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.

What is Autarky?

Autarky refers to a nation that operates in a state of self-reliance. Nations that follow a policy of autarky are characterized by self-sufficiency and limited trade with global partners. The definition of autarky comes from the Greek—autos, meaning “self” and arkein, meaning “to ward off” and “to be strong enough, to suffice.” A fully autarkic nation would be a closed economy and lacking any sources of external support, trade or aid. In practice, however, no modern nation has achieved this level of autarky, even when subjected to punishing sanctions. This is because the global supply chain has made true economic isolation difficult, so any policy of autarky is a matter of degrees rather than a complete isolation.

Understanding Autarky

Autarky can be thought of as an extreme form of economic nationalism and protectionism. The motivation behind a policy of autarky is usually a combination of securing the supply of important goods and a desire to reduce the dependence on other nations in general. Depending on the type of political structure in a nation, the goal of reducing dependence on outside nations may be related to reducing the influence of competing political and economic systems. At various points in history, however, autarky has been proposed by groups all across the political spectrum. When framed in terms of keeping domestic spending at home or stopping the transfer of wealth to bad political actors, autarky touches populist themes and appears to make practical sense.

In practice, however, autarky has economic downsides that are not immediately apparent in the populist arguments. Autarky was first questioned by economist Adam Smith, and then David Ricardo. Smith suggested that countries should engage in free trade and specialize in goods they have an absolute advantage in producing, in order to generate more wealth. This is one of the core arguments Smith made in favor of free trade in The Wealth of Nations. Ricardo amended this argument slightly, saying that countries should also produce goods in which they have a comparative advantage. By leveraging comparative advantages, countries are able to work together to create more wealth in the global system of trade.

Put another way, opting out of global trade in favor of doing it all domestically has a high opportunity cost for nations, just as it does for individuals. For example, a family preoccupied with sewing their own clothes, building their own furniture, and growing their own food will necessarily have less time to work outside the home for wages. This will likely result in less income for the household and less workers for nearby employers – and, ultimately, a smaller economy due to the high degree of self-sufficiency being practiced. This is true on a global scale as well.

Real World Examples of Autarky

Historically, autarkic policies have been deployed to different extents. Western European countries deployed them under mercantilist policies from the 16th to the 18th century. This spurred economists like Smith, Ricardo, and Frederic Bastiat to refine free-market and free-trade philosophies as counter arguments.

Nazi Germany also implemented a form or autarky to ensure the strategic supply needed for its war efforts. Today, North Korea stands as the main example of a policy of autarky. North Korea’s economic isolation is a mixture of intentional self-reliance to reduce international political influence and imposed self-reliance due to being cut out of international trade through sanctions.

Autarky and the Autarkic Price

A related term, autarky price or autarkic price, refers to the cost of a good in an autarkic state. The cost of producing in a closed economy must be covered by the price charged for the good. If the cost is higher relative to other nations, then the autarky price is a dead loss for that national economy. The autarkic price is sometimes used as an economic variable when roughly calculating where a nation’s comparative advantages are. In practice, however, comparative advantages are discovered through market mechanisms rather than an economic model.

What Is the Adjusted Closing Price?

The adjusted closing price amends a stock’s closing price to reflect that stock’s value after accounting for any corporate actions. It is often used when examining historical returns or doing a detailed analysis of past performance.

Understanding the Adjusted Closing Price

Stock values are stated in terms of the closing price and the adjusted closing price. The closing price is the raw price, which is just the cash value of the last transacted price before the market closes. The adjusted closing price factors in anything that might affect the stock price after the market closes.

A stock’s price is typically affected by supply and demand of market participants. However, some corporate actions, such as stock splits, dividends, and rights offerings, affect a stock’s price. Adjustments allow investors to obtain an accurate record of the stock’s performance. Investors should understand how corporate actions are accounted for in a stock’s adjusted closing price. It is especially useful when examining historical returns because it gives analysts an accurate representation of the firm’s equity value.

