Profit maximization

From Wikipedia, the free encyclopedia

An example diagram of Profit Maximization: In the supply and demand graph, the output of ${\displaystyle Q^{\ast }}$ is the intersection point of ${\displaystyle \text{MR}}$ (Marginal Revenue) and ${\displaystyle \text{MC}}$ (Marginal Cost), where ${\displaystyle \text{MR}=\text{MC}}$. The firm which produces at this output level is said to maximize profits. If the output produced is less than the equilibrium quantity (${\displaystyle Q^{\ast }}$), as shown in the red part, then ${\displaystyle \text{MR}}$ is greater than ${\displaystyle \text{MC}}$ (${\displaystyle \text{MR}>\text{MC}}$), and the profit is not maximized. The firm has in its interest to raise its output level to maximize profits, because the revenue gained will be more than the cost to pay. However, if the output level is greater than ${\displaystyle Q^{\ast }}$ (${\displaystyle \text{MR}<\text{MC}}$), as shown in the blue part, the firm's overall profit will decrease because the additional unit produced will increase the overall cost. Here too the profit is not maximized and the firm has to lower its output level to maximize profits.

In economics, profit maximization is the short run or long run process by which a firm may determine the price, input and output levels that will lead to the highest possible total profit (or just profit in short). In neoclassical economics, which is currently the mainstream approach to microeconomics, the firm is assumed to be a "rational agent" (whether operating in a perfectly competitive market or otherwise) which wants to maximize its total profit, which is the difference between its total revenue and its total cost.

Measuring the total cost and total revenue is often impractical, as the firms do not have the necessary reliable information to determine costs at all levels of production. Instead, they take a more practical approach by examining how small changes in production influence revenues and costs. When a firm produces an extra unit of product, the additional revenue gained from selling it is called the marginal revenue (${\displaystyle \text{MR}}$), and the additional cost to produce that unit is called the marginal cost (${\displaystyle \text{MC}}$). When the level of output is such that the marginal revenue is equal to the marginal cost (${\displaystyle \text{MR}=\text{MC}}$), then the firm's total profit is said to be maximized. If the marginal revenue is greater than the marginal cost (${\displaystyle \text{MR}>\text{MC}}$), then its total profit is not maximized, because the firm can produce additional units to earn additional profit. In other words, in this case, it is in the "rational" interest of the firm to increase its output level until its total profit is maximized. On the other hand, if the marginal revenue is less than the marginal cost (${\displaystyle \text{MR}<\text{MC}}$), then too its total profit is not maximized, because producing one unit less will reduce total cost more than total revenue gained, thus giving the firm more total profit. In this case, a "rational" firm has an incentive to reduce its output level until its total profit is maximized.^[1]

There are several perspectives one can take on profit maximization. First, since profit equals revenue minus cost, one can plot graphically each of the variables revenue and cost as functions of the level of output and find the output level that maximizes the difference (or this can be done with a table of values instead of a graph). Second, if specific functional forms are known for revenue and cost in terms of output, one can use calculus to maximize profit with respect to the output level. Third, since the first order condition for the optimization equates marginal revenue and marginal cost, if marginal revenue (${\displaystyle \text{MR}}$) and marginal cost (${\displaystyle \text{MC}}$) functions in terms of output are directly available one can equate these, using either equations or a graph. Fourth, rather than a function giving the cost of producing each potential output level, the firm may have input cost functions giving the cost of acquiring any amount of each input, along with a production function showing how much output results from using any combination of input quantities. In this case one can use calculus to maximize profit with respect to input usage levels, subject to the input cost functions and the production function. The first order condition for each input equates the marginal revenue product of the input (the increment to revenue from selling the product caused by an increment to the amount of the input used) to the marginal cost of the input.

For a firm in a perfectly competitive market for its output, the revenue function will simply equal the market price times the quantity produced and sold, whereas for a monopolist, which chooses its level of output simultaneously with its selling price. In the case of monopoly, the company will produce more products because it can still make normal profits. To get the most profit, you need to set higher prices and lower quantities than the competitive market. However, the revenue function takes into account the fact that higher levels of output require a lower price in order to be sold. An analogous feature holds for the input markets: in a perfectly competitive input market the firm's cost of the input is simply the amount purchased for use in production times the market-determined unit input cost, whereas a monopsonist’s input price per unit is higher for higher amounts of the input purchased.

The principal difference between short run and long run profit maximization is that in the long run the quantities of all inputs, including physical capital, are choice variables, while in the short run the amount of capital is predetermined by past investment decisions. In either case, there are inputs of labor and raw materials.

Basic definitions

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Any costs incurred by a firm may be classified into two groups: fixed costs and variable costs. Fixed costs, which occur only in the short run, are incurred by the business at any level of output, including zero output. These may include equipment maintenance, rent, wages of employees whose numbers cannot be increased or decreased in the short run, and general upkeep. Variable costs change with the level of output, increasing as more product is generated. Materials consumed during production often have the largest impact on this category, which also includes the wages of employees who can be hired and laid off in the short run span of time under consideration. Fixed cost and variable cost, combined, equal total cost.

Revenue is the amount of money that a company receives from its normal business activities, usually from the sale of goods and services (as opposed to monies from security sales such as equity shares or debt issuances).

The five ways formula is to increase leads, conversation rates, average dollar sales, the average number of sales, and average product profit. Profits can be increased by up to 1,000 percent, this is important for sole traders and small businesses let alone big businesses but none the less all profit maximization is a matter of each business stage and greater returns for profit sharing thus higher wages and motivation.^{[2][full citation needed]}

Marginal cost and marginal revenue, depending on whether the calculus approach is taken or not, are defined as either the change in cost or revenue as each additional unit is produced or the derivative of cost or revenue with respect to the quantity of output. For instance, taking the first definition, if it costs a firm $400 to produce 5 units and $480 to produce 6, the marginal cost of the sixth unit is 80 dollars. Conversely, the marginal income from the production of 6 units is the income from the production of 6 units minus the income from the production of 5 units (the latter item minus the preceding item).

