Full Competition and Innovation

Abstract

Economic science is built on the basis of the concept of competition. Classical School economists have not defined this concept with precision. The “Neoclassic Revolution” defined the concept of perfect competition as an ideal combination of productive resources accessible to all permanently (optimal size). Within this framework, competition ensures that suppliers will cover demand by matching market prices to both average and marginal costs corresponding to the optimal size. Large and persistent differences in profit and wage rates, when interpreted from a perfect competition perspective, will always be considered a sign of the absence of competition. Only an alternative concept of competition can modify such an interpretation. In this context, the objective of this work was to develop an alternative concept of full competition, which is formally formulated, to foster a more sustainable environment for the coexistence of enterprises of different sizes. The full competition definition assumes that firms maximize long-term benefits (fixed-capital amortization period) by trying to ensure full use of productive capacity and achieving relative advantages through innovation instead of merely adjusting prices to maximize short-term benefits. This approach provides a different explanation for inequalities in profit and wage rates, from simple adjustment in prices (perfect competition) to the search for new and better opportunities through innovation (full competition). This could change the meaning and scope of economic policies, which are influenced by both Neoclassical and Keynesian approaches, when addressing the entrepreneurial challenges of sustainable development.

1. Introduction

The concept of competition serves as a foundation upon which economic science is built. Although it seems that due to its level of abstraction, it moves away from economic reality and has no practical influence, it plays a decisive role in shaping contemporary economic policy.

The first economists of the Classical School considered competition a key concept in their vision, but they did not precisely define what they understood through it. Ultimately, the Neoclassical School provided the definition of “perfect competition”. As is well known, this concept implies that a competitive market where the profit rate is zero and consequently equal for all firms leads to an equal wage rate.

There is abundant empirical evidence dating back many years that refutes the expected outcomes of this conception of competition, confirming the persistence of positive and varied profit and wage rates. However, practical research has not been sufficient alone to displace a theoretical concept. Only a concept with the same level of abstraction can serve as a substitute for another. The task of conferring novelty to old concepts and authority to new concepts is not easy. Changes in language are inherent to the history of conceptual applications, making it difficult for concepts to evolve beyond their previous meaning. A new concept is not an isolated term, and to understand it, it is necessary to retire the previous theory that shapes the usual forms of expression and thought. That is why it is important to formulate competition, like its current concept, formally.

As long as the concept of perfect competition prevails, the aforementioned empirical results are usually interpreted as evidence of a lack of competition. Empirical analyses have increased in an effort to identify factors or variables that slow down trend towards homogeneous and zero profit rates and equal wage rates. Certainly, large differences in earnings and salary rates are often indicative of a lack of competition. However, the problem does not lie so much in the obstacles that prevent price adjustment, as the concept of perfect competition presupposes, but in the control over large market shares derived from institutional support and agreements that slow down or nullify the capacity for innovation, which is essentially the core of competition. The existence of different profit and salary rates, even within the same market, does not necessarily indicate an absence of competition if they reflect the varying competitive capacities of individual entrepreneurial efforts.

Among profuse economic literature, there are several examples of persistence in different profit rates, where Mueller’s works [1,2,3] stand out. Subsequently, many researchers have confirmed the persistence of inequality in profit rates, as follows: Ref. [4] for Europe; Refs. [5,6,7] for emerging markets; Refs. [8,9] for the United Kingdom; Ref. [10] for Japan; Ref. [11] for Japan and the United States; Refs. [12,13] for the United States and European Union food processing industries; Ref. [14] for Brazil; Ref. [15] for Turkey; Refs. [16,17] for Spain; Ref. [18] for Greek manufacturing; Ref. [19] for the Italian industry; Ref. [20] for the construction industry in the United Kingdom; Ref. [21] for the Italian banking sector; Refs. [22,23] for the Turkish banking system; Ref. [24] for European banks; Ref. [25] for the pharmaceutical industry in the United States; Ref. [26] for the Indian industry, and so on.

Something similar occurs with wage differences, although the relevant literature is more fragmented. Empirical analyses have focused on discrimination factors such as the type of contract, gender, race, and nationality. Particular attention has been given to the structure and effects of unionism and collective bargaining. Reference [27] reviews economic literature about this latter item. The author concluded that many indicators of institutional structure used in empirical research do not measure concepts stressed by theory. In any case, measures of bargaining coordination seem preferable to those of bargaining level.

Reference [28], in addition to reviewing various contributions to discrimination, argues that many experimental studies have confirmed hiring as the key factor in labor discrimination. Reference [29] observed how personal relations throughout the personal labor course alter individual progress through hierarchy shifting the wage distribution away from strict knowledge capacities of the population. This aligns with the importance of social skills [30], as the abilities of human interaction in workplaces to allow better adaptation and flexibility enhance productivity. Reference [31] focused on labor market concentration, asserting that hiring by firms is associated with a decline in labor share because wages are fixed below their marginal productivity. The lack of competition in the labor market, from both the business and workers’ sides, has become increasingly relevant [32,33,34,35,36,37,38,39,40,41,42].

Most empirical results are difficult to reconcile with theoretical concepts. Human capital theory [43], which is related to the Neoclassical competition concept, recognizes that there may be wage differences derived from the qualifications and experience of workers or some job characteristics, especially painful or dangerous characteristics, that justify a higher salary. Therefore, labor supply factors dominate current empirical research on wage determination. It has not been acknowledged that there are salary differences derived from demand factors associated with a worker’s company or establishment. It is assumed that if there is competition, all firms are of optimal size, and, as for business profit rates, wage rates (remuneration by investment in human capital) tend to equalize.

Nevertheless, Reference [44] demonstrated that intraindustry differences explain a large portion of wage variation. References [45,46] concluded that establishments that pay well for one occupation also pay well for all others. Reference [47] argues that wage differences are more strongly related to employers than to worker heterogeneity. References [48,49,50,51,52] report similar findings. Although these authors pointed out the predominance of demand factors, no new competition concept has been proposed. References [53,54] showed that establishments in the Spanish fertilizer and pesticide sector with the greatest benefit rates were also those with the highest wages. Reference [55] analyzed differentiating elements of wages, concluding that demand factors associated with establishments seem to have a greater influence than supply factors linked to workers’ characteristics, with their qualifications and experience standing out.

