Abstract
In this chapter a survey is given of models in the literature that can be used to explain the number of self-employed individuals in the framework of a competitive market.1 Most of these models were actually developed for other goals. Some of the models discussed were developed to explain the number of firms, the size distribution of firms, or the number of entrepreneurs. Others were developed to explain other phenomena, for example the optimal tax rate, while making the number of self-employed individuals endogenous as an extra complication. For this reason this survey is more than a trivial enumeration of models present in the literature.
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This survey is based on De Wit (1993).
As the authors note themselves, the model is a simplified version of that of Lucas (1978) that will be described in Section 2.4.
As Lucas notes himself on p. 510, his model is inspired by that of Kihlstrom and Laffont (1979), to be discussed in Section 2.6, that came under his attention before the actual publication.
Actually, this result is due to Lippman and McCall (1981). Sheshinski and Drèze (1976) only prove that an increase in the variance of Xd(p) causes the number of self-employed to increase.
It is noteworthy that Appelbaum and Lim (1982) overlooked this second effect. So they were led to the — false — conclusion that an increase in price uncertainty necessarily lowers the equilibrium number of self-employed individuals.
The negativity of l w is guaranteed if xv>0, x lv >0, and if the absolute risk aversion of the self-employed individuals is non-increasing in income [cf. the discussion below (2.12)]. This condition is given by Kanbur (1979, p. 794) and by Kihlstrom and Laffont (1979, p. 731). It is noted that the latter also give two alternative conditions. The negativity of l p is guaranteed if xv>0 and x lv >0. This is a special case of the condition given by Kihlstrom and Laffont (1979, p. 729). The negativity of Eu w is easy to derive without needing extra conditions. Finally, the negativity of Eu p is proved in Kihlstrom and Laffont (1979, p. 725), also without extra conditions.
Kanbur (1979, pp. 793–796, and 1981) also works out a model with ex-ante flexibility, but only for the case that all individuals have the same risk aversion. It is noted that Kanbur developed his models independently from Kihlstrom and Laffont.
If ex-ante flexibility is assumed, an increase in risk aversion p decreases labor demand (as discussed above). To clear the labor market the wage will therefore decrease. This influences (the expected utility of) profits positively. However, the expected utility of profits is also influenced negatively due to the increase in risk aversion (Eu p < 0). Thus, an increase in risk aversion can increase as well as decrease the number of self-employed individuals.
This follows from (2.19). Greater detail is provided in Calvo and Wellisz (1980, p. 674).
So while there is a time lag in the adjustment of the number of self-employed individuals, the self-employed individuals can adjust their output instantaneously in order to maximize their profits in this model. Myers and Weintraub (1971) and Okuguchi (1971) extend the model to a setting where there is also a time lag in the adjustment of output.
In Kihlstrom and Laffont (1979) labor is the single factor of production. In Kihlstrom and Laffont (1983b) this production factor is reinterpreted as capital. The results discussed in this section are not dependent on this reinterpretation, so they are presented as if they were derived with labor as the factor of production.
If one assumes non-increasing absolute risk aversion and non-decreasing relative risk aversion, this third effect certainly works out advantageously for the employees [see Kihlstrom and Laffont (1983b, p. 168]. For it can be proved that under these assumptions an increase in the tax rate has the same effect as an overall decrease in the absolute risk aversion of the individuals and it was already observed in footnote 13 that the demand for labor increases if absolute risk aversion decreases.
A self-financing tax scheme is such that the total receipts are zero. Thus, it only establishes a redistribution of income.
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© 1993 Physica-Verlag Heidelberg
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de Wit, G. (1993). Models of self-employment in a competitive market. In: Determinants of Self-employment. Studies in Contemporary Economics. Physica-Verlag HD. https://doi.org/10.1007/978-3-642-50300-9_2
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DOI: https://doi.org/10.1007/978-3-642-50300-9_2
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