Total revenue – total cost perspective

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Profit maximization using the total revenue and total cost curves of a perfect competitor

To obtain the profit maximizing output quantity, we start by recognizing that profit is equal to total revenue (${\displaystyle \text{TR}}$) minus total cost (${\displaystyle \text{TC}}$). Given a table of costs and revenues at each quantity, we can either compute equations or plot the data directly on a graph. The profit-maximizing output is the one at which this difference reaches its maximum.

In the accompanying diagram, the linear total revenue curve represents the case in which the firm is a perfect competitor in the goods market, and thus cannot set its own selling price. The profit-maximizing output level is represented as the one at which total revenue is the height of ${\displaystyle \text{C}}$ and total cost is the height of ${\displaystyle \text{B}}$; the maximal profit is measured as the length of the segment ${\displaystyle \overline{\text{CB}}}$. This output level is also the one at which the total profit curve is at its maximum.

If, contrary to what is assumed in the graph, the firm is not a perfect competitor in the output market, the price to sell the product at can be read off the demand curve at the firm's optimal quantity of output. This optimal quantity of output is the quantity at which marginal revenue equals marginal cost.

Marginal revenue – marginal cost perspective

Profit maximization using the marginal revenue and marginal cost curves of a perfect competitor

Price setting by a monopolist

An equivalent perspective relies on the relationship that, for each unit sold, marginal profit (${\displaystyle \text{M}\pi }$) equals marginal revenue (${\displaystyle \text{MR}}$) minus marginal cost (${\displaystyle \text{MC}}$). Then, if marginal revenue is greater than marginal cost at some level of output, marginal profit is positive and thus a greater quantity should be produced, and if marginal revenue is less than marginal cost, marginal profit is negative and a lesser quantity should be produced. At the output level at which marginal revenue equals marginal cost, marginal profit is zero and this quantity is the one that maximizes profit.^[3] Since total profit increases when marginal profit is positive and total profit decreases when marginal profit is negative, it must reach a maximum where marginal profit is zero—where marginal cost equals marginal revenue—and where lower or higher output levels give lower profit levels.^[3] In calculus terms, the requirement that the optimal output have higher profit than adjacent output levels is that:^[3]

${\displaystyle \frac{{\mathrm{d}}^{2}R}{{\mathrm{d}Q}^2}<\frac{{\mathrm{d}}^{2}C}{{\mathrm{d}Q}^2}.}$

The intersection of ${\displaystyle \text{MR}}$ and ${\displaystyle \text{MC}}$ is shown in the next diagram as point ${\displaystyle \text{A}}$. If the industry is perfectly competitive (as is assumed in the diagram), the firm faces a demand curve (${\displaystyle \text{D}}$) that is identical to its marginal revenue curve (${\displaystyle \text{MR}}$), and this is a horizontal line at a price determined by industry supply and demand. Average total costs are represented by curve ${\displaystyle \text{ATC}}$. Total economic profit is represented by the area of the rectangle ${\displaystyle \overline{\text{PABC}}}$. The optimum quantity (${\displaystyle Q}$) is the same as the optimum quantity in the first diagram.

If the firm is a monopolist, the marginal revenue curve would have a negative slope as shown in the next graph, because it would be based on the downward-sloping market demand curve. The optimal output, shown in the graph as ${\displaystyle Q_m}$, is the level of output at which marginal cost equals marginal revenue. The price that induces that quantity of output is the height of the demand curve at that quantity (denoted ${\displaystyle P_m}$).

A generic derivation of the profit maximisation level of output is given by the following steps. Firstly, suppose a representative firm ${\displaystyle i}$ has perfect information about its profit, given by:

${\displaystyle {\pi }_i={\text{TR}}_i-{\text{TC}}_i}$

where ${\displaystyle \text{TR}}$ denotes total revenue and ${\displaystyle \text{TC}}$ denotes total costs. The above expression can be re-written as:

${\displaystyle {\pi }_i=p_i\cdot q_i-c_i\cdot q_i}$

where ${\displaystyle p}$ denotes price (marginal revenue), ${\displaystyle q}$ quantity, and ${\displaystyle c}$ marginal cost. The firm maximises their profit with respect to quantity to yield the profit maximisation level of output:

${\displaystyle \frac{\left(\mathrm{\partial }{\pi }_i\right)}{\left(\mathrm{\partial }{q}_i\right)}=p_i-c_i=0}$

As such, the profit maximisation level of output is marginal revenue ${\displaystyle p_i}$ equating to marginal cost ${\displaystyle c_i}$.

In an environment that is competitive but not perfectly so, more complicated profit maximization solutions involve the use of game theory.

Case in which maximizing revenue is equivalent

In some cases a firm's demand and cost conditions are such that marginal profits are greater than zero for all levels of production up to a certain maximum.^[4] In this case marginal profit plunges to zero immediately after that maximum is reached; hence the ${\displaystyle \text{M}\pi =0}$ rule implies that output should be produced at the maximum level, which also happens to be the level that maximizes revenue.^[4] In other words, the profit-maximizing quantity and price can be determined by setting marginal revenue equal to zero, which occurs at the maximal level of output. Marginal revenue equals zero when the total revenue curve has reached its maximum value. An example would be a scheduled airline flight. The marginal costs of flying one more passenger on the flight are negligible until all the seats are filled. The airline would maximize profit by filling all the seats.

Maximizing profits in the real world

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In the real world, it is not easy to achieve profit maximization. The company must accurately know the marginal income and the marginal cost of the last commodity sold because of MR.

The price elasticity of demand for goods depends on the response of other companies. When it is the only company raising prices, demand will be elastic. If one family raises prices and others follow, demand may be inelastic.

Companies can seek to maximize profits through estimation. When the price increase leads to a small decline in demand, the company can increase the price as much as possible before the demand becomes elastic. Generally, it is difficult to change the impact of the price according to the demand, because the demand may occur due to many other factors besides the price.

The company may also have other goals and considerations. For example, companies may choose to earn less than the maximum profit in pursuit of higher market share. Because price increases maximize profits in the short term, they will attract more companies to enter the market.