Only a few contributions suggest a different view of competition, although they do not fully define an alternative concept. Reference [56] employed a newly developed methodology allowing the persistence parameter to vary with time. Reference [57] proposes a trend-based model, an alternative to the standard first-order autoregression model, in profit persistence studies. Reference [58] argues for relative profitability because profits in capital-intensive industries depend on productive capacity utilization, which shifts across firms. This revision allows us to conclude that if the labor market cannot be understood independently from product markets, then the competition concept affects both product and labor markets.

Although economic literature acknowledges that labor demand depends on product market demands [59], definitions of labor market competitive equilibrium are usually not considered in the context of product market competition. Reference [60] examined this relation between product and labor markets, highlighting that “it is perfectly possible for wages to change if market power of all firms in an economy is increased, even if the labor market is perfectly competitive”.

The concept of perfect competition does not allow extrapolation of productivity differences between firms in a competitive market. Furthermore, wages cannot be adjusted to productivity, even if the labor market is competitive. Therefore, to consider the possibility of benefit and wage rates differences in competitive markets, it is necessary to reformulate the Neoclassical concept of competition. Nevertheless, as the Austrian School pointed out, there is no static equilibrium because the key to competition is innovation. Every company or agent must try to improve knowledge, which is always partial (no agent knows everything) and dispersed (many agents have valid knowledge). Contrary to perfect competition and its assumptions, the objective of this work was to develop an alternative concept of full competition, which was formally formulated to foster a more sustainable environment for the coexistence of enterprises of different sizes. Consequently, this paper proceeds as follows. First, the “full competition” concept is developed, including both product and labor market functioning. The next section presents a methodological exercise where profits are maximized from different cost functions under a demand–price function to compare “perfect” and “full” competition scenarios. The discussion section reviews the consequences for economic policies of starting from one concept of competition or another and highlights the importance of innovation for better functioning of economic competence and wellbeing as bases for sustainable development [61]. Finally, brief conclusions are presented.

2. Meaning and Scope of Competition Revised

Competition is the most commonly used word in practical economics and the fundamental concept upon which economic science is built. Classical economists have argued that competition is essential for economic progress. However, they have not defined exactly what they mean by competence. They believe that competition tends to equalize rates of profit and wages. Salary differences only reflect work difficulty and hazardousness, and wages therefore revolve around subsistence level. Under these assumptions, value theory was established. Classical economists also reject demand’s influence on product value, so competition is conceived as a behavior that depends not so much on having many buyers and sellers but on the lack of obstacles for any single initiative. This approach ensures that production continues to grow until a stationary state is reached and guarantees a fair distribution of value added among factors contributing to the production process.

The Neoclassical “revolution” transformed this value theory associated with production cost, positing that prices depend on both supply and demand. As [62] observed, Neoclassical thought refined the Classical concept of competition by defining it more precisely. The Neoclassical definition posits that there are numerous applicants (customers) and bidders (producers) to ensure that price aligns with average and marginal costs [63,64,65]. In conditions of perfect competition, it is assumed that demand reaches its maximum potential once prices are established. This implies that the demand curve that a producer faces is perfectly elastic. Thus, competition across all markets (Walrasian general equilibrium) ensures that the quantity supplied will always be purchased, affirming Say’s Law.

Say’s Law will be true even when there is monopolistic competition. In this case, demand is reduced because supply restrictions raise prices. A monopolist will decide to reduce supply for the price to increase instead of increasing the price to reduce demand. It is assumed that there is a short-term adjustment of prices. This is what allows the determination of prices in different restricted supply situations and is associated with game theory models of imperfect competition (Cournot joint profit maximization or Stackelberg, among others).

In Neoclassical economics, competition is conceived as static and timeless. As price adjustments are immediate, perfect competition implies that any short-term change in the combination of factors that leads to higher costs is inefficient, as fixed capital cannot be adjusted. The maximum benefit is obtained when price equalizes average and marginal costs, which is understood as null profit. Technology, which determines the combination of different factors and productive resources, is supposed to be unique, so technological change is an extraordinary phenomenon distinct from the competing forces acting in markets.

Fundamental criticism of this concept has come from the Austrian School [66,67,68,69]. They emphasized the role of innovation and the entrepreneur as an innovator [70,71,72]. Nevertheless, as Kirzner highlights, Schumpeter himself conceives innovation as an extraordinary phenomenon rather than as a common practice to compete. Other alternative approaches have been associated with the idea of “perfectly contestable markets” [73,74] and the concepts of monopolistic competition [75] or imperfect competition [76]. All these criticisms have not displaced the established concept of perfect competition, either because they are ultimately defined in relation to it or because they are not sufficiently precise to allow the formalization of a new concept.

An alternative definition of competition must assume that the benefit rate will be maximized over the long term (amortization period of fixed capital). To describe maximum competition, the term “full competition” is proposed instead of “perfect competition” because, as [3] points out, competition takes form not from lower prices for a given set of products but from new and more advantageous ideas.

In contrast to the assumption of perfect information and capital mobility in the concept of perfect competition, full competition assumes that knowledge and information are both partial and dispersed and that displacement between markets is limited, since capital mobility has costs. This means that companies with different production capacities and cost functions can coexist in the same market. As there are fixed costs, to maximize benefits in the long term, companies should try to ensure full utilization of their productive capacity. The most advanced companies, which can be assimilated to those of optimal size, do not seek to monopolize the market by lowering prices until it is equalized to their average and marginal costs. They exploit a competitive advantage by establishing their production capacity so that it never exceeds existing demand, at least during the fixed-capital amortization period, and trying to maintain or expand this advantage through innovation.

If firms with lower costs (optimal size) tried to maximize short-term profits by adjusting prices, they would monopolize the entire market, driving out other companies and restricting competition. However, to maximize long-term benefits, the most rational behavior is to try to ensure full utilization of their productive capacity. In doing so, they maintain their production at the minimum long-run average costs even if demand drops to its lowest level. When demand exceeds the minimum level, sales of less efficient companies, usually smaller ones, supply the difference. In such cases, prices increase, and optimal-size companies’ profit rates increase while their sales volume is maintained. Any change in demand means there are market entries and exits without companies of optimal size being negatively affected.

