What is the relationship between the ATC and the MC?

Main Concept

In a perfectly competitive market, there are many economic participants but none have the power to set the market price for a particular product. The price per unit is completely controlled by the market forces of supply and demand, and each firm in the market must sell their product at this predetermined market price. Marginal revenue (MR) can be defined as the additional revenue a firm receives for selling one additional unit of output, and so in perfect competition, it equals the price of the product and can represented by a horizontal line (MR = P) as in the graph below. 

Review of the costs incurred when producing and selling products

Fixed costs (FC) are expenses to that do not vary with the quantity of output produced (Q). Examples of fixed costs include rent and annual salaries. Variable costs (VC) are expenses which increase with the quantity of output produced (Q). Examples of variable costs include hourly and piece-rate wages, and raw materials used in manufacturing. Total cost (TC) is the sum of the fixed costs and variable costs, so TC = FC + VC.

The graph below shows four costs curves for a firm operating in a perfectly competitive market:

Average fixed cost (AFC) refers to fixed costs divided by the total quantity of output produced, AFC = FCQ.

Average variable cost (AVC) refers to variable costs divided by the total quantity of output produced, AVC = VCQ.

Average total cost (ATC) refers to total cost divided by the total quantity of output produced, ATC = TCQ.

Marginal cost (MC) refers to the additional cost incurred by producing one additional unit of output, MC = ΔTCΔQ.

As you will notice in the diagram below, the MC curve always intersects both the AVC curve and the ATC curve at their respective minimum points. When marginal cost is less than average variable or average total cost, AVC or ATC must be decreasing. When marginal cost is greater than average variable or average total cost, AVC or ATC must be increasing. Therefore, the only possible point at which marginal cost equals average variable or average total cost is the minimum point. 

Break-even Point

The point at which marginal cost equals average total cost (MC = ATC) is known as the break-even point. When the MR = P line crosses through this point, as is highlighted by the black circle on the graph, the product is said to be selling at its break-even price because the marginal revenue will exactly offset the marginal cost of production, and total revenue will exactly offset total cost. In this situation, the firm will break even: it will not be earning any profits, but it will not be losing money either. If the MR = P line lies above the break-even point, the firm will be operating at a profit, since the revenue earned on each unit of output sold will exceed the average cost of producing a unit of output, and thus total revenue will exceed total cost. If the MR = P line lies below the break-even point, the firm will be operating at a loss because the revenue earned on each unit of output will be less than the average cost of producing a unit of output, and so total revenue will be less that total cost.

The graph below is based on a more complex economic model, but can still be useful for exploring the cost curves of an individual firm. The amount of capital used (K) directly impacts the productive capacity of the firm and so changes the quantity of output produced at any given cost. The rental price of capital (k) affects the fixed costs of the firm by adjusting how expensive it is for the firm to operate with their current level of capital investment. Finally, the hourly wage paid to employees (w) affects the firm's variable costs, since producing more output requires more hours of labor, increasing the cost of wages as well.

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