Many companies try to minimize costs by shifting production to foreign locations with cheap labor (e.g. Nike, Inc.). However, moving the production line to a foreign location may cause unnecessary transportation costs. Close market locations for producing and selling products can improve demand optimization, but when the production cost is much higher, it is not a good choice.

Tools

Profit analysis

Habitually recording and analyzing the business costs of all products/services sold. There are many miscellaneous items in the cost including labor, materials, transportation, advertising, storage, etc. related to any goods or services sold, which become expenses.

Business intelligence tools

may be needed to integrate all financial information to record expense reports so that the business can clearly understand all costs related to operations and their accuracy.

Planning and actual execution

when implementing a "what if" solution to help in sales and operation planning process, familiarity with the company's operations, including the supply chain, inventory management and sales process is useful. Constraints are required to prevent corporate plans from becoming unfeasible.

Changes in total costs and profit maximization

A firm maximizes profit by operating where marginal revenue equals marginal cost. This is stipulated under neoclassical theory, in which a firm maximizes profit in order to determine a level of output and inputs, which provides the price equals marginal cost condition.^{[5][full citation needed]} In the short run, a change in fixed costs has no effect on the profit maximizing output or price.^[6] The firm merely treats short term fixed costs as sunk costs and continues to operate as before.^[7] This can be confirmed graphically. Using the diagram illustrating the total cost–total revenue perspective, the firm maximizes profit at the point where the slopes of the total cost line and total revenue line are equal.^[4] An increase in fixed cost would cause the total cost curve to shift up rigidly by the amount of the change.^[4] There would be no effect on the total revenue curve or the shape of the total cost curve. Consequently, the profit maximizing output would remain the same. This point can also be illustrated using the diagram for the marginal revenue–marginal cost perspective. A change in fixed cost would have no effect on the position or shape of these curves.^[4] In simple terms, although profit is related to total cost, ${\displaystyle \text{Profit}=\text{TR}-\text{TC}}$, the enterprise can maximize profit by producing to the maximum profit (the maximum value of ${\displaystyle \text{TR}-\text{TC}}$) to maximize profit. But when the total cost increases, it does not mean maximizing profit Will change, because the increase in total cost does not necessarily change the marginal cost. If the marginal cost remains the same, the enterprise can still produce to the unit of (${\displaystyle \text{MR}=\text{MC}=\text{Price}}$) to maximize profit. In the long run, a firm will theoretically have zero expected profits under the competitive equilibrium. The market should adjust to clear any profits if there is perfect competition. In situations where there are non-zero profits, we should expect to see either some form of long run disequilibrium or non-competitive conditions, such as barriers to entry, where there is not perfect competition between firms.^{[5][full citation needed]}

Markup pricing

In addition to using methods to determine a firm's optimal level of output, a firm that is not perfectly competitive can equivalently set price to maximize profit (since setting price along a given demand curve involves picking a preferred point on that curve, which is equivalent to picking a preferred quantity to produce and sell). The profit maximization conditions can be expressed in a "more easily applicable" form or rule of thumb than the above perspectives use.^{[8][full citation needed]} The first step is to rewrite the expression for marginal revenue as

${\displaystyle \begin{array}{rl}\text{MR}=& \frac{\mathrm{\Delta }\text{TR}}{\mathrm{\Delta }Q}\\ =& \frac{P\mathrm{\Delta }Q+Q\mathrm{\Delta }P}{\mathrm{\Delta }Q}\\ =& P+\frac{Q\mathrm{\Delta }P}{\mathrm{\Delta }Q}\end{array}}$

, where ${\displaystyle P}$ and ${\displaystyle Q}$ refer to the midpoints between the old and new values of price and quantity respectively.^[8] The marginal revenue from an incremental unit of output has two parts: first, the revenue the firm gains from selling the additional units or, giving the term ${\displaystyle P\mathrm{\Delta }Q}$. The additional units are called the marginal units.^{[9][full citation needed]} Producing one extra unit and selling it at price ${\displaystyle P}$ brings in revenue of ${\displaystyle P}$. Moreover, one must consider "the revenue the firm loses on the units it could have sold at the higher price"^[9]—that is, if the price of all units had not been pulled down by the effort to sell more units. These units that have lost revenue are called the infra-marginal units.^[9] That is, selling the extra unit results in a small drop in price which reduces the revenue for all units sold by the amount ${\displaystyle Q\cdot \left(\frac{\mathrm{\Delta }P}{\mathrm{\Delta }Q}\right)}$. Thus, ${\displaystyle \text{MR}=P+Q\cdot \frac{\mathrm{\Delta }P}{\mathrm{\Delta }Q}=P+P\cdot \frac{Q}{P}\cdot \frac{\mathrm{\Delta }P}{\mathrm{\Delta }Q}=P+\frac{P}{\text{PED}}}$, where ${\displaystyle \text{PED}}$ is the price elasticity of demand characterizing the demand curve of the firms' customers, which is negative. Then setting ${\displaystyle \text{MC}=\text{MR}}$ gives ${\displaystyle \text{MC}=P+\frac{P}{\text{PED}}}$ so ${\displaystyle \frac{P-\text{MC}}{P}=\frac{-1}{\text{PED}}}$ and ${\displaystyle P=\frac{MC}{1+\left(\frac{1}{\text{PED}}\right)}}$. Thus, the optimal markup rule is:

${\displaystyle \frac{\left(P-\text{MC}\right)}{P}=\frac{1}{\left(-\text{PED}\right)}}$

or equivalently

${\displaystyle P=\frac{\text{PED}}{1+\text{PED}}\cdot \text{MC}}$.^{[10][11][full citation needed]}

In other words, the rule is that the size of the markup of price over the marginal cost is inversely related to the absolute value of the price elasticity of demand for the good.^[10]

The optimal markup rule also implies that a non-competitive firm will produce on the elastic region of its market demand curve. Marginal cost is positive. The term ${\displaystyle \frac{PED}{1+\text{PED}}}$ would be positive so ${\displaystyle P>0}$ only if ${\displaystyle \text{PED}}$ is between ${\displaystyle -1}$ and ${\displaystyle -\mathrm{\infty }}$ (that is, if demand is elastic at that level of output).^{[12][full citation needed]} The intuition behind this result is that, if demand is inelastic at some value ${\displaystyle Q_1}$ then a decrease in ${\displaystyle Q}$ would increase ${\displaystyle P}$ more than proportionately, thereby increasing revenue ${\displaystyle P\cdot Q}$; since lower ${\displaystyle Q}$ would also lead to lower total cost, profit would go up due to the combination of increased revenue and decreased cost. Thus, ${\displaystyle Q_1}$ does not give the highest possible profit.