In this context, optimal-size companies adjust their supply (production capacity) after conducting market research to ensure it does not exceed the demand level at any time. It is assumed that the distribution of long-term sales probabilities fits a normal function with an average “a” and standard deviation “d”. The level of secure demand will be the average minus the standard deviation (a − d), which is called the sales minimum trend. Accordingly, there are two critical points: the minimum level mentioned and the average plus the standard deviation (a + d), which is referred to as the sales maximum trend. Both points represent sales quantities whose probability of varying below or above, respectively, is very low. The average “a” corresponds to the sales level with the highest probability.

Figure 1 illustrates the sales probabilistic function for the estimated fixed-capital amortization period (long term). The abscissa axes correspond to sales quantity (demand), “Q”. The ordinate axis shows the probability that each of these sales quantities will be reached, “Pr(Q)”. In a normal function, as already mentioned, the highest probability corresponds to the average level “a”. Symmetric inflection points correspond to the sales minimum trend (a − d) and the sales maximum trend (a + d), respectively. When sales changes (demand) are expected in the very long term, beyond the amortization period, companies will try to adapt their production capacity according to these expected changes. Normal distributions will move right or left depending on whether demand increases or decreases. Simultaneously, they will flatten or become more acute depending on the sales probability variation. The demand level and supply composition determine the market configuration.

Here, we compare different market configurations derived from “perfect competition”, which his based on short-term price adjustments, and from “full competition”, which is founded on innovation, starting from a company profit function:

πi = p ∗ qi − ci ∗ qi

(1)

where “π” is the net profit of firm “I”; “p” is the product price; “qi” is the quantity produced by the firm; and “ci” is the total cost per unit of output or the average total cost.

The inverse of the market demand function is p = α − βQ, where Q is the total market supply ${\sum }_{i=1}^n{q}_i$, α is a given parameter, and $\beta =-{\displaystyle \frac{\partial p}{\partial Q}}\beta$.

The condition of profit maximization is obtained by differentiating the above function and equating it to zero:

$${\displaystyle \frac{\partial \pi }{\partial q}}=p+q{\displaystyle \frac{\partial p}{\partial Q}}{\displaystyle \frac{\partial Q}{\partial q}}-c=0$$

(2)

With perfect competition, demand elasticity is infinite:

$$\beta =-{\displaystyle \frac{\partial p}{\partial Q}}\beta =0$$

(3)

Since p = α − βQ, the previous equation is adjusted as follows:

$$p-c=q\beta {\displaystyle \frac{\partial Q}{\partial q}}=0$$

(4)

Hence, p = c and profits are zero, so the market price equals the average and marginal costs, which means that companies are “price takers”, with no profits. Companies with costs above Cc (optimal companies with minimum costs) not using the latest (exogenous) technology accessible to anyone (perfect information) disappear from the market as the price falls to Pc (see Figure 2). All companies remaining are equal, have the same cost function, and earn a null profit. Companies lack any innovative initiative and act passively as price takers, adopting the technology offered equally to all. Innovation is only stimulated by restricted competition (absence of perfect competition), and, as various models of imperfect competition show, positive benefits can reward innovative effort.

In intermediate situations, everything depend on the proportion of firms acting as monopolists (joint profit maximization) or as followers (Cournot model). The Stackelberg model supposes that one company acts as a monopolist, while others act as followers. In this case, the incentive to innovate is lower than that in the Cournot model, but monopolists certainly have a greater incentive to innovate. In the dominant firm model, follower companies act in a market segment as if they were perfectly competitive, while dominant firms act as monopolists in the rest of the market [77,78,79]. Schumpeter pointed out that monopolists have an incentive to innovate until other companies imitate this innovation and perfect competition is reestablished.

When competition is assimilated with innovation, some assumptions traditionally supported by Austrian School acquire full meaning. As information and knowledge are partial and dispersed, there business skills are diverse. An entrepreneur is first and foremost an innovator, with technology as an endogenous factor. Therefore, there is not a single technology but a spectrum of costs and technological levels.

Companies do not expand supply indefinitely until an equilibrium price is reached. Demand elasticity is not infinite for each firm. The offering price depends not only on demand elasticity (the slope of the demand function) but also on demand fluctuations (shifts in the demand function) and the elasticity of the market supply function. Full competition allows positive benefits, and the profit rate can be different for each company. In this context, to maximize profits, they do not compete primarily on price but on innovation, and the production quantity is therefore set regardless of the other firms (under the Cournot assumption). Contrary to the assumptions of the Neoclassical model, companies are not all the same. Each one has different production functions.

When starting from the company profit function:

πi = p ∗ qi − ci ∗ qi

(5)

the profit maximization benefit function derived and equalized to zero is:

$${\displaystyle \frac{\partial \pi }{\partial q}}=P+q{\displaystyle \frac{\partial p}{\partial Q}}{\displaystyle \frac{\partial Q}{\partial q_i}}-c_i=0$$

(6)

The Cournot assumption implies that each firm expects that others will not change their production (null conjectural variations) in the following form:

$${\displaystyle \frac{\partial q_2}{\partial q_1}}={\displaystyle \frac{\partial q_3}{\partial q_1}}=\dots ={\displaystyle \frac{\partial q_n}{\partial q_1}}=0; \mathit{so} {\displaystyle \frac{\partial Q}{\partial q}}=1$$

(7)

Therefore, the price–cost margin of each company depends on the inverse of price demand elasticity:

$$P+q_1{\displaystyle \frac{\partial p}{\partial Q}}-c_1=0;P-c_1={-q}_1{\displaystyle \frac{\partial p}{\partial Q}}$$

(8)

For a given demand, higher elasticity means a lower price cost margin and vice versa. Market distribution depends on each company’s strategies to meet demand. The quantity produced by each company and its respective costs will vary. The market price depends on the cost of the least efficient company remaining in the market. Although a single market price is maintained, there could be different prices without affecting the full competition definition. With full competition, the market price depends on the total demand and tends to equalize the average cost of the last firm that remains in the market. Instead of exploiting short-term cost advantages over other companies (as in perfect competition) or reducing the amount offered to increase prices (monopolistic behavior that is restrictive of competition), companies try to maintain or improve their position in the market through productive process innovation.