Types of Adjustments

Adjusting Prices for Stock Splits

A stock split is a corporate action intended to make the firm’s shares more affordable for average investors. A stock split does not change a company’s total market capitalization, but it does affect the company’s stock price.

For example, a company’s board of directors may decide to split the company’s stock 3-for-1. Therefore, the company’s shares outstanding increase by a multiple of three, while its share price is divided by three. Suppose a stock closed at $300 the day before its stock split. In this case, the closing price is adjusted to $100 ($300 divided by 3) per share to maintain a consistent standard of comparison. Similarly, all other previous closing prices for that company would be divided by three to obtain the adjusted closing prices.

Adjusting for Dividends

Common distributions that affect a stock’s price include cash dividends and stock dividends. The difference between cash dividends and stock dividends is that shareholders are entitled to a predetermined price per share and additional shares, respectively.

For example, assume a company declared a $1 cash dividend and was trading at $51 per share before then. All other things being equal, the stock price would fall to $50 because that $1 per share is no longer part of the company’s assets. However, the dividends are still part of the investor’s returns. By subtracting dividends from previous stock prices, we obtain the adjusted closing prices and a better picture of returns.

Adjusting for Rights Offerings

A stock’s adjusted closing price also reflects rights offerings that may occur. A rights offering is an issue of rights given to existing shareholders, which entitles the shareholders to subscribe to the rights issue in proportion to their shares. That will lower the value of existing shares because supply increases have a dilutive effect on the existing shares.

For example, assume a company declares a rights offering, in which existing shareholders are entitled to one additional share for every two shares owned. Assume the stock is trading at $50, and existing shareholders can purchase additional shares at a subscription price of $45. After the rights offering, the adjusted closing price is calculated based on the adjusting factor and the closing price.

Benefits of the Adjusted Closing Price

The main advantage of adjusted closing prices is that they make it easier to evaluate stock performance. Firstly, the adjusted closing price helps investors understand how much they would have made by investing in a given asset. Most obviously, a 2-for-1 stock split does not cause investors to lose half their money. Since successful stocks often split repeatedly, graphs of their performance would be hard to interpret without adjusted closing prices.

Secondly, the adjusted closing price allows investors to compare the performance of two or more assets. Aside from the clear issues with stock splits, failing to account for dividends tends to understate the profitability of value stocks and dividend growth stocks. Using the adjusted closing price is also essential when comparing the returns of different asset classes over the long term. For example, the prices of high-yield bonds tend to fall in the long run. That does not mean these bonds are necessarily poor investments. Their high yields offset the losses and more, which can be seen by looking at the adjusted closing prices of high-yield bond funds.

Criticism of the Adjusted Closing Price

The nominal closing price of a stock or other asset can convey useful information. This information is destroyed by converting that price into an adjusted closing price. In actual practice, many speculators place buy and sell orders at certain prices, such as $100. As a result, a sort of tug of war can take place between bulls and bears at these key prices. If the bulls win, a breakout may occur and send the asset price soaring. Similarly, a win for the bears can lead to a breakdown and further losses. The adjusted close stock price obscures these events.

By looking at the actual closing price at the time, investors can get a better idea of what was going on and understand contemporary accounts. If investors look at historical records, they will find many examples of tremendous public interest in nominal levels. Perhaps the most famous is the role that Dow 1,000 played in the 1966 to 1982 secular bear market. During that period, the Dow Jones Industrial Average (DJIA) repeatedly hit 1,000, only to fall back shortly after that. The breakout finally took place in 1982, and the Dow never dropped below 1,000 again. This phenomenon is covered up somewhat by adding dividends to obtain the adjusted closing prices.