Marginal product of labor, marginal revenue product of labor, and profit maximization

The general rule is that the firm maximizes profit by producing that quantity of output where marginal revenue equals marginal cost. The profit maximization issue can also be approached from the input side. That is, what is the profit maximizing usage of the variable input? ^[13] To maximize profit the firm should increase usage of the input "up to the point where the input's marginal revenue product equals its marginal costs".^[14] Mathematically, the profit-maximizing rule is ${\displaystyle {\text{MRP}}_L={\text{MC}}_L}$, where the subscript ${\displaystyle {}_L}$ refers to the commonly assumed variable input, labor.

The marginal revenue product is the change in total revenue per unit change in the variable input, that is, ${\displaystyle {\text{MRP}}_L=\frac{\mathrm{\Delta }\text{TR}}{\mathrm{\Delta }L}}$.

${\displaystyle {\text{MRP}}_L}$ is the product of marginal revenue and the marginal product of labor or ${\displaystyle {\text{MRP}}_L=\text{MR}\cdot {\text{MP}}_L}$.

Sub-optimal Profit maximization

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Oftentimes, businesses will attempt to maximize their profits even though their optimization strategy typically leads to a sub-optimal quantity of goods produced for the consumers. When deciding a given quantity to produce, a firm will often try to maximize its own producer surplus, at the expense of decreasing the overall social surplus. As a result of this decrease in social surplus, consumer surplus is also minimized, as compared to if the firm did not elect to maximize their own producer surplus.

Government Regulation

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Market quotas reflect the power of a firm in the market, a firm dominating a market is very common, and too much power often becomes the motive for non-Hong behavior. Predatory pricing, tying, price gouging and other behaviors are reflecting the crisis of excessive power of monopolists in the market. In an attempt to prevent businesses from abusing their power to maximize their own profits, governments often intervene to stop them in their tracks. A major example of this is through anti-trust regulation which effectively outlaws most industry monopolies. Through this regulation, consumers enjoy a better relationship with the companies that serve them, even though the company itself may suffer, financially speaking.

Surplus value

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Surplus_value

 

In Marxian economics, surplus value is the difference between the amount raised through a sale of a product and the amount it cost to manufacture it: i.e. the amount raised through sale of the product minus the cost of the materials, plant and labour power. The concept originated in Ricardian socialism, with the term "surplus value" itself being coined by William Thompson in 1824; however, it was not consistently distinguished from the related concepts of surplus labor and surplus product. The concept was subsequently developed and popularized by Karl Marx. Marx's formulation is the standard sense and the primary basis for further developments, though how much of Marx's concept is original and distinct from the Ricardian concept is disputed (see § Origin). Marx's term is the German word "Mehrwert", which simply means value added (sales revenue minus the cost of materials used up), and is cognate to English "more worth".

It is a major concept in Karl Marx's critique of political economy. Conventionally, value-added is equal to the sum of gross wage income and gross profit income. However, Marx uses the term Mehrwert to describe the yield, profit or return on production capital invested, i.e. the amount of the increase in the value of capital. Hence, Marx's use of Mehrwert has always been translated as "surplus value", distinguishing it from "value-added". According to Marx's theory, surplus value is equal to the new value created by workers in excess of their own labor-cost, which is appropriated by the capitalist as profit when products are sold. Marx thought that the gigantic increase in wealth and population from the 19th century onwards was mainly due to the competitive striving to obtain maximum surplus-value from the employment of labor, resulting in an equally gigantic increase of productivity and capital resources. To the extent that increasingly the economic surplus is convertible into money and expressed in money, the amassment of wealth is possible on a larger and larger scale (see capital accumulation and surplus product). The concept is closely connected to producer surplus.

Origin

By the Age of Enlightenment in the 18th century the French physiocrats were already writing on the surplus value that was being extracted from labor by "the employer, the owner, and all exploiters" although they used the term net product. The concept of surplus value continued to be developed under Adam Smith who also used the term "net product" while his successors the Ricardian socialists, began using the term "surplus value" decades later after its coinage by William Thompson in 1824:

Two measures of the value of this use, here present themselves; the measure of the laborer, and the measure of the capitalist. The measure of the laborer consists in the contribution of such sums as would replace the waste and value of the capital by the time it would be consumed, with such added compensation to the owner and superintendent of it as would support him in equal comfort with the more actively employed productive laborers. The measure of the capitalist, on the contrary, would be the additional value produced by the same quantity of labor in consequence of the use of the machinery or other capital; the whole of such surplus value to be enjoyed by the capitalist for his superior intelligence and skill in accumulating and advancing to the laborers his capital or the use of it.

— William Thompson, An Inquiry into the Principles of the Distribution of Wealth (1824), p. 128 (2nd ed.), emphasis added

William Godwin and Charles Hall are also credited as earlier developers of the concept. Early authors also used the terms "surplus labor" and "surplus produce" (in Marx's language, surplus product), which have distinct meanings in Marxian economics: surplus labor produces surplus product, which has surplus value. Some authors consider Marx as completely borrowing from Thompson, notably Anton Menger:

... Marx is completely under the influence of the earlier English socialists, and more particularly of William Thompson. ... [T]he whole theory of surplus value, its conception, its name, and the estimates of its amounts are borrowed in all essentials from Thompson's writings.

...