The figure below (Figure 3) shows how demand fluctuations tend to affect less efficient companies. When demand remains at its highest level or near it (the probability average of the normal long-term sales function), price remains around Pb. This price coincides with the cost of the least competitive company covering demand. If demand falls, the price falls to Pa, adjusting to the marginal cost of the less competitive company remaining in the market. When demand increases, the price increases, allowing new firms to enter the market. Only in extreme circumstances, if demand reaches the minimum level of sales, can the price approach the production cost of the most efficient company, Cc (optimal size).

Competition does not prevent coexistence in the same market of companies with different technologies, costs, and benefits. What is relevant for competition is that there are no obstacles to innovation. This means that any firm that feels capable of competing can enter the market and have access to any productive resources. If market entry or access to any productive resources are restricted, there is no competition, or it has been limited.

Supply distribution and market price are quite different according to the perfect competition definition or the one proposed as an alternative. In this sense, it is useful to compare both concepts from a set of cost functions corresponding to different companies or establishments. Under the Neoclassical model, market concentration is greater, and all companies share a zero profit rate. The full competition model shows a lower market concentration for companies with different sizes, costs, and profit rates.

The Neoclassical conception, by identifying competition with simple price adjustments, maximizes short-term profits. However, competition is not produced exclusively through price but primarily through innovation. Price becomes the sole element of competition when technology is considered exogenous to entrepreneurship because it is generally assumed that technology is widely known and freely accessible for all. In this way, anyone can maximize short-term profits and immediately move out of business if profits are higher in other markets since there are no costs in capital mobility (the Walrasian general equilibrium).

Competition leads to continuous innovation to adapt to the changes in the needs and demands of customers. Instead of trying to capture the largest possible market share to maximize short-term profits, it seeks to maximize long-term profits, ensuring the full utilization of productive capacity and guaranteeing the lowest costs during all amortization periods. This explains why companies with different sizes and costs coexist in the same market with positive and different profit rates. Similarly, labor market competition makes it possible to see why workers with different salaries exist, not only because of their different characteristics, especially their qualifications and experience, but also because of the productivity differences in their respective firms.

Full competition does not exclude collaboration between companies to enhance their innovation capacity and improve competitiveness. Competition with respect to innovation changes the direction of not only industrial policies (regulations affecting different markets) but also macroeconomic policies. The way to introduce competition is not to deregulate and adopt automatic monetary policies as suggested by Friedman [80,81]. Market regulations and macroeconomic policies can foster competition and avoid a disconnection between the financial economy and the real economy.

Neoclassical theory admits that labor demand is a derived demand, which depends on markets for goods and services, although this relation is frequently ignored. “If the labor market is perfectly competitive, firms take wages as given and the capture of income obviously does not occur. Therefore, if wages are influenced by market power, then wage determination must be noncompetitive”. Nevertheless, “it is perfectly possible for wages to change if the market power of all companies in an economy increases, even if the labor market is perfectly competitive” [60].

Stating that wages are reduced because of increased unemployment implies that value-added increases obtained from greater market power do not transfer to wages. The threat of unemployment, when there is supply and excess work availability, allows this reduction. However, as Keynes suggests, this leads to a deflationary spiral, and demand and employment are increasingly reduced. The Keynesian solution is to encourage an increase in demand by raising nominal wages and stimulating public spending, even though this action does not address the essential issue of a lack of competition.

The concept of perfect competition prevents declaring that market power can imply an increase in productivity because it associates market power with a lack of competition [82]. Consequently, it rejects the idea that wages can be equalized to productivity in a competitive labor market [83]. Therefore, income capture by employees is only possible when the labor market is not competitive. Several publications in recent years on competition have a fundamentally empirical nature, confirming the fulfillment of outcomes expected from competition as defined by the concept of perfect competition. All studies corroborate the persistence of positive and varying profit rates across all sectors and regions, as well as wage inequality that cannot be explained by differences in workers’ qualifications and experience [84,85,86,87,88,89,90].

The perspective of full competition assumes that workers share rents derived from a lack of competition in product markets. Since value added per worker increases due to higher prices, labor market competition implies that wages equalize apparent marginal productivity. Thus, if productivity is higher in a company, either because it benefits from a lack of competition or because it is more competitive, labor market competition will equalize wages to productivity. In this way, unemployment and wage differences observed not only across different markets but also between companies within the same market are better explained.

Keynes, like the Neoclassical School, asserted that an increase in employment tends to reduce productivity, stating that “…any means of increasing employment must lead at the same time to a diminution of the marginal product and, hence of the rate of wages measured in terms of this product” [91] (p. 18). However, Keynes departs from Neoclassical thought considering that it holds that market adjustments do not lead automatically to full employment. He considers that full employment is achieved more efficiently by lowering real wages, encouraging effective demand, and increasing prices rather than trying to reduce nominal wages.

Under the perfect competition concept, it is not possible to realize simultaneous increases in employment and real wages because all companies would need to achieve an optimal size. Competition prevents either incumbents or new start-ups from improving productivity. As Schumpeter stated, innovation can occur only in an extraordinary way, generating a comparative advantage until all companies adopt the new technologies. In contrast, the full competition concept considers innovation to be a common phenomenon since it is in fact the way to compete. Innovation requires knowledge, but this does not necessarily imply a high scientific character, nor should innovation always be understood as a radical change. Reference [92] emphasized that innovation does not refer exclusively or principally to major technological and organizational changes since small improvements often allow even greater increases in productivity than changes in basic methods.

In summary, the concept of perfect competition holds that unemployment is due to a lack of competition in the labor market. When this situation extends to all product markets, rent capture can occur with a competitive labor market. Then, workers will receive benefits from part of the extra income derived from the market power, but more can be obtained from the restriction of competition rather than from being a more competitive company.

The full competition concept confirms differences in wage and profit rates, allowing companies with different levels of costs and productivity to coexist even in the same product market. Wage differences are not exclusively derived from the labor supply side; they are also due to demand. Wages adjust to productivity within a competitive labor market, regardless of what happens in product markets. Therefore, unemployment can be the result of both restrictions on competition in product markets that reduce the demand for labor and a lack of competition in the labor market that generates a mismatch between wages and productivity. In sum, the full competition perspective allows differences in wage and profit rates to be adjusted to the productivity of every firm because, as [93] (pp. 91–92) stated, it is impossible to distribute the added value of a product among the different productive factors according to an automatic principle.

