Breakeven Analysis

Companies can be grouped as operating in perfect or imperfect competitive environments depending on the slope of the demand curve.

Perfectly Competitive Environment

In a perfectly competitive environment, firms are price takers and, therefore, have an elastic horizontal demand curve. The marginal revenue of a firm in a perfectly competitive environment is equal to the price per unit, and the average revenue (revenue per unit). The total revenue (TR) is equal to price per unit(P) times quantity(Q), TR=P×Q. Since the firm is a price taker, total revenue increases by the exact amount of price per unit sold.

Imperfectly Competitive Environment

Firms operating in an imperfectly competitive environment have control over the pricing of their products, and as such, price is a function of quantity, i.e.,

$$ P=f(Q) $$

And:

$$ TR = f(Q)\times Q $$

Such firms have a linear and negatively sloped demand curve.

Suppose the firm is a monopoly, i.e., the only seller in the market; its total revenue is equal to the total expenditure of the buyers within that market. If the firm lowers the price of its products, the decrease in price will initially increase the total expenditure of buyers and total revenue to the firm since the increase in units sold will outweigh the increase in price. However, a further decrease in price will outweigh the increase in quantity sold, thereby decreasing the total expenditure of buyers and the firm’s total revenue, as illustrated in the graphs below.

Profit-Maximization, Breakeven, and Shutdown Points of Production

We use a firm’s short-run total cost curve (STC) and its TR curve to show its profit maximization point.

The short run is the amount of time during which at least one of the factors of production, such as technology, physical capital, and plant size, is fixed. On the other hand, the long run is the time during which all factors of production are variable.

Profit-Maximization Point

Under Perfect Competition

Consider the following demand and average and marginal cost curves for a firm under conditions of perfect competition:

The company maximizes its profit by producing at an output level of Q∗, where the price equals the short-run marginal cost (SMC) curve and the SMC is rising. Note that at a different output level, Q’, even though the price is equivalent to the SMC, the SMC is falling, discrediting Q’ from being the company’s point of profit maximation.

If the market price were to increase, the company’s demand and marginal revenue (MR) curve would shift upwards, creating a new profit maximization point to the right of Q∗. On the contrary, if the market price were to decrease, the demand and MR curve would move downward, creating a new profit maximization point to the left of Q∗.As shown in the image, this company is realizing positive economic profits since the market price is greater than the average total cost (ATC) when producing at Q∗.

This kind of profit is achievable in the short run. However, in the long run, rival companies would likely enter the market aiming to obtain some of these profits, subsequently pushing the market price down to match each company’s ATC.

Under Imperfect Competition

Consider the following demand and average and marginal cost curves for a firm under imperfect competition (monopolist) conditions.

Despite the Marginal Revenue and demand curves for firms facing imperfect competition being different, the profit-maximizing rule is the same. The marginal revenue (MR) and demand curves for a monopolist are not the same. However, the rule for maximizing profits remains consistent: Identify the quantity (Q) where short-term marginal cost (SMC) equals MR, which in this instance is at Q∗. The optimal price to charge is then given by the company’s demand curve at P*.

As depicted in the image above, this monopolistic company is enjoying positive economic profits since its price is higher than its average total cost (ATC). Being a monopolistic firm, the barriers to entry are high. Therefore, competitors will be unable to compete away this firm’s profits.

Breakeven Analysis

A firm reaches its breakeven point when its total revenue (TR) matches its total cost (TC). Similarly, a firm is at the breakeven point when its average revenue (AR) is precisely equal to its average total cost (ATC). This holds true in both perfect and imperfect competitive environments.

While management usually aims for maximum profits, some firms can only cover their economic costs. Economic costs include both accounting and implicit opportunity costs. When the firm’s revenue is equal to its economic costs, it implies that the company can cover the opportunity cost of all factors of production. In this case, the firm is said to be earning normal profit but not positive economic profit.

