What Is Acceptable Quality Level (AQL)?

The acceptable quality level (AQL) is a measure applied to products and defined in ISO 2859-1 as the “quality level that is the worst tolerable.” The AQL tells you how many defective components are considered acceptable during random sampling quality inspections. It is usually expressed as a percentage or ratio of the number of defects compared to the total quantity.

How Acceptable Quality Level (AQL) Works

Goods in a sample are tested at random, and if the number of defective items is below the predetermined amount, that product is said to meet the acceptable quality level (AQL). If the acceptable quality level (AQL) is not reached for a particular sampling of goods, manufacturers will review the various parameters in the production process to determine the areas causing the defects.

As an example, consider an AQL of 1% on a production run. This percentage means that no more than 1% of the batch can be defective. If a production run is composed of 1,000 products, only 10 products can be defective. If 11 products are defective, the entire batch is scrapped. This figure of 11 or more defective products is known as the rejectable quality level (RQL).

The AQL is an important statistic for companies seeking a Six Sigma level of quality control, which is a quality-control methodology developed in 1986 by Motorola, Inc. AQL is also known as the acceptable quality limit.

Industry Differences in AQL Standards

The AQL of a product can vary from industry to industry. For example, medical products are more likely to have more stringent AQL because defective products can result in health risks.

In contrast, a product with benign side-effects from a possible defect may have a less strict AQL, such as the remote control for a TV. Companies have to weigh the added cost associated with the stringent testing and potentially higher spoilage due to a lower defect acceptance with the potential cost of a product recall.

Customers would, of course, prefer zero-defect products or services; the ideal acceptable quality level. However, sellers and customers usually try to arrive at and set acceptable quality limits based on factors typically related to business, financial, and safety concerns.

Using AQL Tables

AQL tables (also sometimes called AQL charts) are designed to allow users to reference a standard for what qualifies as an acceptable number of defects in manufacturing. They allow a person to see how many defects would be allowed for a company to achieve a certain AQL. The tables are part of ISO 2859.

So for example, let’s say a company orders 30,000 hats from a clothing manufacturer that will be produced in one batch, and the buyer and producer have agreed on AQL 0.0 for critical defects, AQL 3.0 for major defects, and AQL 5.0 for minor defects. Referencing the AQL tables would allow the buyer and producer to determine how many hats would need to be inspected to ensure that the agreed upon AQL is being met during production.

AQL Defects

Instances of failure to meet customer quality requirements are termed as defects. In practice, there are three categories of defects:

1. Critical defects: Defects that, when accepted, could harm users. Such defects are unacceptable. Critical defects are defined as 0% AQL.
2. Major defects: Defects usually not acceptable by the end-users, as they are likely to result in failure. The AQL for major defects is 2.5%.
3. Minor defects: Defects not likely to reduce materially the usability of the product for its intended purpose but that differ from specified standards; some end users will still buy such products. The AQL for minor defects is 4%.

AQL in Practice

Acceptable quality level (AQL): AQL is typically considered to be the worst quality level that is still considered satisfactory. It is the maximum percent defective that can be considered satisfactory. The probability of accepting an AQL lot should be high. A probability of 0.95 translates to a risk of 0.05.

Rejectable quality level (RQL): This is considered an unsatisfactory quality level and is sometimes known as lot tolerance percent defective (LTPD). The consumer’s risk has been standardized in some tables as 0.1. The probability of accepting an RQL lot is low.

Indifference quality level (IQL): This quality level is somewhere between AQL and RQL. Different companies maintain different interpretations of each defect type. However, buyers and sellers agree on an AQL standard that is appropriate to the level of risk each party assumes. These standards are used as a reference during a pre-shipment inspection.

The Bottom Line

AQL can be a useful figure to help ensure that large orders for manufacturing are completed to a level of standard that a buyer demands. It also allows the seller to be efficient in their production while maintaining the standard set by the buyer. It is generally used in large-scale orders of production, and is helpful in keeping both buyer and seller happy while producing good quality products.

What Is an Accounting Ratio?

Accounting ratios, an important sub-set of financial ratios, are a group of metrics used to measure the efficiency and profitability of a company based on its financial reports. They provide a way of expressing the relationship between one accounting data point to another and are the basis of ratio analysis.

Understanding an Accounting Ratio

An accounting ratio compares two line items in a company’s financial statements, namely made up of its income statement, balance sheet, and cash flow statement. These ratios can be used to evaluate a company’s fundamentals and provide information about the performance of the company over the last quarter or fiscal year.