3. A Methodological Exercise: Empirical Results

Under the definitions of perfect and full competition, we constructed an exercise to analyze how a market is structured according to each framework. Given the production cost functions and the demand–price function, the total quantity produced and the resulting market price were calculated, as well as the distribution of the product supply among the different companies or establishments. Accordingly, it was initially assumed that there was an arbitrary number of establishments of different sizes (

Table 1. Minimum average cost.

Establishment	Total Cost Function	Average Cost	Minimun Average Cost
421	$C\left(q_i\right)=8+18q_i+{\displaystyle \frac{q_i^2}{2}}$	${\displaystyle \frac{C\left(q_i\right)}{q_i}}={\displaystyle \frac{8}{q_i}}+18+{\displaystyle \frac{q_i}{2}}$	$\partial {\displaystyle \frac{C\left(q_i\right)}{q_i}}=-{\displaystyle \frac{8}{q_i^2}}+{\displaystyle \frac{1}{2}};q2=16;q=4. Average cost 22$
215	$C\left(q_i\right)=100+2q_i+q_i^2$	${\displaystyle \frac{C\left(q_i\right)}{q_i}}={\displaystyle \frac{100}{q_i}}+2+q_i$	$\partial {\displaystyle \frac{C\left(q_i\right)}{q_i}}=-{\displaystyle \frac{100}{q_i^2}}+1;q2=16;q=4. Average cost 22$
180	$C\left(q_i\right)=100+1.5q_i+q_i^2$	${\displaystyle \frac{C\left(q_i\right)}{q_i}}={\displaystyle \frac{100}{q_i}}+1.5+q_i$	$\partial {\displaystyle \frac{C\left(q_i\right)}{q_i}}=-{\displaystyle \frac{100}{q_i^2}}+1;q2=100;q=10. Average cost 21.5$
163	$C\left(q_i\right)=50+3q_i+{\displaystyle \frac{q_i^2}{2}}$	${\displaystyle \frac{C\left(q_i\right)}{q_i}}={\displaystyle \frac{50}{q_i}}+3+{\displaystyle \frac{q_i}{2}}$	$\partial {\displaystyle \frac{C\left(q_i\right)}{q_i}}=-{\displaystyle \frac{50}{q_i^2}}+{\displaystyle \frac{1}{2}};q2=100;q=10. Average cost 13$
15	$C\left(q_i\right)=100+q_i+{\displaystyle \frac{q_i^2}{400}}$	$C\left(q_i\right)={\displaystyle \frac{100}{q_i}}+1+{\displaystyle \frac{q_i^2}{400}}$	$\partial {\displaystyle \frac{C\left(q_i\right)}{q_i}}=-{\displaystyle \frac{100}{q_i^2}}+{\displaystyle \frac{1}{400}};q2=\mathrm{40,000};q=200. Average cost 2$

, column 1) at each time (t) with different cost functions (column 2) in response to a hypothetical market aggregate demand function of P = 12,880 − 2Q.

Then, the average cost for each group of establishments was calculated by dividing the total cost by the quantity produced (column 3). Subsequently, by deriving and setting the equation to zero, the minimum average cost for each group was obtained (column 4).

Under perfect competition, the price equals the marginal and average costs, and all establishments reach the optimal size with the lowest average cost. Therefore, all companies will produce 200 units.

If the market aggregate demand function is P = 12,880 − 2Q and Cma = 2, then Q = 12,878/2 = 6439. Then, the number of optimal establishments will be 6439/200 = 32.2. This means that each of these 32.2 establishments will produce 200 units at a price of 2. As technology is given, it is an exogenous factor equally accessible to all. Consequently, given a certain function of market demand, price determines the quantity demanded. As companies are price takers, the elasticity of demand for each company is infinite.

Under full competition, the optimal size corresponds to the cost function of the most efficient company, which produces 200 units. However, in this scenario, the most efficient companies do not monopolize the market by lowering the price until it is equal to the minimum average cost, which corresponds to the marginal cost. To maximize long-term benefits, companies aim to ensure full utilization of their production capacity. Then, they adjust their production to the sales level at which the probability of falling below their productive capacity is very small during the fixed-capital amortization period.

During this period, we assume that the probability function of expected sales is adjusted to a normal function, which reaches its maximum with sales of 6250 units, corresponding to the average (a). If the function’s standard deviation (d) is 3250, the most efficient companies will establish their productive capacity according to the expected level of sales with a very low probability of being smaller. This level corresponds to a normal function average less its standard deviation (sales minimum trend), 3000 units in this case, because a − d = 6250 − 3250. Then, there will be 15 optimal-size establishments (3000/200 = 15) whose optimal production level is 200 and sales minimum trend is 3000.

Other establishments will cover the remaining demand when the minimum is exceeded. Logically, this happens during most of the period considered. As sales exceed the minimum, the probability increases until the probability function average is reached. Then, the sales probability decreases until the sales maximum trend (the average plus standard deviation of the sales probability function) is reached, which was 9500 units (6250 + 3250) in our exercise.

As optimal-size establishments only cover 3000 units, others of suboptimal sizes cover the remaining demand. In this case, 163 establishments with a minimum efficient size of 10 an and average cost of 13 will add 1630 units, while 180 establishments with a minimum efficient size of 10 and an average cost of 21.5 will add 1800 units. This satisfies the total demand of 6430 units. The price for this demand level is 21.5, which is equivalent to the average and marginal costs of the last establishments covering market demand. Given demand–price function P = 12,880 − 2Q, market production (Q) exactly aligns with our example of 6430 units. Thus, market supply must adapt to fluctuations in demand and price as the result of the demand level and the market marginal cost, which depends on the last establishments covering the demand. As we can be see, competition does not act primarily through price adjustments but through innovation. This is how companies try to safeguard their relative advantage. Innovation, as Kirzner highlights against what Schumpeter supposes, is not an extraordinary phenomenon. Innovation at different degrees occurs continuously when competition really exists. Continuous innovation and demand fluctuations cause most markets to have frequent company entries and exits.