Firms operating in a perfectly competitive environment will not be able to earn a positive economic profit in the long run because an excess rate of return will lure new entrants into the market. These newcomers would increase the supply, subsequently pushing the market price down until every firm merely achieves a normal profit. It’s crucial to understand that this scenario doesn’t mean the firm is making zero accounting profit.

Consider the following graph of a firm under perfect competition:

Recall that the best a firm can do is to break even. Note that in the graph above, the level of output where SMC = MR is where P = ATC, and at this point, the economic profit is zero, and the firm is at a breakeven point.

The break-even point graph of a monopolist firm / a firm in an imperfectly competitive environment is shown below.

Shutdown Analysis

A firm that cannot earn at least a zero economic profit will shut down in the long run since it will be unable to cover the opportunity costs of its factors of production, capital, and labor. However, the firm may continue to operate in the short run even if it cannot make at least a zero economic profit.

Recall that fixed costs are expenses that remain constant regardless of a company’s production level, such as rent and fixed interest charges. On the other hand, variable costs are directly tied to the volume of production and include items like raw materials, wages, and other costs that vary based on production levels.

A firm can continue operating in the short run if its revenues cover at least its variable costs. This is possible when the price exceeds the average variable cost, as then the price will cover the variable costs and part of the fixed costs. However, in the long run, unless the market price increases, the firm will be forced to exit the market.

Note that sunk costs (costs that have already been incurred) are ignored when deciding whether to continue operations in the short run.

This is shown in the graph below (for a firm under conditions of perfect competition):

At a price higher than P1, the firm should continue to operate as it can earn positive profits. The firm should shut down at a price below P2 (the minimum AVC) as it cannot cover its variable costs. The firm should continue to operate in the short run between prices P1 and P2 since it is able to cover all its variable costs and part of its fixed costs. The lowest point on the AVC curve is the shutdown point, and the lowest point on the average total cost (ATC) is the breakeven point.

The following table shows the conditions for a firm to operate, shut down, or exit the market in the short and long run.

$$ \begin{array}{l|l|l}
{\textbf{Relationship between} \\ \textbf{Revenue and Costs}} & \textbf{Short-Term Decision} & \textbf{Long-Run-Decision} \\ \hline
{\text{Total cost = Total} \\ \text{revenue} } & \text{Remain in the market} & \text{Remain in the market} \\ \hline
{ \text{Total revenue < Total} \\ \text{costs and > Total} \\ \text{variable costs}} & \text{Remain in the market} & \text{Exit the market} \\ \hline
{ \text{Total revenue < Total} \\ \text{variable cost}} & \text{Exit the market} & { \text{Exit the market} }
\end{array} $$

Example: Shut-down Point of Production

Assume that a manufacturing company produces 1000 units and sells them at $5 each (Total Revenue (TR) is 5 × 1,000=$5,000), Average Total Cost (ATC) is $7,000, fixed cost (FC) is $4000, and variable cost (VC) is $3,000 for all units.

Evidently, this manufacturing company is operating at a loss of -$2000 (economic loss). In economics, we assume that the FC cannot be avoided. The company is obliged to pay it up regardless of whether it operates or not. That is, if it closes its operations, the revenue will be zero, but it will still incur a $4,000 fixed cost.

If it continues its operations (in the short run), it will earn a revenue of $5,000, pay a variable cost of $3,000, and use $2,000 to pay part of the fixed cost. Its net loss will, therefore, be lower than if it were to stop its operations. However, the company will exit the market in the long run unless prices increase.

Economies and Diseconomies of Scale with Short-run and Long-run Cost Analysis

Recall that the time frame that distinguishes the short run from the long run for a firm depends on the firm’s ability to adjust the quantities of its fixed resources. The time period within which at least one of the factors of production (technology, physical capital, plant size) is fixed is the short run, whereas the time period within which all factors of production are variable is the long run.

The time required for long-run adjustments varies across industries, with capital-intensive firms generally requiring more time and firms using little technology and less capital requiring less time.

