Entrepreneurial activity and technological progress: a mathematical model.

Lewer, Joshua J.

ABSTRACT

The purpose of this paper is to examine one of the many channels of endogenous technological progress. Technology growth is usually the result of intentional and costly effort, and a significant amount of new innovation is driven by entrepreneurs who seek to introduce new products and new methods in order to earn profit. In this article, a mathematical model based on Schumpeterian theory and entrepreneurial activities is developed and examined.

INTRODUCTION

Most economic models assume that technological progress is an externality to some other form of economic activity such as investment or production. These models are convenient in that they generate permanent economic growth while maintaining an environment of perfect competition. They clash with the observed behavior of many entrepreneurs, however. Innovation and the application of new ideas are usually the result of intentional and costly effort. As (Schmookler's, 1966) classic study of innovation in several U.S. industries found that, invariably, inventions and discoveries were the result of profit-seeking behavior rather than independent intellectual inquiry. More recent research has confirmed Smookler's findings; see for example, (OECD, 1997; Thompson, 2001; and The World Bank, 2002).

Once it becomes accepted that innovation is not costless, the standard neo-classical perfect competition model must be modified to accurately depict the models of economic growth. Research, experimentation, analysis, planning, designing production equipment, and all the other activities related to the creation and application of new ideas that must somehow be paid for. When innovation has direct costs, technological progress becomes more like an investment that requires up-front costs in order to achieve expected future gains. Models that describe the process of innovation must therefore identify the incentives that induce people to incur the up-front costs of innovation. This makes models that assume perfect competition particularly awkward; when the costs of production exactly add up to the competitive price of a good, there is nothing left over to cover the up-front costs of research and development activities.

The most popular models of technological progress assume that innovation is driven by entrepreneurs who seek to introduce new products and new methods in order to earn a profit. These models drop the usual assumption of perfect competition and instead assume that innovators gain market power that permits them to charge prices above their marginal production costs. These types of models of innovation under imperfect competition are often referred to as Schumpeterian models, in honor of the twentieth century economist Joseph Schumpeter.

The purpose of this article is to develop a simple yet informative model of technological progress based on Schumpeterian theory and the natural activities of the entrepreneur. This article is organized as follows: section II presents a brief review of Schumpter's creative destruction hypothesis, section III discusses the importance of entrepreneurial activity in the creative destruction process, section IV develops the foundations and assumptions of the technology model, section V presents the mathematical model, and section VI draws conclusions and offers some remaining research questions on the topic.

SCHUMPETER'S CREATIVE DESTRUCTION HYPOTHESIS

In the early twentieth century, most mainstream economists focused on economic efficiency and resource allocation, but Joseph Schumpeter (Schumpeter ,1912; Schumpeter, 1934) stood out with his alternative viewpoints and his "anti-neoclassical" view of economic growth. Schumpeter has been classified as a radical economist for his description of the capitalist system as a dynamic system that continually generates change and technological progress. He viewed the capitalist system as one that does not reach a stable equilibrium; rather he saw it as an evolutionary process that never reverts to a stationary equilibrium. Schumpeter saw an ever-changing economy in which each innovation sets in motion activities that cause further innovations. Schumpeter's model was a truly dynamic one in that he described an equilibrium path that the economy follows over time, not the stable equilibrium described by the familiar supply and demand models that were in vogue when Schumpeter first described his concept of creative destruction early in the twentieth century.

Schumpeter described the capitalist economy as a "perennial gale of creative destruction" in which each firm sought to gain an advantage in the marketplace through innovation. He complained that "the problem that is usually being visualized is how capitalism administers existing structures, whereas the relevant problem is how it creates and destroys them" (1934, page 84). Each innovation, such as a more attractive design, a lowering of production costs, a new product, a new source of supply of inputs or raw materials, or improved management methods was pursued because it held the possibility of generating higher profit for the innovating firm. Such creative activity also destroyed the monopoly power that its competitors had gained by means of their earlier innovations.

Each innovator's gain is, therefore, only temporary because the creative innovation of its competitors will, sooner or later, destroy its hard-earned market power. This continual creation and destruction prevents permanent monopolies from developing, and in the process, society enjoys continuous technological progress. Creative destruction was, according to Schumpeter, the source of economic growth and the enormous increases in living standards that the world was experiencing in the early 1900s (Lewer and Van den Berg, 2004).

Schumpeter's idea of competition did not revolve around price competition; rather it was technological competition. Competition to develop new products and production processes served to create the temporary monopoly profits necessary to cover the up-front costs of innovation, but these profits would eventually be eliminated by the "creative destruction" of competing innovators. Everyone in society benefited from the technological progress; in fact, the power of compounding over time ensured that competition through innovation would raise human welfare much more than the traditional form of price competition within a perfectly competitive environment could ever do.