We can extend the previous example to examine what happens if, five years later, the cost functions of companies are modified, with some establishments remaining and others being new entrants. The cost functions, the average cost, the minimum average cost, and their sets of equations assuming that the sales probability function remains unchanged are presented in

Table 2. Minimum average cost five years later.

Establishment	Total Cost Function	Average Cost	Minimun Average Cost
421	$C\left(q_i\right)=48+q_i+1+{\displaystyle \frac{q_i^2}{300}}$	${\displaystyle \frac{C\left(q_i\right)}{q_i}}={\displaystyle \frac{48}{q_i}}+1+{\displaystyle \frac{q_i}{300}}$	$\partial {\displaystyle \frac{C\left(q_i\right)}{q_i}}=-{\displaystyle \frac{48}{q_i^2}}+{\displaystyle \frac{1}{300}}=0;q2=\mathrm{14,400};q=120. Average cost 1.8$
215	$C\left(q_i\right)=50+3q_i+1+{\displaystyle \frac{q_i^2}{2}}$	${\displaystyle \frac{C\left(q_i\right)}{q_i}}={\displaystyle \frac{50}{q_i}}+3+{\displaystyle \frac{q_i}{2}}$	$\partial {\displaystyle \frac{C\left(q_i\right)}{q_i}}=-{\displaystyle \frac{50}{q_i^2}}+{\displaystyle \frac{1}{2}}=0;q2=100;q=10. Average cost 13$
180	$C\left(q_i\right)=64+{2q}_i+q_i^2$	${\displaystyle \frac{C\left(q_i\right)}{q_i}}={\displaystyle \frac{64}{q_i}}+2+q_i$	$\partial {\displaystyle \frac{C\left(q_i\right)}{q_i}}=-{\displaystyle \frac{64}{q_i^2}}+1=0;q2=64;q=8. Average cost 18$
163	$C\left(q_i\right)=100+{1.5q}_i+q_i^2$	${\displaystyle \frac{C\left(q_i\right)}{q_i}}={\displaystyle \frac{100}{q_i}}+1.5+q_i$	$\partial {\displaystyle \frac{C\left(q_i\right)}{q_i}}=-{\displaystyle \frac{100}{q_i^2}}+1=0;q2=100;q=10. Average cost 21.5$
15	$C\left(q_i\right)=100+{2q}_i+q_i^2$	${\displaystyle \frac{C\left(q_i\right)}{q_i}}={\displaystyle \frac{100}{q_i}}+2+q_i$	$\partial {\displaystyle \frac{C\left(q_i\right)}{q_i}}=-{\displaystyle \frac{100}{q_i^2}}+1=0;q2=100;q=10. Average cost 22$

.

Under perfect competition, the price equals the average and marginal costs, and all establishments are of optimal size at the lowest average cost. If the demand function remains as P = 12,880 − 2Q and Cma = 1.8, then 2Q = 12,880 − 1.8 and Q = 12,880/2 = 6439. Then, the number of optimal establishments will be 53.7 (6439/120). This means that each of these 53.7 establishments will produce 120 units at a price of 1.8.

According to the full competition definition, optimal-size establishments will cover only the sales minimum trend. If we suppose the same parameters as those in the previous situation, that is, 3000 units (6250 − 3250), at the new optimal size of 120, there will be 25 establishments meeting that condition (3000/120 = 25). The remaining demand is covered by establishments with higher average costs, including 60 establishments with a size of 10 and an average cost of 13 supplying 600 units, 75 establishments with a size of 8 and an average cost of 18 covering another 600 units, 90 establishments with a size of 10 and an average cost of 21.5 producing 900 additional units, and 133 establishments with a size of 10 and an average cost of 22 covering 1330 more units, thus fulfilling the total quantity demand of 6430 units. Therefore, the price will be the marginal cost of the last establishments meeting the demand, which is equal to 22.

If the demand grows, even more new establishments with higher average costs will enter and push up the price. If the demand falls to 3000 units, the price could drop to the average cost of the most efficient companies, which is 1.8 in this example. However, it is more likely to stay slightly below 13. Since the price is forced out of the market, all existing companies will not achieve the optimal level at that price. Companies with optimal cost functions will reduce their profit rates at that time, but profit rates will remain positive and increase again when the demand recovers. This enables them to maximize long-term benefits.

When optimal-size companies choose to reduce prices to try to dominate the market, they can maximize benefits in the short term. However, long-term benefits will be lower, and they may even incur losses if they have not amortized their fixed capital. Setting production capacity to the maximum level of sales expected or higher will force establishments to close or reduce productive capacity use proportionately to the sales decrease. During the amortization period, there will be many times when sales are below their productive capacity level. Underutilization of production capacity implies cost increases, even above those of other companies that can provide supply at such sales levels at lower costs.

Perfect competition, since it assumes that all firms can achieve maximum productivity and compete exclusively through short-term price adjustments, implies a greater market concentration, as shown by the results of the exercises proposed above. To measure the concentration level, the Hirschman–Herfindahl index (H) was calculated [94], with H being the weighted sum of squared market shares:

$${\sum }_{i=1}^n{({\displaystyle \frac{q_i}{q}})}^2={\sum }_{i=1}^n{s}_i^2$$

The first exercise proposed shows H values of 0.030863 under perfect competition and 0.014512 under full competition, while in the second exercise, the H values are 0.018749 and 0.009508, respectively. Since the concentration is lower when H is closer to zero, it is evident that the market is much more concentrated under the perfect competition assumption. This apparent paradox is easily explained because perfect competition implies that all firms that do not reach an optimal size disappear. However, under the full competition assumption, in addition to optimal-size companies, others with different sizes and levels of productivity, especially the small ones, can coexist normally.

In the business world, information and knowledge are not imperfect but partial and dispersed, as the Austrian School emphasizes. Industrial and labor policies could try to improve the overall market by raising the bottom tier, which is generally made up of small- and medium-sized enterprises.

4. Discussing Economic Policies and Enterprise Performances

Full competition implies innovation instead of short-term price adjustments, which alters the meaning of industrial policies. Thus, the primary objective of competition policy should be to promote innovation. Markets do not truly become competitive simply by eliminating certain rules to allow companies to engage in price wars to reduce costs. True competition requires the removal of all obstacles to market access and the fostering of environments that facilitate innovation.