Cf. Marx, Das Kapital, English trans. 1887, pp. 156, 194, 289, with Thompson, Distribution of Wealth, p. 163; 2nd ed. p. 125. ... The real discovers of the theory of surplus value are Godwin, Hall, and especially W. Thompson.

— Anton Menger, The Right to the Whole Produce of Labour (1886)

This claim of priority has been vigorously contested, notably in an article by Friedrich Engels, completed by Karl Kautsky and published anonymously in 1887, reacting to and criticizing Menger in a review of his The Right to the Whole Produce of Labour, arguing that there is nothing in common but the term "surplus value" itself.

An intermediate position acknowledges the early development by Ricardian socialists and others, but credits Marx with substantial development. For example:

What is original in Marx is the explanation of the manner in which surplus value is produced.

— John Spargo, Socialism (1906)

Johann Karl Rodbertus developed a theory of surplus value in the 1830s and 1840s, notably in Zur Erkenntnis unserer staatswirthschaftlichen Zustände (Toward an appreciation of our economic circumstances, 1842), and claimed earlier priority to Marx, specifically to have "shown practically in the same way as Marx, only more briefly and clearly, the source of the surplus value of the capitalists". The debate, taking the side of Marx's priority, is detailed in the Preface to Capital, Volume II by Engels.

Marx first elaborated his doctrine of surplus value in 1857–58 manuscripts of A Contribution to the Critique of Political Economy (1859), following earlier developments in his 1840s writings. It forms the subject of his 1862–63 manuscript Theories of Surplus Value (which was subsequently published as Capital, Volume IV), and features in his Capital, Volume I (1867).

Theory

The problem of explaining the source of surplus value is expressed by Friedrich Engels as follows:

Whence comes this surplus-value? It cannot come either from the buyer buying the commodities under their value, or from the seller selling them above their value. For in both cases the gains and the losses of each individual cancel each other, as each individual is in turn buyer and seller. Nor can it come from cheating, for though cheating can enrich one person at the expense of another, it cannot increase the total sum possessed by both, and therefore cannot augment the sum of the values in circulation. (...) This problem must be solved, and it must be solved in a purely economic way, excluding all cheating and the intervention of any force — the problem being: how is it possible constantly to sell dearer than one has bought, even on the hypothesis that equal values are always exchanged for equal values?

Marx's solution was first to distinguish between labor-time worked and labor power, and secondly to distinguish between absolute surplus value and relative surplus value. A worker who is sufficiently productive can produce an output value greater than what it costs to hire him. Although his wage seems to be based on hours worked, in an economic sense this wage does not reflect the full value of what the worker produces. Effectively it is not labour which the worker sells, but his capacity to work.

Imagine a worker who is hired for an hour and paid $10 per hour. Once in the capitalist's employ, the capitalist can have him operate a boot-making machine with which the worker produces $10 worth of work every 15 minutes. Every hour, the capitalist receives $40 worth of work and only pays the worker $10, capturing the remaining $30 as gross revenue. Once the capitalist has deducted fixed and variable operating costs of (say) $20 (leather, depreciation of the machine, etc.), he is left with $10. Thus, for an outlay of capital of $30, the capitalist obtains a surplus value of $10; his capital has not only been replaced by the operation, but also has increased by $10.

This "simple" exploitation characterizes the realization of absolute surplus value, which is then claimed by the capitalist. The worker cannot capture this benefit directly because he has no claim to the means of production (e.g. the boot-making machine) or to its products, and his capacity to bargain over wages is restricted by laws and the supply/demand for wage labour. This form of exploitation was well understood by pre-Marxian Socialists and left-wing followers of Ricardo, such as Proudhon, and by early labor organizers, who sought to unite workers in unions capable of collective bargaining, in order to gain a share of profits and limit the length of the working day.

Relative surplus value is not created in a single enterprise or site of production. It arises instead from the total relation between multiple enterprises and multiple branches of industry when the necessary labor-time of production is reduced, effecting a change in the value of labor-power. For example, when new technology or new business practices increase the productivity of labor a capitalist already employs, or when the commodities necessary for workers' subsistence fall in value, the amount of socially necessary labor-time is decreased, the value of labor-power is reduced, and a relative surplus value is realized as profit for the capitalist, increasing the overall general rate of surplus value in the total economy:

The surplus-value produced by prolongation of the working day, I call absolute surplus-value. On the other hand, the surplus-value arising from the curtailment of the necessary labour-time, and from the corresponding alteration in the respective lengths of the two components of the working day, I call relative surplus-value.

In order to effect a fall in the value of labour-power, the increase in the productiveness of labour must seize upon those branches of industry whose products determine the value of labour-power, and consequently either belong to the class of customary means of subsistence, or are capable of supplying the place of those means. But the value of a commodity is determined, not only by the quantity of labour which the labourer directly bestows upon that commodity, but also by the labour contained in the means of production. For instance, the value of a pair of boots depends not only on the cobbler’s labour, but also on the value of the leather, wax, thread, &c. Hence, a fall in the value of labour-power is also brought about by an increase in the productiveness of labour, and by a corresponding cheapening of commodities in those industries which supply the instruments of labour and the raw material, that form the material elements of the constant capital required for producing the necessaries of life.

— Marx, Capital Vol. 1, ch. 12, "The Concept of Relative Surplus-Value" 

Definition

Total surplus-value in an economy (Marx refers to the mass or volume of surplus-value) is basically equal to the sum of net distributed and undistributed profit, net interest, net rents, net tax on production and various net receipts associated with royalties, licensing, leasing, certain honorariums etc. (see also value product). Of course, the way generic profit income is grossed and netted in social accounting may differ somewhat from the way an individual business does that (see also Operating surplus).

Marx's own discussion focuses mainly on profit, interest and rent, largely ignoring taxation and royalty-type fees which were proportionally very small components of the national income when he lived. Over the last 150 years, however, the role of the state in the economy has increased in almost every country in the world. Around 1850, the average share of government spending in GDP (See also Government spending) in the advanced capitalist economies was around 5%; in 1870, a bit above 8%; on the eve of World War I, just under 10%; just before the outbreak of World War II, around 20%; by 1950, nearly 30%; and today the average is around 35–40%. (see for example Alan Turner Peacock, "The growth of public expenditure", in Encyclopedia of Public Choice, Springer 2003, pp. 594–597).