In general, adjusted closing prices are less useful for more speculative stocks. Jesse Livermore provided an excellent account of the impact of key nominal prices, such as $100 and $300, on Anaconda Copper in the early 20th century. In the early 21st century, similar patterns occurred with Netflix (NFLX) and Tesla (TSLA). William J. O’Neil gave examples where stock splits, far from being irrelevant, marked the beginnings of real declines in the stock price. While arguably irrational, the impact of nominal prices on stocks could be an example of a self-fulfilling prophecy.

What Is Additional Paid-in Capital (APIC)?

Additional paid-in capital (APIC) is an accounting term referring to money an investor pays above and beyond the par value price of a stock.

Often referred to as “contributed capital in excess of par,” APIC occurs when an investor buys newly-issued shares directly from a company during its initial public offering (IPO) stage. APIC, which is itemized under the shareholder equity (SE) section of a balance sheet, is viewed as a profit opportunity for companies as it results in them receiving excess cash from stockholders.

How Additional Paid-in Capital (APIC) Works

During its IPO, a firm is entitled to set any price for its stock that it sees fit. Meanwhile, investors may elect to pay any amount above this declared par value of a share price, which generates the APIC.

Let us assume that during its IPO phase the XYZ Widget Company issues one million shares of stock, with a par value of $1 per share, and that investors bid on shares for $2, $4, and $10 above the par value. Let us further assume that those shares ultimately sell for $11, consequently making the company $11 million. In this instance, the APIC is $10 million ($11 million minus the par value of $1 million). Therefore, the company’s balance sheet itemizes $1 million as “paid-in capital,” and $10 million as “additional paid-in capital.”

Once a stock trades in the secondary market, an investor may pay whatever the market will bear. When investors buy shares directly from a given company, that corporation receives and retains the funds as paid-in capital. But after that time, when investors buy shares in the open market, the generated funds go directly into the pockets of the investors selling off their positions.

Special Considerations

APIC is generally booked in the SE section of the balance sheet. When a company issues stock, there are two entries that take place in the equity section: common stock and APIC. The total cash generated by the IPO is recorded as a debit in the equity section, and the common stock and APIC are recorded as credits.

The APIC formula is:

APIC = (Issue Price – Par Value) x Number of Shares Acquired by Investors.

Par Value

Due to the fact that APIC represents money paid to the company above the par value of a security, it is essential to understand what par actually means. Simply put, “par” signifies the value a company assigns to stock at the time of its IPO, before there is even a market for the security. Issuers traditionally set stock par values deliberately low—in some cases as little as a penny per share—in order to preemptively avoid any potential legal liability, which might occur if the stock dips below its par value.

Market Value

Market value is the actual price a financial instrument is worth at any given time. The stock market determines the real value of a stock, which shifts continuously as shares are bought and sold throughout the trading day. Thus, investors make money on the changing value of a stock over time, based on company performance and investor sentiment.

Additional Paid-in Capital vs. Paid-in Capital

Paid-in capital, or contributed capital, is the full amount of cash or other assets that shareholders have given a company in exchange for stock. Paid-in capital includes the par value of both common and preferred stock plus any amount paid in excess.

Additional paid-in capital, as the name implies, includes only the amount paid in excess of the par value of stock issued during a company’s IPO.

Both of these items are included next to one another in the SE section of the balance sheet.

Benefits of Additional Paid-in Capital

For common stock, paid-in capital consists of a stock’s par value and APIC, the latter of which may provide a substantial portion of a company’s equity capital, before retained earnings begin to accumulate. This capital provides a layer of defense against potential losses, in the event that retained earnings begin to show a deficit. 

Another huge advantage for a company issuing shares is that it does not raise the fixed cost of the company. The company doesn’t have to make any payment to the investor; even dividends are not required. Furthermore, investors do not have any claim on the company’s existing assets.

After issuing stock to shareholders, the company is free to use the funds generated any way it chooses, whether that means paying off loans, purchasing an asset, or any other action that may benefit the company.

Correction—March 29, 2022: A previous version of this article inaccurately represented where APIC appears on the balance sheet.