Perfect competition presents a linear view of the innovation process, portraying it as exogenous to market forces. According to this perspective, the key lies in scientific research, both basic and applied, which then leads to the development of new products or technologies and ultimately to marketable goods. This process culminates with technological dissemination and assimilation, with scientific researchers as the main protagonists.

In contrast, the full competition view of the innovation process acknowledges the importance of various environments related to innovation and technological changes, as well as their interaction. At the core of this innovation process under full competition is the business environment, which acts as the principal protagonist (see Figure 4). Innovation is the way to maximize profits in the long run (amortization period of fixed capital), and the business environment helps drive the competition process. Technological innovation is considered endogenous to market forces. In this model, businessmen are not passive agents, as assumed under perfect competition, but active entrepreneurial agents.

Full competition policies favoring innovation contribute not only to fostering continues entrepreneurial development but also to promoting their reputation and social responsibility to meet the several demands for goods and services from society with innovative solutions. Innovation is a key element in creating and distributing value, as well as creating competitive advantages for enterprises of all sizes that prioritize sustainable wellbeing [95].

Promoting competition is linked to educational policy and research but also requires a financial, governance, and social environment conducive to innovation. Competition needs operational rules and specific regulation for every market. If some of those environments fail, competition will vanish or be greatly reduced. The consequences are greater in concentrated markets, with worse results in terms of income and employment and a tendency to increase inequality.

Industrial policies must induce market improvement, facilitating, above all, the enhancement of smaller or less productive companies. Uncompetitive markets are often dominated by a small number of oversized companies. Nevertheless, a lack of competition sometimes allows smaller and more inefficient companies to survive. One of the difficulties in implementing industrial policies lies in distinguishing whether differences in profit or wage rates are a consequence of a competitive situation. In the first case, these differences respond to different entrepreneurial capabilities. In the second, they are a consequence of competition restrictions that discriminate between companies. Industrial policy should focus especially on small and medium enterprises, which constitute the foundations of any economy. Regardless of smaller companies’ relative weight, their role in most markets is crucial because they establish the market marginal cost and therefore the price at which products tend to sell. In addition, they cover tasks and market niches that larger companies generally do not reach.

As small and medium enterprises often have more difficulty interacting with each other and with external environments, industrial policy should stimulate and facilitate inter-company cooperation and their relations with educational–scientific, institutional, financial, and social environments. Industrial policy cannot be only or primarily a policy of competition defense but should also mainly consider its promotion [96]. The development of educational and research policies, financing for business investment projects, and regulations to expedite procedures and provide legal certainty to businesses are crucial.

Increasing production integration on a global scale makes it necessary to establish regulations at different levels and areas to avoid an excessive market concentration that limits competition. However, above production costs and even capital and technology management, information flows and knowledge capacity to process them are the keys to competition. Global value chains imply that each one contributes what they know best. Specialization is essential, but it requires a previous set of knowledge and non-specialized ideas acquired through the development of intellectual faculties and social skills. Premature and extreme specialization carries risks of losing skills and knowledge diversity, neglecting basic knowledge, and reducing skills required for good social and productive performance. Reading, writing, numerical calculation, resolution of problems associated with learning, and thinking creatively, together with computer management and communication skills, are indispensable [97].

Innovation cultures usually have territorial projections. Although markets have a global dimension, they appear geographically segmented. Skills and knowledge differ around the world, and it is beneficial for all to try to take advantage of these. The main problem arises when merely defensive positions are adopted with restrictive practices of competition, which are often associated with administrative corruption.

Technology imports are certainly essential and beneficial. However, they become an easy but expensive resource when there is no parallel capacity for their own innovation. Without competitive institutions to diffuse new methods and to guide adaptation to change, imported technology will always be a costly mistake [62] (p. 280).

The convergence of different competitive environments is vital to achieving an innovation culture. Territories become compromised by closing in on themselves through protectionist practices. Territories that take advantage of their own resources and knowledge enforce them competitively, making their own innovation efforts while opening themselves to external influences. Competition understood as innovation is not exclusionary and does not cause zero- or negative-sum practices but generates integration and mutual gains.

In addition, when product markets are noncompetitive, collective bargaining in the best case only works for a more equitable value-added distribution to avoid conflicts that endanger market dominance. In these situations, it is difficult to maintain labor market competition. Dominant companies in non-competitive markets make their interests prevail in negotiations over the collective objectives of their respective employers and workers’ organizations. Corporatism contributes to sustaining and increasing the lack of competition rather than increasing it

Furthermore, a lack of competition in product markets generates unemployment, even if there is competition in the labor market. Therefore, it is essential to clarify whether the lack of competition comes from product markets, the labor market, or both. If the extent to which it is due to labor or product markets is not examined, there is a risk of establishing policies that worsen the problem instead of contributing to solving it. When the origin is related to product markets, wage moderation policies generate a regressive spiral, productivity tends to decline, and, in the long run, unemployment grows despite a reduction in labor costs. When the origin of unemployment is mainly related to the labor market, it is necessary to determine whether the organizational structure of employers and unions is generating imbalances that reduce competition or labor legislation is distorting the labor market instead of helping to make it more efficient.

Active policies in labor and products markets are required beyond simple competition defense. Better regulation of markets must stimulate productivity, especially for small- and medium-sized enterprises, which is typically set as each market is being configured, cooperation between companies increases, and collective bargaining moves forward. The role of the state is to protect compliance with rules established in this regard, suggest corrections, and establish measures to improve innovation in different environments.

When there is competition, it is common for there to be different earnings and wages between companies, even in the same market. Therefore, profit and wage rate inequalities cannot be interpreted by themselves as being related to a lack of competition. It will be necessary to verify whether these inequalities respond to different capacities and business efforts or are the result of anticompetitive practices. Relevant indicators will be increasing market concentration and inflation or price reductions associated with losses in product quality and job downgrading. Each market has its own rules, and it is necessary to examine market structure and its evolution to interpret whether this market regulation is met or not. The “rule of reason” formulated by Judge Brandeis makes more sense, stating “the true test of legality is whether the restraint imposed is such as merely regulates and perhaps thereby promotes competition or whether it is such as may suppress or even destroy competition” [98].

