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A South African company selling mining and construction equipment is experiencing significant business growth, as shown by the numbers in the table below.

| Number of Clients | Total Fixed Costs | Total Variable Cost | Total Costs | Marginal Costs |
|-------------------|-------------------|---------------------|-------------|----------------|
| 0 | 20000 | 0 | 20000 | -------- |
| 1000 | 20000 | 30000 | -------- | 30 |
| 2000 | 20000 | 50000 | 70000 | -------- |
| 3000 | 20000 | -------- | 85000 | 15 |
| 4000 | -------- | 85000 | 105000 | 20 |
| 5000 | 20000 | 110000 | ------- | 25 |
| 6000 | 20000 | 150000 | 170000 | -------- |
| 7000 | 20000 | 210000 | 230000 | 60 |

Tasks:
a) Fill in the missing figures in the table. (8 points)

b) Use the completed table to draw the total cost curves for the business. (6 points)

c) Use the marginal costs to describe their behavior as the production level changes. (6 points)

d) Following the example provided, calculate and use the figures to plot the average costs. Add 3 columns to the table and plot the average and marginal costs on the same graph.

Answer :

Final answer:

The total cost, average cost and marginal cost are defined with per unit basis not total. Average total cost and average variable cost are calculated by dividing total and variable cost by quantity respectively and the marginal cost is calculated by change in total cost divided by change in quantity. Their curves are typically U-shaped and the marginal cost curve tends to slope upwards.

Explanation:

Firstly, Average Total Cost, Average Variable Cost, and Marginal Cost are calculated per unit, not total basis. The missing figures in the table can be filled using these concepts, average total cost (ATC) is calculated by dividing total cost by the total quantity produced and the average variable cost (AVC) is calculated by dividing variable cost by the quantity produced. Marginal cost is calculated by taking the change in total cost and dividing it by the change in quantity.

To draw the new business’s total cost curves, one needs to plot these costs against the number of clients. The curves typically appear U-shaped. The average variable cost curve lies below the average total cost curve. The marginal cost curve is generally upward-sloping, indicating that additional units are more costly to produce due to diminishing marginal returns.

The behavior of marginal costs when the level of production changes can be defined by noting the slope of the marginal cost curve. The marginal cost increases as the level of production increases, indicating that the cost to produce an extra unit increases with the level of production.

The same approach can be used to calculate average costs and marginal costs and to plot them on a graph. Average costs decrease with an increase in clients initially due to economies of scale, but after a certain point, it starts to increase due to diseconomies of scale. Marginal costs are generally upward sloping indicating the additional cost to produce an extra unit.

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