Interpretations

Surplus-value may be viewed in five ways:

• As a component of the new value product, which Marx himself defines as equal to the sum of labor costs in respect of capitalistically productive labor (variable capital) and surplus-value. In production, he argues, the workers produce a value equal to their wages plus an additional value, the surplus-value. They also transfer part of the value of fixed assets and materials to the new product, equal to economic depreciation (consumption of fixed capital) and intermediate goods used up (constant capital inputs). Labor costs and surplus-value are the monetary valuations of what Marx calls the necessary product and the surplus product, or paid labour and unpaid labour.
• Surplus-value can also be viewed as a flow of net income appropriated by the owners of capital in virtue of asset ownership, comprising both distributed personal income and undistributed business income. In the whole economy, this will include both income directly from production and property income.
• Surplus-value can be viewed as the source of society's accumulation fund or investment fund; part of it is re-invested, but part is appropriated as personal income, and used for consumptive purposes by the owners of capital assets (see capital accumulation); in exceptional circumstances, part of it may also be hoarded in some way. In this context, surplus value can also be measured as the increase in the value of the stock of capital assets through an accounting period, prior to distribution.
• Surplus-value can be viewed as a social relation of production, or as the monetary valuation of surplus-labour – a sort of "index" of the balance of power between social classes or nations in the process of the division of the social product.
• Surplus-value can, in a developed capitalist economy, be viewed also as an indicator of the level of social productivity that has been reached by the working population, i.e. the net amount of value it can produce with its labour in excess of its own consumption requirements.

Equalization of rates

Marx believed that the long-term historical tendency would be for differences in rates of surplus value between enterprises and economic sectors to level out, as Marx explains in two places in Capital Vol. 3:

If capitals that set in motion unequal quantities of living labour produce unequal amounts of surplus-value, this assumes that the level of exploitation of labour, or the rate of surplus-value, is the same, at least to a certain extent, or that the distinctions that exist here are balanced out by real or imaginary (conventional) grounds of compensation. This assumes competition among workers, and an equalization that takes place by their constant migration between one sphere of production and another. Assume a general rate of surplus value of this kind, as a tendency, like all economic laws, as a theoretical simplification; but in any case this is in practice an actual presupposition of the capitalist mode of production, even if inhibited to a greater or lesser extent by practical frictions that produce more or less significant local differences, such as the settlement laws for agricultural labourers in England, for example. In theory, we assume that the laws of the capitalist mode of production develop in their pure form. In reality, this is only an approximation; but that approximation is all the more exact, the more the capitalist mode of production is developed and the less it is adulterated by survivals of earlier economic conditions with which it is amalgamated – Capital Vol. 3, ch. 10, Pelican edition p. 275.

Hence, he assumed a uniform rate of surplus value in his models of how surplus value would be shared out under competitive conditions.

Appropriation from production

Both in Das Kapital and in preparatory manuscripts such as the Grundrisse and Results of the immediate process of production, Marx asserts that commerce by stages transforms a non-capitalist production process into a capitalist production process, integrating it fully into markets, so that all inputs and outputs become marketed goods or services. When that process is complete, according to Marx, the whole of production has become simultaneously a labor process creating use-values and a valorisation process creating new value, and more specifically a surplus-value appropriated as net income (see also capital accumulation).

Marx contends that the whole purpose of production in this situation becomes the growth of capital; i.e. that production of output becomes conditional on capital accumulation. If production becomes unprofitable, capital will be withdrawn from production sooner or later.

The implication is that the main driving force of capitalism becomes the quest to maximise the appropriation of surplus-value augmenting the stock of capital. The overriding motive behind efforts to economise resources and labor would thus be to obtain the maximum possible increase in income and capital assets ("business growth"), and provide a steady or growing return on investment.

Absolute vs. relative

According to Marx, absolute surplus value is obtained by increasing the amount of time worked per worker in an accounting period. Marx talks mainly about the length of the working day or week, but in modern times the concern is about the number of hours worked per year.

In many parts of the world, as productivity rose, the workweek decreased from 60 hours to 50, 40 or 35 hours.

Relative surplus value is obtained mainly by:

• Reducing wages — this can only go to a certain point, because if wages fall below the ability of workers to purchase their means of subsistence, they will be unable to reproduce themselves and the capitalists will not be able to find sufficient labor power.
• Reducing the cost of wage-goods by various means, so that wage increases can be curbed.
• Increasing the productivity and intensity of labour generally, through mechanisation and rationalisation, yielding a bigger output per hour worked.

The attempt to extract more and more surplus-value from labor on the one side, and on the other side the resistance to this exploitation, are according to Marx at the core of the conflict between social classes, which is sometimes muted or hidden, but at other times erupts in open class warfare and class struggle.

Production versus realisation

Marx distinguished sharply between value and price, in part because of the sharp distinction he draws between the production of surplus-value and the realisation of profit income (see also value-form). Output may be produced containing surplus-value (valorisation), but selling that output (realisation) is not at all an automatic process.

Until payment from sales is received, it is uncertain how much of the surplus-value produced will actually be realised as profit from sales. So, the magnitude of profit realised in the form of money and the magnitude of surplus-value produced in the form of products may differ greatly, depending on what happens to market prices and the vagaries of supply and demand fluctuations. This insight forms the basis of Marx's theory of market value, prices of production and the tendency of the rate of profit of different enterprises to be levelled out by competition.

In his published and unpublished manuscripts, Marx went into great detail to examine many different factors which could affect the production and realisation of surplus-value. He regarded this as crucial for the purpose of understanding the dynamics and dimensions of capitalist competition, not just business competition but also competition between capitalists and workers and among workers themselves. But his analysis did not go much beyond specifying some of the overall outcomes of the process.