THE ROLE OF THE ENTREPRENEUR

Central to Schumpeter's process of creative destruction is the entrepreneur, the person who initiates the process of innovation. The entrepreneur is the one who recognizes and grasps the opportunities for introducing a new product, changing a firm's management organization, exploiting a new market, finding a new source of raw materials, cutting the costs of production, or motivating the labor force. Entrepreneurs are often more managers than inventors. They are the ones who see the economic potential of inventions. They need not themselves be the owners of the venture; they may simply manage for those who provide the funds for the enterprise. But they have the ideas, the ambition, and the organizational skills to bring projects to fruition (Lewer and Van den Berg, 2004). Schumpeter attached great importance to the social climate within which the entrepreneur had to operate. If the rate of technological progress of an economy depends on how aggressively entrepreneurs innovate, the incentives and barriers they face are critical to the process of economic growth. Among the critical institutions are society's attitude toward business success, the prestige of business activity, how well the education system prepared potential entrepreneurs, and how much freedom "mavericks" have to pursue their ambitions. Schumpeter referred to entrepreneurs as "social deviants" who act counter to the wishes of vested interests and often clash with tradition. The need for the entrepreneur to break with tradition can explain the apparent lack of entrepreneurs in some societies. Schumpeter pointed out that entrepreneurs are often immigrants and minority groups. Migrants are less attached to the traditions of society, less inhibited by how people see them, and, through natural selection, often more optimistic, more willing to take risks, and more willing to sacrifice current welfare for future gain. Hence, societies that tolerate people who break with tradition, think differently, and compete with vested interests will have higher levels of technological progress than societies that restrict economic and social freedoms (Lewer and Van den Berg, 2004).

Even though entrepreneurs featured prominently in Schumpeter's writing, he was not the first to elevate the entrepreneur to a position of importance in the economy. The early French economist, Richard Cantillon wrote in 1730 that producers in an economy consisted of two classes: hired people who received fixed wages and entrepreneurs with non-fixed, uncertain returns. Other French Physiocrats, as their school of thought has come to be known, such as Francois Quesnay also discussed entrepreneurs, as did the well-known French classical economics Jean-Baptiste Say. Even Adam Smith referred to "philosophers and men of speculation" who greatly increased "the quantity of science."

THE FOUNDATIONS OF THE SCHUMPETERIAN R&D MODEL

Romer (1990), Grossman and Helpman (1991), Aghion and Howitt (1992) are among those who have developed models of endogenous growth based on the assumption that R&D activities are carried out by profit-seeking entrepreneurs. There are subtle differences between the many models that have been developed, but most of them incorporate the following ideas:

1. Innovations are the result of intentional application of costly resources to R&D activities to create new products, ideas, processes, techniques, etc.

2. Profit-seeking innovators compete to employ the economy's scarce, and thus costly, resources in an attempt to generate innovations

3. Innovation creates new products that are better, cheaper, more attractive, or in some other way superior to existing products, which permits innovators to charge more and earn profits in excess of the costs of production.

4. Potential innovators make rational decisions, and they employ resources only when discounted expected future profits from innovation exceed the costs of the resources employed.

5. Each new innovation gives innovators profits but reduces or eliminates earlier innovators' profits.

Schumpeter's emphasis on entrepreneurs and the incentive of profits is built into many of the recent "Schumpeterian" models of innovation. The models essentially show technological progress as an ongoing activity where individuals, firms, organizations, universities, or governments have an incentive to employ scarce resources in order to generate new knowledge, ideas, methods, forms of economic organization, and any other changes that increase the value of output derived from the economy's set of productive inputs. Clearly, investment in the creation of new knowledge should only be undertaken if the returns exceed the costs, just like any other form of investment.

Unlike a perfectly competitive firm, which faces a horizontal demand curve and takes the price for its product as given, an imperfectly competitive producer faces a downward-sloping demand curve, as in Figure 1. Suppose that the marginal cost of production is constant at w, in which case the marginal cost (MC) curve is a horizontal line at price w. The downward-sloping demand curve (D) implies that a producer can always sell more by lowering the price of its product. The profit-maximizing producer, producing up to the point where marginal revenue (MR) equals marginal cost, thus sets the price p and produces quantity q. The difference between the price p and the marginal cost w, (p-w), is defined as the markup . Profits are equal to the shaded rectangular area in Figure 1, which is equal to the quantity of products sold times the markup. Schumpeter pointed out that innovative activity would in fact not take place unless profits are large enough and the time period during which producers earn the profit is long enough to cover the costs of innovation.

[FIGURE 1 OMITTED]

A MATHEMATICAL VERSION OF THE SCHUMPETERIAN MODEL

Growth models are normally presented in mathematical form. In this section, a relatively simple mathematical growth model is presented that closely summarizes the above theory and assumptions. That is, it captures the essentials of (Romer, 1990; Grossman and Helpman, 1991; Aghion and Howitt's, 1992) well-known Schumpeterian models of technological progress and includes entrepreneurial activity.

