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Define the term tariff.

Economics

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Step-by-step solution

8 steps
  1. Define the term tariff.

    A tariff is a charge or fee imposed by a municipality or service provider for the use of a service, such as water, electricity, or waste removal.

  2. Verify Pieter's claim about water usage cost.

    Pieter uses 35 kl of water.

    • Fixed charge (since 35 kl > 6 kl): R80.70
    • Fee for infrastructure (since 35 kl > 6 kl): R7.15
    • Cost for water usage:
      • Block 1 (0-6 kl): 6 kl×R0.00/kl=R0.006 \text{ kl} \times \text{R}0.00/\text{kl} = \text{R}0.00
      • Block 2 (7-30 kl): 24 kl×R6.48/kl=R155.5224 \text{ kl} \times \text{R}6.48/\text{kl} = \text{R}155.52
      • Block 3 (30.1-60 kl): 5 kl×R16.20/kl=R81.005 \text{ kl} \times \text{R}16.20/\text{kl} = \text{R}81.00
    • Total cost:
    Total cost=R80.70+R7.15+R0.00+R155.52+R81.00=R324.37\text{Total cost} = \text{R}80.70 + \text{R}7.15 + \text{R}0.00 + \text{R}155.52 + \text{R}81.00 = \text{R}324.37

    Pieter's claim that he will pay more than R350.00 is ❌ Incorrect, as the total cost is R324.37.

  3. Calculate the VAT amount for block 3.

    The rate for block 3 is R16.20, which is inclusive of 15% VAT.
    Let the original price be PP. Then P+0.15P=R16.20P + 0.15P = \text{R}16.20.

    1.15P=R16.201.15P = \text{R}16.20 P=R16.201.15≈R14.0869P = \frac{\text{R}16.20}{1.15} \approx \text{R}14.0869

    The VAT amount is 0.15P0.15P:

    VAT amount=R16.20−R14.0869=R2.1131\text{VAT amount} = \text{R}16.20 - \text{R}14.0869 = \text{R}2.1131

    Rounded to two decimal places, the VAT amount is R2.11\boxed{\text{R}2.11}.

  4. Give two explanations for why municipalities impose tariffs on customers.

    • To cover the cost of providing essential services such as water, electricity, and waste management, including maintenance of infrastructure and operational expenses.
    • To generate revenue that can be used for municipal development projects, improving public services, and funding other community needs.
  5. Write down the formula for calculating the cost of baking bread.

    From the problem statement, the cost of baking one loaf is R4.00, and from TABLE 3, the fixed cost (for 0 loaves) is R450.00.
    Let CC be the total cost and NN be the number of loaves.

    C=R450.00+(R4.00×N)C = \text{R}450.00 + (\text{R}4.00 \times N)

    The formula for calculating the cost of baking bread is C=450+4N\boxed{C = 450 + 4N}.

  6. Calculate the missing values A and B.

    • Value A (Total cost for 300 loaves): Using the formula from Step 5: A=R450.00+(R4.00×300)A = \text{R}450.00 + (\text{R}4.00 \times 300) A=R450.00+R1200.00A = \text{R}450.00 + \text{R}1200.00 A=R1650.00A = \text{R}1650.00
    • Value B (Total income for 180 loaves): From the problem statement, a loaf is sold at R6.50. B=R6.50×180B = \text{R}6.50 \times 180 B=R1170.00B = \text{R}1170.00

    The missing values are A=R1650.00\boxed{A = \text{R}1650.00} and B=R1170.00\boxed{B = \text{R}1170.00}.

  7. Calculate the cost of baking 50 loaves.

    Using the formula from Step 5:

    C=R450.00+(R4.00×50)C = \text{R}450.00 + (\text{R}4.00 \times 50) C=R450.00+R200.00C = \text{R}450.00 + \text{R}200.00 C=R650.00C = \text{R}650.00

    The cost of baking 50 loaves is R650.00\boxed{\text{R}650.00}.

  8. Describe how to draw the graphs for income and cost.

    To draw the graphs, you would set up a coordinate system:

    • The x-axis (horizontal) represents the "Number of loaves" (from 0 to 300).
    • The y-axis (vertical) represents "Cost/Income (in rands)" (from 0 to at least R2000).

    For the Cost graph (using values from TABLE 3 and calculated A):
    Plot the following points:
    (0, R450), (60, R690), (120, R930), (180, R1170), (240, R1410), (300, R1650).
    Draw a straight line connecting these points. This line represents the total cost.

    For the Income graph (using values from TABLE 4 and calculated B):
    Plot the following points:
    (0, R0), (60, R390), (120, R780), (180, R1170), (240, R1560), (300, R1950).
    Draw a straight line connecting these points. This line represents the total income.

    The point where the two lines intersect is the break-even point, where total cost equals total income. In this case, it appears to be at 180 loaves and R1170.

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