His main conclusion though is that employers will aim to maximise the productivity of labour and economise on the use of labour, to reduce their unit-costs and maximise their net returns from sales at current market prices; at a given ruling market price for an output, every reduction of costs and every increase in productivity and sales turnover will increase profit income for that output. The main method is mechanisation, which raises the fixed capital outlay in investment.

In turn, this causes the unit-values of commodities to decline over time, and a decline of the average rate of profit in the sphere of production occurs, culminating in a crisis of capital accumulation, in which a sharp reduction in productive investments combines with mass unemployment, followed by an intensive rationalisation process of take-overs, mergers, fusions, and restructuring aiming to restore profitability.

Relation to taxation

S&P 500 dividends and buybacks vs. Federal and State tax collections
  State tax revenue
  Federal tax revenue
  S&P 500 Stock buyback
  S&P 500 Dividends

In general, business leaders and investors are hostile to any attempts to encroach on total profit volume, especially those of government taxation. The lower taxes are, other things being equal, the bigger the mass of profit that can be distributed as income to private investors. It was tax revolts that originally were a powerful stimulus motivating the bourgeoisie to wrest state power from the feudal aristocracy at the beginning of the capitalist era.

In reality, of course, a substantial portion of tax money is also redistributed to private enterprise in the form of government contracts and subsidies. Capitalists may therefore be in conflict among themselves about taxes, since what is a cost to some, is a source of profit to others. Marx never analysed all this in detail; but the concept of surplus value will apply mainly to taxes on gross income (personal and business income from production) and on the trade in products and services. Estate duty for example rarely contains a surplus value component, although profit could be earned in the transfer of the estate.

Generally, Marx seems to have regarded taxation imposts as a "form" which disguised real product values. Apparently following this view, Ernest Mandel in his 1960 treatise Marxist Economic Theory refers to (indirect) taxes as "arbitrary additions to commodity prices". But this is something of a misnomer, and disregards that taxes become part of the normal cost-structure of production. In his later treatise on late capitalism, Mandel astonishingly hardly mentions the significance of taxation at all, a very serious omission from the point of view of the real world of modern capitalism since taxes can reach a magnitude of a third, or even half of GDP (see E. Mandel, Late Capitalism. London: Verso, 1975).For example in the United Kingdom alone 75% of all taxation revenue comes from just three taxes Income tax, National insurance and VAT which in reality is 75% of the GDP of the country.

Relation to the circuits of capital

Generally, Marx focused in Das Kapital on the new surplus-value generated by production, and the distribution of this surplus value. In this way, he aimed to reveal the "origin of the wealth of nations" given a capitalist mode of production. However, in any real economy, a distinction must be drawn between the primary circuit of capital, and the secondary circuits. To some extent, national accounts also do this.

The primary circuit refers to the incomes and products generated and distributed from productive activity (reflected by GDP). The secondary circuits refer to trade, transfers and transactions occurring outside that sphere, which can also generate incomes, and these incomes may also involve the realisation of a surplus-value or profit.

It is true that Marx argues no net additions to value can be created through acts of exchange, economic value being an attribute of labour-products (previous or newly created) only. Nevertheless, trading activity outside the sphere of production can obviously also yield a surplus-value which represents a transfer of value from one person, country or institution to another.

A very simple example would be if somebody sold a second-hand asset at a profit. This transaction is not recorded in gross product measures (after all, it isn't new production), nevertheless a surplus-value is obtained from it. Another example would be capital gains from property sales. Marx occasionally refers to this kind of profit as profit upon alienation, alienation being used here in the juridical, not sociological sense. By implication, if we just focused on surplus-value newly created in production, we would underestimate total surplus-values realised as income in a country. This becomes obvious if we compare census estimates of income & expenditure with GDP data.

This is another reason why surplus-value produced and surplus-value realised are two different things, although this point is largely ignored in the economics literature. But it becomes highly important when the real growth of production stagnates, and a growing portion of capital shifts out of the sphere of production in search of surplus-value from other deals.

Nowadays the volume of world trade grows significantly faster than GDP, suggesting to Marxian economists such as Samir Amin that surplus-value realised from commercial trade (representing to a large extent a transfer of value by intermediaries between producers and consumers) grows faster than surplus-value realised directly from production.

Thus, if we took the final price of a good (the cost to the final consumer) and analysed the cost structure of that good, we might find that, over a period of time, the direct producers get less income and intermediaries between producers and consumers (traders) get more income from it. That is, control over the access to a good, asset or resource as such may increasingly become a very important factor in realising a surplus-value. In the worst case, this amounts to parasitism or extortion. This analysis illustrates a key feature of surplus value which is that it accumulated by the owners of capital only within inefficient markets because only inefficient markets – i.e. those in which transparency and competition are low – have profit margins large enough to facilitate capital accumulation. Ironically, profitable – meaning inefficient – markets have difficulty meeting the definition a free market because a free market is to some extent defined as an efficient one: one in which goods or services are exchanged without coercion or fraud, or in other words with competition (to prevent monopolistic coercion) and transparency (to prevent fraud).

Measurement

The first attempt to measure the rate of surplus-value in money-units was by Marx himself in chapter 9 of Das Kapital, using factory data of a spinning mill supplied by Friedrich Engels (though Marx credits "a Manchester spinner"). Both in published and unpublished manuscripts, Marx examines variables affecting the rate and mass of surplus-value in detail.

Some Marxian economists argue that Marx thought the possibility of measuring surplus value depends on the publicly available data. We can develop statistical indicators of trends, without mistakenly conflating data with the real thing they represent, or postulating "perfect measurements or perfect data" in the empiricist manner.

Since early studies by Marxian economists like Eugen Varga, Charles Bettelheim, Joseph Gillmann, Edward Wolff and Shane Mage, there have been numerous attempts by Marxian economists to measure the trend in surplus-value statistically using national accounts data. The most convincing modern attempt is probably that of Anwar Shaikh and Ahmet Tonak.

Usually this type of research involves reworking the components of the official measures of gross output and capital outlays to approximate Marxian categories, in order to estimate empirically the trends in the ratios thought important in the Marxian explanation of capital accumulation and economic growth: the rate of surplus-value, the organic composition of capital, the rate of profit, the rate of increase in the capital stock, and the rate of reinvestment of realised surplus-value in production.

