\text{PED}|}$ .
With inelastic demand, a bigger harvest can mean lower farm revenue.

Sources and credits

Excise duty rates: Declare your excise duty, Rwanda Revenue Authority (RRA), rates table as published in 2026.
Video: Y1 11) PED and Total Revenue, EconplusDal, embedded from YouTube.

Written by Ganzaa: the text, the tax-incidence and harvest diagrams (drawn to scale from their equations), the tables, the worked examples and the practice items. The fuel and bean markets are illustrative; only the tax rates are real.

1Why tax beer, cigarettes and fuel?

21. What makes demand elastic or inelastic?

32. Uses of PED

Why tax beer, cigarettes and fuel?

1. What makes demand elastic or inelastic?

2. Uses of PED