Analyzing accounting ratios is an important step in determining the financial health of a company. It can often point out areas that are bringing the profitability of a company down and therefore need improvement. The efficacy of new management plans, new products, and changes in operational procedures, can all be determined by analyzing accounting ratios.

Accounting ratios also work as an important tool in company comparison within an industry, for both the company itself and investors. A company can see how it stacks up against its peers and investors can use accounting ratios to determine which company is the better option.

A thorough accounting analysis can be a complex task, but calculating accounting ratios is a simple process of dividing two line items found on a financial statement, that provide a quick form of clear analysis to a business owner or investor.

Types of Accounting Ratios

Gross Margin and Operating Margin

The income statement contains information about company sales, expenses, and net income. It also provides an overview of earnings and the number of shares outstanding used to calculate earnings per share (EPS). These are some of the most popular data points analysts use to assess a company’s profitability.

Gross profit as a percent of sales is referred to as gross margin. It is calculated by dividing gross profit by sales. For example, if gross profit is $80,000 and sales are $100,000, the gross profit margin is 80%. The higher the gross profit margin, the better, as it indicates that a company is keeping a higher proportion of revenues as profit rather than expenses.

Operating profit as a percentage of sales is referred to as operating margin. It is calculated by dividing operating profit by sales. For example, if the operating profit is $60,000 and sales are $100,000, the operating profit margin is 60%.

Debt-To-Equity Ratio

The balance sheet provides accountants with a snapshot of a company’s capital structure, one of the most important measures of which is the debt-to-equity (D/E) ratio. It is calculated by dividing debt by equity. For example, if a company has debt equal to $100,000 and equity equal to $50,000, the debt-to-equity ratio is 2 to 1. The debt-to-equity ratio shows how much a business is leveraged; how much debt it is using to finance operations as opposed to its own internal funds.

The Quick Ratio

The quick ratio, also known as the acid-test ratio, is an indicator of a company’s short-term liquidity and measures a company’s ability to meet its short-term obligations with its most liquid assets. Because we’re only concerned with the most liquid assets, the ratio excludes inventories from current assets.

Dividend Payout Ratio

The cash flow statement provides data for ratios dealing with cash. For example, the dividend payout ratio is the percentage of net income paid out to investors through dividends. Both dividends and share repurchases are considered outlays of cash and can be found on the cash flow statement.

For example, if dividends are $100,000 and income is $400,000, the dividend payout ratio is calculated by dividing $100,000 by $400,000, which is 25%. The higher the dividend payout ratio the higher percentage of income a company pays out as dividends as opposed to reinvesting back into the company.

The examples above are just a few of the many accounting ratios that corporations and analysts utilize to evaluate a company. There are many more that highlight different aspects of a company.

What Is Ability-To-Pay Taxation?

The ability-to-pay philosophy of taxation maintains that taxes should be levied according to a taxpayer’s ability to pay. The idea is that people, businesses, and corporations with higher incomes can and should pay more in taxes. 

Understanding the Ability-To-Pay Principle

Ability-to-pay taxation argues that those who earn higher incomes should pay a greater percentage of those incomes in taxes compared with those who earn less. For example, in 2020 individuals in the United States with taxable income less than $9,875 faced a 10% income tax rate, while those with taxable income of more than $518,000 faced a rate of 37%, the nation’s top individual rate. Earnings between those amounts face tax rates as set by income brackets.

The idea underlying ability-to-pay taxation is that everyone should make an equal sacrifice in paying taxes, and because people with more money effectively have less use for a given dollar, paying more of them in taxes does not impose a greater burden. Think of it this way: To a person with earns $1 million a year, $10,000 will make very little difference in their life, while it will make a big difference to a person earning only $60,000 a year.

History of Ability-to-Pay Taxation

The idea of a progressive income tax—that is, that people with the ability to pay more should pay a higher percentage of their income—is centuries old. In fact, it was espoused by none other than Adam Smith, considered the father of economics, in 1776.

Smith wrote: “The subjects of every state ought to contribute toward the support of the government, as near as possible, in proportion to their respective abilities; that is in proportion to the revenue which they respectively enjoy under the protection of the state.”

