Graphically the marginal cost curve the average total cost curve and the average fixed cost curve

Because so much of economics is taught using graphical analysis, it's very important to think about what the various costs of production look like in graphical form. Let's examine the graphs for the different measures of cost.

Total cost is graphed with output quantity on the horizontal axis and dollars of total cost on the vertical axis. There are a few features to note about the total cost curve:

• The total cost curve is upward sloping (i.e. increasing in quantity). This simply reflects the fact that it costs more in total to produce more output.
• The total cost curve is generally bowed upwards. This isn't necessarily always the case- the total cost curve could be linear in quantity, for example- but is fairly typical for a firm for reasons that will be explained later.
• The intercept on the vertical axis represents the firm's fixed total fixed cost since this is the cost of production even when output quantity is zero.

As stated earlier, total cost can be broken down into total fixed cost and total variable cost. The graph of total fixed cost is simply a horizontal line since total fixed cost is constant and not dependent on output quantity. Variable cost, on the other hand, is an increasing function of quantity and has a similar shape to the total cost curve, which is a result of the fact that total fixed cost and total variable cost have to add to total cost. The graph for total variable cost starts at the origin because the variable cost of producing zero units of output, by definition, is zero.

Since average total cost is equal to total cost divided by quantity, the average total cost can be derived from the total cost curve. Specifically, the average total cost for a given quantity is given by the slope of the line between the origin and the point on the total cost curve that corresponds to that quantity. This is simply because the slope of a line is equal to the change in the y-axis variable divided by the change in the x-axis variable, which in this case is, in fact, equal to total cost divided by quantity.

Since, as stated earlier, marginal cost is the derivative of total cost, marginal cost at a given quantity is given by the slope of the line tangent to the total cost curve at that quantity.

When graphing average costs, units of quantity are on the horizontal axis and dollars per unit are on the vertical axis. As shown above, the average fixed cost has a downward-sloping hyperbolic shape, since average fixed cost is just a constant number divided by the variable on the horizontal axis. Intuitively, an average fixed cost is downward sloping because, as quantity increases, fixed cost gets spread out over more units.

For most firms, marginal cost is upward sloping after a certain point. It's worth acknowledging, however, that it's entirely possible for marginal cost to initially be decreasing before it starts increasing in quantity.

Some firms, referred to as natural monopolies, enjoy such strong cost advantages to being big (economies of scale, in economic terms) that their marginal cost never starts sloping upwards. In these cases, marginal cost looks like the graph on the right (though marginal cost doesn't technically have to be constant) rather than the one on the left. It's worth keeping in mind, however, that few firms are truly natural monopolies.

Fixed costs are those that do not vary with output and typically include rents, insurance, depreciation, set-up costs, and normal profit. They are also called overheads.

Variable costs are costs that do vary with output, and they are also called direct costs. Examples of typical variable costs include fuel, raw materials, and some labour costs.

Consider the following hypothetical example of a boat building firm. The total fixed costs, TFC, include premises, machinery and equipment needed to construct boats, and are £100,000, irrespective of how many boats are produced. Total variable costs (TVC) will increase as output increases.

Plotting this gives us Total Cost, Total Variable Cost, and Total Fixed Cost.

Total fixed costs

Given that total fixed costs (TFC) are constant as output increases, the curve is a horizontal line on the cost graph.

Total variable costs

The total variable cost (TVC) curve slopes up at an accelerating rate, reflecting the law of diminishing marginal returns.

Total costs

The total cost (TC) curve is found by adding total fixed and total variable costs. Its position reflects the amount of fixed costs, and its gradient reflects variable costs.

Average fixed costs

Average fixed costs are found by dividing total fixed costs by output. As fixed cost is divided by an increasing output, average fixed costs will continue to fall.

The average fixed cost (AFC) curve will slope down continuously, from left to right.

Average variable costs

Average variable costs are found by dividing total fixed variable costs by output.

The average variable cost (AVC) curve will at first slope down from left to right, then reach a minimum point, and rise again.

AVC is ‘U’ shaped because of the principle of variable Proportions, which explains the three phases of the curve:

1. Increasing returns to the variable factors, which cause average costs to fall, followed by:
2. Constant returns, followed by:
3. Diminishing returns, which cause costs to rise.

Average total cost

Average total cost (ATC) is also called average cost or unit cost. Average total costs are a key cost in the theory of the firm because they indicate how efficiently scarce resources are being used. Average variable costs are found by dividing total fixed variable costs by output.

Average total cost (ATC) can be found by adding average fixed costs (AFC) and average variable costs (AVC). The ATC curve is also ‘U’ shaped because it takes its shape from the AVC curve, with the upturn reflecting the onset of diminishing returns to the variable factor.

Areas for total costs

Total Fixed costs and Total Variable costs are the respective areas under the Average Fixed and Average Variable cost curves.

Marginal costs

Marginal cost is the cost of producing one extra unit of output.  It can be found by calculating the change in total cost when output is increased by one unit.

It is important to note that marginal cost is derived solely from variable costs, and not fixed costs.

The marginal cost curve falls briefly at first, then rises. Marginal costs are derived from variable costs and are subject to the principle of variable proportions.

The significance of marginal cost

The marginal cost curve is significant in the theory of the firm for two reasons:

1. It is the leading cost curve, because changes in total and average costs are derived from changes in marginal cost.
2. The lowest price a firm is prepared to supply at is the price that just covers marginal cost.

ATC and MC

Average total cost and marginal cost are connected because they are derived from the same basic numerical cost data.  The general rules governing the relationship are:

1. Marginal cost will always cut average total cost from below.
2. When marginal cost is below average total cost, average total cost will be falling, and when marginal cost is above average total cost, average total cost will be rising.
3. A firm is most productively efficient at the lowest average total cost, which is also where average total cost (ATC) = marginal cost (MC).

Total costs and marginal costs

Marginal costs are derived exclusively from variable costs, and are unaffected by changes in fixed costs. The MC curve is the gradient of the TC curve, and the positive gradient of the total cost curve only exists because of a positive variable cost. This is shown below:

Sunk costs

Sunk costs are those that cannot be recovered if a firm goes out of business. Examples of sunk costs include spending on advertising and marketing, specialist machines that have no scrap value, and stocks which cannot be sold off.

Sunk costs are a considerable barrier to entry and exit.

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