The Marxian mathematicians Emmanuel Farjoun and Moshé Machover argue that "even if the rate of surplus value has changed by 10–20% over a hundred years, the real problem [to explain] is why it has changed so little" (quoted from The Laws of Chaos: A Probabilistic Approach to Political Economy (1983), p. 192). The answer to that question must, in part, be sought in artifacts (statistical distortion effects) of data collection procedures. Mathematical extrapolations are ultimately based on the data available, but that data itself may be fragmentary and not the "complete picture".

Different conceptions

In neo-Marxist thought, Paul A. Baran for example substitutes the concept of "economic surplus" for Marx's surplus value. In a joint work, Paul Baran and Paul Sweezy define the economic surplus as "the difference between what a society produces and the costs of producing it" (Monopoly Capitalism, New York 1966, p. 9). Much depends here on how the costs are valued, and which costs are taken into account. Piero Sraffa also refers to a "physical surplus" with a similar meaning, calculated according to the relationship between prices of physical inputs and outputs.

In these theories, surplus product and surplus value are equated, while value and price are identical, but the distribution of the surplus tends to be separated theoretically from its production; whereas Marx insists that the distribution of wealth is governed by the social conditions in which it is produced, especially by property relations giving entitlement to products, incomes and assets (see also relations of production).

In Kapital Vol. 3, Marx insists strongly that:

...the specific economic form, in which unpaid surplus labour is pumped out of direct producers, determines the relationship of rulers and ruled, as it grows directly out of production itself and, in turn, reacts upon it as a determining element. Upon this, however, is founded the entire formation of the economic community which grows up out of the production relations themselves, thereby simultaneously its specific political form. It is always the direct relationship of the owners of the conditions of production to the direct producers – a relation always naturally corresponding to a definite stage of the methods of labour and thereby its social productivity – which reveals the innermost secret, the hidden basis of the entire social structure, and with it the political form of the relation of sovereignty and dependence, in short, the corresponding specific form of the state. This does not prevent the same economic basis – the same from the standpoint of its main conditions – due to innumerable different, empirical circumstances, natural environment, racial relations, external historical influence, etc. from showing infinite variations and gradations in appearance, which can be ascertained only by analysis of the empirically given circumstances.

This is a substantive – if abstract – thesis about the basic social relations involved in giving and getting, taking and receiving in human society, and their consequences for the way work and wealth is shared out. It suggests a starting point for an inquiry into the problem of social order and social change. But obviously it is only a starting point, not the whole story, which would include all the "variations and gradations".

Morality and power

A textbook-type example of an alternative interpretation to Marx's is provided by Lester Thurow. He argues: "In a capitalistic society, profits – and losses – hold center stage." But what, he asks, explains profits?

There are five reasons for profit, according to Thurow:

• Capitalists are willing to delay their own personal gratification, and profit is their reward.
• Some profits are a return to those who take risks.
• Some profits are a return to organizational ability, enterprise, and entrepreneurial energy
• Some profits are economic rents – a firm that has a monopoly in producing some product or service can set a price higher than would be set in a competitive market and, thus, earn higher than normal returns.
• Some profits are due to market imperfections – they arise when goods are traded above their competitive equilibrium price.

The problem here is that Thurow doesn't really provide an objective explanation of profits so much as a moral justification for profits, i.e. as a legitimate entitlement or claim, in return for the supply of capital.

He adds that "Attempts have been made to organize productive societies without the profit motive (...) [but] since the industrial revolution... there have been essentially no successful economies that have not taken advantage of the profit motive." The problem here is again a moral judgement, dependent on what you mean by success. Some societies using the profit motive were ruined; profit is no guarantee of success, although you can say that it has powerfully stimulated economic growth.

Thurow goes on to note that "When it comes to actually measuring profits, some difficult accounting issues arise." Why? Because after deduction of costs from gross income, "It is hard to say exactly how much must be reinvested to maintain the size of the capital stock". Ultimately, Thurow implies, the tax department is the arbiter of the profit volume, because it determines depreciation allowances and other costs which capitalists may annually deduct in calculating taxable gross income.

This is obviously a theory very different from Marx's. In Thurow's theory, the aim of business is to maintain the capital stock. In Marx's theory, competition, desire and market fluctuations create the striving and pressure to increase the capital stock; the whole aim of capitalist production is capital accumulation, i.e. business growth maximising net income. Marx argues there is no evidence that the profit accruing to capitalist owners is quantitatively connected to the "productive contribution" of the capital they own. In practice, within the capitalist firm, no standard procedure exists for measuring such a "productive contribution" and for distributing the residual income accordingly.

In Thurow's theory, profit is mainly just "something that happens" when costs are deducted from sales, or else a justly deserved income. For Marx, increasing profits is, at least in the longer term, the "bottom line" of business behaviour: the quest for obtaining extra surplus-value, and the incomes obtained from it, are what guides capitalist development (in modern language, "creating maximum shareholder value").

That quest, Marx notes, always involves a power relationship between different social classes and nations, inasmuch as attempts are made to force other people to pay for costs as much as possible, while maximising one's own entitlement or claims to income from economic activity. The clash of economic interests that invariably results, implies that the battle for surplus value will always involve an irreducible moral dimension; the whole process rests on complex system of negotiations, dealing and bargaining in which reasons for claims to wealth are asserted, usually within a legal framework and sometimes through wars. Underneath it all, Marx argues, was an exploitative relationship.

That was the main reason why, Marx argues, the real sources of surplus-value were shrouded or obscured by ideology, and why Marx thought that political economy merited a critique. Quite simply, economics proved unable to theorise capitalism as a social system, at least not without moral biases intruding in the very definition of its conceptual distinctions. Hence, even the most simple economic concepts were often riddled with contradictions. But market trade could function fine, even if the theory of markets was false; all that was required was an agreed and legally enforceable accounting system. On this point, Marx probably would have agreed with Austrian School economics – no knowledge of "markets in general" is required to participate in markets.