Arguments for Progressive Taxation

Advocates of ability-to-pay taxation argue that those who have benefitted most from the nation’s way of life in the form of higher incomes and greater wealth can afford and should be obligated to give back a little more to keep the system running.

The argument is that the society that government tax revenue has helped build—infrastructure such as highways and fiberoptic communications networks, a strong military, public schools, a free market system—provide the environment in which their success is possible and in which they can continue to enjoy that success.

Criticism of Ability-to-Pay Taxation

Critics of progressive taxation argue that it is fundamentally unfair. They say it penalizes hard work and success and reduces the incentive to make more money. Many argue that everyone should pay the same income-tax rate—a “flat tax”—to make the system more equitable.

Progressive Taxation and Inequality

While the U.S. still maintains a progressive tax system, tax rates for the rich have plummeted over the past several decades. When President Ronald Reagan took office in 1981, the highest income tax bracket for individuals was 70%. In 2020, the top rate for incomes is 37%. Meanwhile, inequality has reached levels not seen in at least a century. The top 1% now holds more wealth than the bottom 90%.

What Is Arc Elasticity?

Arc elasticity is the elasticity of one variable with respect to another between two given points. It is used when there is no general way to define the relationship between the two variables. Arc elasticity is also defined as the elasticity between two points on a curve.

The concept is used in both economics and mathematics. In economics, is it commonly used to measure the changes between the quantity of goods demanded and their prices.

Understanding Arc Elasticity

In economics, arc elasticity is commonly used in relation to the law of demand to measure percentage changes between the quantity of goods demanded and prices.

There are two possible ways of calculating elasticity—price (or point) elasticity of demand and arc elasticity of demand. Price elasticity of demand measures the responsiveness of quantity demanded to a price. It takes the elasticity of demand at a particular point on the demand curve, or between two points on the curve. Arc elasticity of demand uses a midpoint between the two points.

Formula for Price (Point) Elasticity of Demand


$PE_d = \dfrac{\text{\% Change in Qty}}{\text{\% Change in Price}}$PEd​=% Change in Price% Change in Qty​

How to Calculate the Price Elasticity of Demand

If the price of a product decreases from $10 to $8, leading to an increase in quantity demanded from 40 to 60 units, then the price elasticity of demand can be calculated as:

• % change in quantity demanded = (Qd₂ – Qd₁) / Qd₁ = (60 – 40) / 40 = 0.5
• % change in price = (P₂ – P₁) / P₁ = (8 – 10) / 10 = -0.2
• Thus, PE_d= 0.5 / -0.2 = 2.5

Since we’re concerned with the absolute values in price elasticity, the negative sign is ignored. You can conclude that the price elasticity of this good, when the price decreases from $10 to $8, is 2.5.

Arc Elasticity of Demand

One of the problems with the price elasticity of demand formula is that it gives different values depending on whether price rises or falls. If you were to use different start and end points in our example above—that is, if you assume the price increased from $8 to $10—and the quantity demanded decreased from 60 to 40, the Pe_d will be:

• % change in quantity demanded = (40 – 60) / 60 = -0.33
• % change in price = (10 – 8) / 8 = 0.25
• PE_d = -0.33 / 0.25 = 1.32, which is much different from 2.5

How to Calculate the Arc Elasticity of Demand

To eliminate this problem, the arc elasticity of demand can be used. Arc elasticity of demand measures elasticity at the midpoint between two selected points on the demand curve by using a midpoint between the two points. The arc elasticity of demand can be calculated as:

• Arc E_d = [(Qd₂ – Qd₁) / midpoint Qd] ÷ [(P₂ – P₁) / midpoint P]

Let’s calculate the arc elasticity following the example presented above:

• Midpoint Qd = (Qd₁ + Qd₂) / 2 = (40 + 60) / 2 = 50
• Midpoint Price = (P₁ + P₂) / 2 = (10 + 8) / 2 = 9
• % change in qty demanded = (60 – 40) / 50 = 0.4
• % change in price = (8 – 10) / 9 = -0.22
• Arc E_d = 0.4 / -0.22 = 1.82

When you use arc elasticity of demand you do not need to worry about which point is the starting point and which point is the ending point since the arc elasticity gives the same value for elasticity whether prices rise or fall.

The Bottom Line

Arc elasticity is commonly used in economics to determine the percentage of change between the demand for goods and their price. Elasticity can be calculated in two ways—price elasticity of demand and arc elasticity of demand. The latter is more useful when there is a significant change in price.