First, suppose that each act of innovation consists of creating a new firm that produces a new product. Start with n firms in the economy, each producing one of n different products. Suppose also that each product requires one unit of labor, so that the marginal (and average) cost of producing each good is equal to w, the wage rate. Because each product is different, each producer enjoys some degree of market power so that each firm faces a downward-sloping demand curve. For simplicity, suppose that each firm faces an identical demand curve, which means that each firm sets the same price equal to

(1) [rho] = w(1/[gamma]),

where 0 < [gamma] < 1 and the price markup p - w = [micrp] = [(1-[gamma])/[gamma ]w. Since w = p[gamma], profit per unit is p(1-[gamma]). That is, because entrepreneurs face downward-sloping demand curves, they can set a price above the marginal cost of production w and, potentially, recover the cost of innovation. The total value of output is GDP, and total profit is

(2) A = GDP(1-[gamma]).

The profit of any one of the n firms is

(3) [pi] = [GDP(1- gamma)]/n.

The present value of the earnings of a successful innovation is equal to the discounted stream of future profits, or

(4) PV = [infinity.summation over (i=0)] [[rho].sup.i] [[pi].sub.t=i],

where [rho] is the discount factor 1/(1+r), where r is the interest rate, and the [[pi].sub.t=i] are the future profits in each future time period t. The present value of all future profits can be thought of as the "stock market value" of the firm.

Next, consider the equilibrium level of entrepreneurial activity. Entrepreneurs will innovate and enter the market so long as the present value of future profits, PV, exceeds the current cost of product development. Suppose that [beta] is the amount of labor required to develop each new product. Then the cost of developing a new product is w[beta]. Assuming that there is a fixed number of workers in the economy, the more firms attempt to hire workers to develop new products, the higher will be w, the opportunity cost of those workers' marginal product in producing goods. Innovation will stop expanding when the discounted future earnings from producing the nth good are exactly equal to the cost of creating the nth good. Putting together the costs and profits from innovation, the innovation profit, defined as [theta], is

(5) [theta] = PV - w[beta].

Greater innovation (and greater innovation profit) takes place the lower [beta] and w and the greater PV. For example, if public policy-makers desire a higher rate of technological progress, they may enact policies that change interest rates and business taxes which favorably influence [theta]. Changes in educational systems could also impact [beta], the amount of labor required to develop a new idea, by promoting science and technology as well as alternative ways of thinking, less resources would need to used to create a new innovation. If there is competitive innovation, meaning that all prospective entrepreneurs can demand resources for innovation and, if successful, market their new products, then [theta] = 0 and

(6) PV = [beta]w.

Equation (6) represents the equilibrium condition for innovation and innovation profits (Lewer and Van den Berg, 2004).

CONCLUSION AND REMAINING ISSUES

Economists have modeled technological progress in two fundamentally-different ways. The earlier models assumed that technological progress is an unintentional by-product, an externality, of some other activity. Most of the more recent models have recognized that most new knowledge is created by intentionally applying scarce and, therefore costly, resources to innovative activities. The second set of endogenous growth models are most valuable for understanding technological progress. This paper adds to the understanding of endogenous technological progress by developing a mathematical model which incorporates effects of entrepreneurial activities on innovation.

After recognizing that it takes costly resources to create knowledge, ideas, and technology, the development of several other useful models of endogenous research and development activity can be created. By modeling technological progress to be the result of intentional efforts to create new ideas, better products, more efficient production processes, etc., policy makers are better advised to focus on how to stimulate such activities.

Many questions still remain and include: How can entrepreneurs be encouraged? What institutions lead entrepreneurs to innovate? Can other organizations generate and disseminate new ideas where entrepreneurs fail to act? How can the costs of innovation be reduced? What resources are most appropriate for creating new ideas? How can developing economies adapt existing ideas and technologies more efficiently to their specific circumstances? Recognizing that technological progress is the result of costly effort is an important precondition for finding the answers to these and many other important questions.

REFERENCES

Aghion, P. & P. Howitt (1992). A model of growth through creative destruction. Econometrica, 60(2), 323-351.

Grossman, G.M., & E. Helpman (1991). Innovation and growth in the global economy. Cambridge, MA: MIT Press.

Lewer, J.J. & H. Van den Berg (2004). International trade: The engine of growth? An analysis of the dynamic relationship between international trade and economic growth. West Texas A&M University and University of Nebraska, unpublished book.

OECD (1997). Technology and industrial performance. Organisation for Economic Co-Operation and Development, Paris.

Romer, P.M. (1990). Endogenous technological change. Journal of Political Economy, 95(1), 71-102.

Schmookler, J. (1966). Invention and economic growth. Cambridge, MA: Harvard University Press.

Schumpeter, J. (1912). Theorie der wirtschaftliche entwicklung. Leipzig: Duncker & Humbolt.

Schumpeter, J. (1934). The theory of economic development. Cambridge, MA: Harvard University Press.

The World Bank (2002). World development indicators. Washington, DC: World Bank.

Thompson, P. (2001). How much did the liberty shipbuilders learn? New evidence for an old case study. Journal of Political Economy, 109(1), 103-137.

Joshua J. Lewer, West Texas A&M University