Tariff Systems (Grade 11 NSC Matric Mathematical Literacy): Revision Notes
Tariff Systems
What are tariff systems?
A tariff system is a pricing structure used by utility companies (like water and electricity providers) to charge customers for the services they use. These systems determine how much you pay based on how much water or electricity you consume each month.
There are different types of tariff systems, but the most common type you'll encounter in Mathematical Literacy is the incremental tariff system.
Tariff systems are designed not just to generate revenue for utility companies, but also to encourage responsible consumption of resources like water and electricity.
Incremental tariff systems
An incremental tariff system means that different portions of the total amount you use are charged at different rates. Instead of charging the same rate for every unit consumed, the price per unit increases as you use more.
This system encourages people to conserve water and electricity because:
- The first portion is often free or very cheap
- Each additional bracket costs more per unit
- Heavy users pay much higher rates
Critical Concept: In incremental tariff systems, you cannot simply multiply your total usage by one rate. You must calculate each bracket separately and then add the costs together.
Water tariffs
Water tariff systems are excellent examples of incremental pricing. Let's look at how they work using a real example from Cape Town's water tariffs for 2011.
The tariff table shows how the price increases for each bracket of water usage, measured in kilolitres (kl).
Calculating water costs step-by-step
To calculate the total cost of water usage, you must break down the consumption into brackets and calculate each portion separately.
Worked Example: Calculate the cost of using 25 kilolitres of water in 2011
Step 1: Break the 25 kl into the correct brackets
- First 6 kl: R0.00 per kl (free)
- Next 4.5 kl (from 6 to 10.5): R4.92 per kl
- Next 9.5 kl (from 10.5 to 20): R10.51 per kl
- Last 5 kl (from 20 to 25): R15.57 per kl
Step 2: Calculate the cost of each bracket
- Cost of first 6 kl =
- Cost of next 4.5 kl =
- Cost of next 9.5 kl =
- Cost of last 5 kl =
Step 3: Add all the costs together
Total cost =
Understanding the step-function graph
When you plot water tariffs on a graph, you get a step-function. This creates a graph that looks like stairs going upward.
The step-function shows that within each bracket, the same rate applies. When consumption moves to the next bracket, the rate jumps to a higher level.
The total cost graph shows how monthly water costs increase as consumption increases. Notice how the curve becomes steeper at higher usage levels - this is because the per-unit rate increases with each bracket.
Step-function graphs are easy to recognize - they look like stairs going up, with flat sections (constant rates within brackets) followed by sudden jumps (rate increases between brackets).
Electricity tariff systems
Electricity can be supplied through two main systems: prepaid and non-prepaid (also called flat rate or billing systems).
Prepaid electricity systems
With a prepaid system, you buy electricity credits in advance using a special meter. You pay a fixed rate per kilowatt-hour (kWh) for all electricity used.
Formula for prepaid electricity:
Worked Example: Prepaid electricity calculation
If you use 725 kWh at a rate of R0.7852 per kWh:
Monthly cost =
Non-prepaid (flat rate) systems
With a non-prepaid system, you receive a monthly bill that includes:
- Service charge - a fixed monthly fee
- Network charge - another fixed monthly fee
- Consumption charge - based on actual usage
Formula for non-prepaid electricity:
Worked Example: Non-prepaid electricity calculation
For a Domestic 3-phase 60A system using 725 kWh:
- Service charge = R198.03
- Network charge = R62.70
- Consumption charge =
Total monthly cost =
Comparing different tariff systems
One of the most important skills in tariff systems is comparing different options to find which is more cost-effective for different usage levels.
When comparing prepaid electricity with non-prepaid electricity on a graph, notice several key features:
- Prepaid line starts at R0 but rises steeply
- Non-prepaid line starts higher (due to fixed charges) but rises more gradually
- The lines intersect at the break-even point
Break-even analysis
The break-even point is where two tariff systems cost exactly the same amount. This helps determine:
- Below the break-even point: one system is cheaper
- Above the break-even point: the other system is cheaper
Finding Break-Even Points: On a graph, the break-even point is where two lines cross. This intersection shows the usage level where both systems cost the same amount.
Worked Example: Mobile phone contract comparison
From a graph comparing two mobile phone contracts, the break-even point occurs at 40 minutes of talk time costing R100.00.
- For less than 40 minutes: LG Allweek 100 is cheaper
- For more than 40 minutes: Nokia ControlChat is cheaper
Understanding percentage increases in tariffs
Utility companies regularly increase their tariffs. Understanding percentage increases helps you compare how different usage brackets are affected.
Notice that in tariff increases:
- Lower usage brackets typically have smaller percentage increases
- Higher usage brackets face larger percentage increases
- This pattern supports the "more you use, more you pay" principle
Formula for percentage increase:
Worked Example: Calculating percentage increase
If the tariff for 20-30 kl increased from R5.87 to R6.61:
Graph interpretation for tariff systems
When interpreting tariff graphs, understanding the visual patterns is crucial for making informed decisions about utility usage and costs.
Graph Reading Tips:
- Flat sections - indicate free allowances or fixed rates
- Increasing steepness - shows higher rates for increased consumption
- Step patterns - indicate bracket-based pricing
- Intersection points - show break-even points between different systems
Key Points to Remember:
- Incremental tariff systems charge different rates for different usage brackets to encourage conservation
- Water tariffs must be calculated bracket by bracket, never as a single multiplication
- Prepaid electricity has no fixed charges but uses a single rate per kWh
- Non-prepaid electricity includes fixed monthly charges plus consumption charges
- Break-even points show where two tariff systems cost the same amount
- Percentage increases help compare how tariff changes affect different user groups
Exam Success Tips:
- Always break water calculations into separate brackets - never multiply total usage by the highest rate
- For break-even questions, find where two graphs cross
- Read tariff tables carefully - check whether rates are per kl, per kWh, or per unit
- When comparing systems, consider both cost and convenience factors
- Show all working steps in calculations
- Remember that steeper graph lines indicate higher per-unit rates