Corner Solutions and Totals

While non-marginal analysis is unusual for microeconomists, relevant tools do exist. In fact, Xiaokai Yang’s pathbreaking research agenda— which aimed to endogenize the productive choices of all individuals in an economy with specialization and division of labor—develops a highly complex set of non-marginal tools.^[12] We thus draw on Yang and several of his colleagues for our approach to the bundled, non-marginal nature of entrepreneurial decision-making, even though he never considers entrepreneurship explicitly as far as we are aware.^[13] In definitional terms, non-marginal decisions should be understood as inframarginal, or binary decisions; they are, as we have been suggesting, decisions over which activities to engage in or not engage in (Yang and Liu 2009, 1).

Before we apply the analysis to entrepreneurial decisions, we briefly review Yang's general approach. To begin, a key feature of what he calls his “new classical model” (2001, 133) assumes individuals are both consumers and producers, which means they produce some good to both consume and sell on the market, and they buy other goods on the market to consume. As such, Yang's decision problem confronting the individual is based, unremarkably, on her utility derived from consuming goods and her budget constraint. What is unusual in his framework, however, is the decision facing the agent also depends upon the agent's produc­tion function (Yang 2001, 135). This complex functional form gives rise to multiple possible optima and since the “local optimum decisions are discontinuous across the profiles, there is no method that can be used to solve for the optimum decision in one step” (134).

In other words, because the choice confronting Yang's agent is discon­tinuous, optimality cannot be determined using the traditional marginal conditions. It is the existence of these multiple, discontinuous local optima that is the basis for classifying the analysis as inframarginal.

According to Yang, a key result—the “Wen Theorem” (1998)—proves that the optimal “...decision does not involve selling more than one good, does not involve selling and buying the same good, and does not involve buying and producing the same good” (Yang 2001, 134). Intuitively, this means “[s]elling and buying the same good involves unnecessary transac­tion costs and therefore is inefficient. Selling two goods is also inefficient since it prevents the full exploitation of the economies of specialization” (2001, 135).^[14] In other words, an individual produces only one type of good or is engaged in one specific type of occupation for returns that are sold to purchase all other goods (Yang 2001, 136); her production of that particular good also entails some self-consumption of that same good.^[15]

We now return to integrating Yang's inframarginal approach with our analysis of the entrepreneur. With Yang's help, the question of what entrepreneurs produce can be understood as a problem involving not just production functions, but also utility functions (the “tastes” of producer­consumers) and constraints (budgets and relative prices). Because of the Wen Theorem, production choices are corner solutions in this infra­marginal world. This means the producer-consumer agent specializes in the production of only one good and produces zero of all other goods. While we forgo illustrating this result, it can be visualized in a production possibility framework as the individual producing at one of the corners: production is either x = 0, or y = 0, where x and y are both consumption and production goods (Yang 2001, 74, 135).

Of course, a key difference between corner solutions and traditional interior optimization solutions is that traditional solutions involve an infinitely divisible continuum that allows infinitely fine adjustments in decisions as the parametric conditions change. Corner solutions, on the other hand, imply that decision variables attain either a lower or upper bound (Yang 2001, 8) and will be invariant to a potentially wide range of parametric changes. In our example, the potential entrepreneur's only choice is “0 or 1” to build a restaurant or “0 or 1” to, for example, remain in a salaried job. our entrepreneur cannot open half an indian restaurant and work half-time at a salaried job (or any other fraction thereof). In such a world, not only will decisions be invariant to wide swings in parameters, but once choice variables do change they will change dramatically, from 0 to 1, or from 1 to O.^[16]

The implications of considering these producer-consumer decisions as binary are profound. Take, for example, a point that is rarely made explicit in Yang: his models imply individuals have preferences over which produc­tive activities they would like to be engaged in and which activities they would not. Consider the following:

As your career develops, you will see that your peers will have very different lives according to their different occupations. To choose an occupation, and a level of specialization in that chosen occupation (that relates to how many activities and subactivities a person does not engage in) is to choose a configuration. This choice of configuration usually has much more important consequences on a person’s future life than does the degree of commitment to a given occupation. (Yang and Liu 2009, 41, emphasis added)

Notice how this choice of a configuration of a future life parallels our emphasis on the bundled nature of the decision. And, importantly, it also includes more than just the simple monetary returns to an occu­pation. It includes countless nonpecuniary aspects, such as the type of people worked with, time away from home, passion for work, among many others.