Short-Run Cost Curves

In short-run curves, we assume that the capital input is constant, implying that the only way to vary output is by changing the variable output—labor. If the capital input(plant and equipment) were to vary, we would have to generate short-run cost curves for each level of capital input.

The short-run total cost (STC) often increases with output. Initially, it rises at a diminishing rate due to the economies of specialization. However, as output grows, the curve ascends at an accelerating rate due to the law of diminishing marginal returns to labor.

Total fixed cost (TFC) determines the vertical intercept of the STC curve. When there’s more fixed input, the total fixed cost (TFC) is higher, but the firm’s production capacity also increases.

For every short-run total cost (STC) curve, there’s a related short-run average total cost (SATC) curve. Additionally, there’s a corresponding long-run average total cost (LRAC) curve, which serves as the envelope curve encompassing all potential short-run average total cost curves. The shape of the LRAC curve reflects the economies and diseconomies of scale concept.

Economies and Diseconomies of Scale

A firm that increases its input to increase its output is said to be scaling up production, whereas one that decreases its input to produce less in the long run is said to be scaling down production.

Economies of scale come into play when the firm experiences a decrease in the cost per unit of production as it increases its output.

In the case of economies of scale, LRAC has a negative slope. Consider the following graph with SATC for each level of capital input (levels 1,2,3 and 4) and the negatively sloped LRAC cost depicting economies of scale.

The following factors can lead to economies of scale:

• Achieving economies of scale through increasing returns to scale, i.e., the production process allows increases in output that are larger than the increase in inputs.
• Implementing a division of labor and management to allow workers to specialize in specific tasks, leading to improved job efficiency.
• Enhancing productivity by investing in more expensive and efficient equipment.
• Effectively reducing waste and lowering costs by capitalizing on marketable by-products, reducing energy consumption, and implementing enhanced quality control measures.
• Utilizing market information and knowledge to make more effective managerial decisions.
• Capitalizing on discounted prices when purchasing resources in larger quantities.

Conversely, diseconomies of scale occur when the cost per unit rises as the firm further increases its production. In this case, the LRAC has a positive slope. Consider the following graph with SATC for each level of capital input (levels 1,2,3 and 4) and the positively sloped LRAC cost depicting diseconomies of scale:

The following factors can result in diseconomies of scale:

• Experiencing diseconomies of scale due to decreasing returns, where the production process results in output increases that are proportionately smaller than the increase in inputs.
• Struggling with proper management due to excessive size.
• Encountering inefficiencies caused by overlapping and duplicating business functions and product lines.
• Facing higher resource prices due to supply constraints when purchasing inputs in large quantities.

Economies of scale and diseconomies of scale can coexist; their effect on the long-run average total cost (LRAC) depends on which one has a stronger influence.

If the economies of scale dominate, the LRAC will decline as output increases. Conversely, if diseconomies of scale dominate, the opposite happens. It’s possible for the LRAC to first decrease (due to economies of scale) over a certain output range, then stabilize over another range, and subsequently increase in a range where diseconomies of scale take effect.

The minimum efficient scale is the minimum point on the LRAC curve, and is the optimal firm size under perfect competition for the long run. Perfect competition forces firms to operate at this point as market prices are established at this level over the long run.

If a firm doesn’t operate at this optimal cost-efficiency point, its sustainability in the long run could be at risk.

Question #1

A firm that increases the quantity it produces without any change in per-unit cost is experiencing:

1. Economies of scale.
2. Diseconomies of scale.
3. Constant returns to scale.

Solution

The correct answer is C.

An increase in output proportional to an increase in input would be considered a constant return to scale. This is neither an economies nor diseconomies of scale.

Question #2

The short-term shut-down point of production for a firm operating under perfect competition will most likely occur when the price per unit is equal to:

1. Marginal cost per unit.
2. Average total cost per unit.
3. Average variable cost per unit.

Solution

The correct answer is C.

Any firm will shut down its production when the marginal cost is less than the average variable cost. We will see later that for a firm in perfect competition to maximize profit, marginal revenue must be equal to marginal cost.