Regulation must always be revised and enhanced, but the absence of regulation inevitably implies imposition of the law of the strongest and consequently leads to the abolition of competition. Frequently, a monopoly or an oligopoly refers not only to large companies but also to small unproductive companies that control some local markets with the complicity of public institutions.

Although concentration on an aggregate scale may not always indicate the presence of less competition, it is clear that market concentration has increased, especially in the most advanced economies. Perhaps this explains why aggregate productivity tends to decline [51,99,100], as its improvement affects an increasingly small fraction of companies. There is a slowdown in productive investment despite lower financing costs and higher profit expectations from some large companies. The undervaluation of intangible capital and a decrease in equipment goods prices makes financial assets grow faster than productive ones, with an increasing demand for safe assets while high-risk financial markets emerge. At the aggregate level, productivity stagnation is usually accompanied by higher profits associated with a decline in the share of wage income in the value added [101].

One of the main problems of the environmental crisis and sustainability growth is the absence of limits, as the Club of Rome’s model put forward half a century ago [102]. The concept of perfect competition presupposes the existence of a static equilibrium as a result of simple price adjustment where there is no limit. Any limit to growth is thus ruled out [103,104]. The concept of “full competition” assumes that companies have differentiated characteristics that limit their competitive capacity. Thus, competition requires regulatory elements that modulate price adjustments and consider diversity as a value, which enables equal opportunities since those who compete have different capacities and costs. This contrasting logic of perfect competition considers unlimited growth that tends to eliminate diversity because all companies must be homogeneous, adopting an intended ideal optimal size.

Production process integration on a global scale continues to advance. Although it is not linear progression, outsourcing and offshoring practices are more and more common, raising the profile of global value chains [105]. When these practices seek to improve product quality, competition is enhanced. However, when the aim is simply to reduce costs to gain market share and increase short-term profits, competition slows down. In those cases, innovation decreases, concentration increases, and product quality often deteriorates. This occurs when dominant companies improve their apparent productivity by reducing costs by subcontracting certain tasks. This allows greater value added per unit invested, reducing the workforce and capital investment. The search for higher short-term profits leads to a higher market concentration, which can only be maintained in the longer term with restrictive competition practices. Nevertheless, outsourcing and relocating may contribute to innovation and product quality improvement through identification of more advanced technology and knowledge. In that case, competitive advantages can be achieved by ensuring the quality of suppliers and distributors instead of trying to cut costs and monopolize sales.

In this context, a sustainable competitive advantage arises, creating differentiation through a unique value proposition, e.g., promotion of local value creation for small producers; targeted market segmentation and a customer focus with more diversified offers and higher-quality products (certifications) with prices in line with their characteristics; continuous innovation and adaptability through sustainable designs and clean technologies and effective resource allocation; and operational efficiency to maximize productivity capacity and minimizes waste. Therefore, full competition contributes to sustainability as a process favoring innovation.

5. Conclusions

The conception of what is understood by competition has practical consequences for the determination of economic policy, especially industrial and labor policies, the behavior of companies, and the definition of business strategies. The perfect competition concept assumes short-term price adjustment enables competition. Consequently, any differences in profits and wage rates are interpreted as indicators of a lack of competition. Therefore, unemployment is a consequence of rigidities in the labor market, which prevents labor costs from being adjusted downwards until full employment is reached.

Although Keynes rejects the Neoclassical vision and proposes to stimulate effective demand to reach full employment, he does not question the perfect competition concept. Both approaches ignore limits of expansionist (Keynesian) and price adjustment (Neoclassical) policies. Keynesian policies tend towards overproduction with inflation, and Neoclassical policies tend towards deflation with underproduction.

If competition is conceived like short-term price adjustment, economic policies are limited, in the best cases, to accommodative measures attempting to adjust wages towards productivity instead of improving the latter. The Neoclassical vision promotes policies to contain public spending accompanied by cuts in labor costs to passively adjust them towards productivity. The Keynesian vision aims to make the same adjustment but in the opposite way of expanding public spending and allowing nominal wage increases to increase effective demand and employment, with inflation helping to accommodate real wages favoring productivity.

The full competition perspective allows a more integrated vision, which requires examining each market and each specific circumstance with solid theoretical knowledge. Competition is understood as a process of continuous innovation that aims to exploit different business capacities to obtain comparative advantages to maximize long-term benefits and requires a long-term period of fixed-capital amortization for a company. Different profit and wage rates are compatible with full competition and associated opportunities for the development of entrepreneurial skills and social wellbeing.

Unemployment situations can be a consequence of both a lack of competition in product markets, which restricts the demand for labor, and imbalances in the labor market that slow down job creation or tend to make employment more precarious. Instead of policies exclusively focused on the labor market and the management of public and private spending, it is necessary to promote measures to introduce competition in product markets and rationalize public spending. This, in turn, will result in positives changes in the distribution of income, private consumption patterns, and social wellbeing improvements.

To promote full competition policies, it is necessary to analyze whether a lack of competition lies principally in the products markets or in the labor market. The bell-shaped concentration in numerous product markets not only contributes to limiting the demand for labor but also leads to an imbalance in the labor market, resulting in wages falling below productivity and slowing the growth of the latter. Industrial policy must promote innovation by improving the functioning of the environments surrounding business activity and facilitating access to them, especially for small companies and new entrepreneurs who have greater difficulties in doing so. Labor policy must, above all, promote a better articulated collective bargaining process with content focused on the organization of work and the establishment of working conditions that help to improve productivity and sustainable performance of the workforce.

In sum, while the concept of perfect competition implies a short-term perspective that denies the meaning of any regulation, the concept of full competition introduces a long-term vision that requires regulation that guarantees equal opportunities for all competitors, whether incumbents or potential competitors. Thus, the establishment of environmental and quality standards in production not only does not contradict the meaning and scope of competition but is also a requirement of it for a sustainable perspective.

The concept of full competition as an alternative to that of perfect competition has many analytical consequences that must be developed. Nevertheless, as Keynes pointed out, the difficulty of assimilating it lies more in moving away from old ideas than in understanding new ones. Keynes adds that ideas often have as much or more influence than interests, but frequently, interests also prevent us from appreciating new ideas.