Thus, unlike most other approaches to entrepreneurship—particularly Kirzner's—we argue the pecuniary (and nonpecuniary) bundle the indi­vidual would like to consume-produce influences what Yang calls her “future life” decisions, and what we have been calling “big picture” decisions. such a perspective underscores that monetary profit is likely not the only force driving entrepreneurs, and, in fact, may not even be the primary driving force.^[18] Enjoyment derived from a type of work, or a desire to consume the product of the work itself must certainly be additional motivations behind entrepreneurial decisions. This implica­tion is consistent with results across many empirical studies. For example, Hamilton (2000), a highly cited article in the empirical literature on self-employment, reports that the

empirical results suggest that the nonpecuniary benefits of self-employment are substantial: Most entrepreneurs enter and persist in business despite the fact that they have both lower initial earnings and lower earnings growth than in paid employment, implying a median earnings differential of 35 percent for individuals in business for 10 years..

Moreover, a substantial empirical literature on this issue supports Hamil­ton’s fundamental results and suggests, directly or indirectly, that nonpe- cuniary considerations must be significant for entrepreneurs.^[20]

Production-consumption decisions will also depend on the entrepreneur’s actual production function, which is to say her existing skill set. An entrepreneur who is already specialized is someone who has devoted time and resources, in the past, to gaining that specialization. Her current production function—the representation of what she is good at—is thus a function of past decisions and experience. Indeed, asymme­tries across all these factors, including constraints, preferences, and skills will combine to account for the variety of ventures that entrepreneurs enter, or whether they decide to enter entrepreneurship at all.

From our perspective, shortcomings do, however, arise in Yang’s approach. Recall that the optimization of net total benefits across all possible decisions means Yang’s agents must maximize across many poten­tial corner solutions, which necessarily involves a complex, second-order optimization process. The presumption that agents can optimize in such a way ignores two dimensions that are important to our analysis. The first is the bundling problem: each “big picture” corner solution—say producing Indian food instead of burgers—can potentially nest tens, hundreds, or even thousands of other decisions: optimizing over each of these dimensions is clearly unrealistic.

Second, any bundled corner solution is likely to involve a range of nonpecuniary costs and benefits. For instance, in deciding between opening an Indian restaurant and staying in salaried employment, the entrepreneur would have to compare the net benefits of each.

Third and most profoundly, Buchanan (1969) argues that while the profession has internalized the notion that benefits are subjective, it has not appreciated that costs are too: the argument is that opportu­nity costs, from the perspective of the individual, are subjective costs. Throughout mainstream economics—and Kirzner's approach, we might add—it is assumed that costs and prices are proxies for the opportunity costs of different options. However, the true subjective opportunity cost disappears after each choice is made because, once a decision is made, its once-attendant options disappear; in other words, once a decision is made, the agent confronts a new set of opportunity costs (Buchanan 1969). Opportunity costs are therefore never realized and, as such, outlays cannot be relied upon as proxies for whether the chosen option was optimal at the time. In sum, Buchanan argues there can be no basis— even at the individual level—to judge optimality because the necessary data have disappeared and cannot be recovered. The implications for social optimality should be clear.

Thus, while Yang's corner-solution models provide a useful framework with which to analyze inframarginal decisions, we argue that he overlooks the computational requirements inherent in the second-order optimiza­tion necessary to determine global optimal quantities of nonpecuniary costs and benefits. Indeed, he places considerably higher computational demands on his agents than even traditional microeconomics does, which raises our earlier point that information is neither perfect nor costless. The computational complexities we outlined above are, moreover, ever present, even for those making decisions over highly local production (i.e., small local business startups).

In sum, our argument, thus far, implies potential entrepreneurs confront complex (discontinuous) sets of decisions for which there are no simple optimization rules. Since our producer-consumer entrepreneurs cannot optimize, we posit that their decision process looks something like “satisficing”—which implies our agents merely aim to meet some acceptable threshold—as Simon has suggested in other contexts.^[22] When comparing states-of-the-world, entrepreneurs are likely to evaluate the total net benefits of just a few of the options available and ignore many other plausible ones. Then, within those highlighted options, they will likely compare just a few of the sub-features (at most) and ignore many other potentially relevant features.