Income Distribution and the Occupational Choices of Entrepreneurs
-
Julia M. Schwenkenberg
Abstract
This article presents a model that analyzes the effects of redistribution on the occupational choices of entrepreneurs. Entrepreneurs can either engage in costly search for projects and produce or become rent-seekers who collect rents for reversing redistribution. The model illustrates that redistribution of aggregate output is possible until a tipping point is reached. Higher levels of redistribution decrease entrepreneurship, employment, and aggregate income. Which level of redistribution is too much depends on the degree of inequality inherent in the firm quality distribution and on the power of rent-seekers to alter redistributive outcomes. An exogenous increase in the ratio of average realized output to output produced at the lowest-productivity firm reduces the gains from entrepreneurship relative to rent-seeking. This happens because entrepreneurs expend search costs to find those high-quality projects that drive up the average production value, but only a few entrepreneurs can realize these big hits. Wages and rent-seeker pay-offs, on the other hand, depend on average realized production. An increase in the power of rent-seekers further reduces the government’s options. The model implies that the government’s ability to redistribute might be declining when inequality rises.
Appendix
Proof of 
The reservation quality [10] is decreasing in the tail index 
of the project quality distribution. The following provides a proof.
If 
, then 
and we must have 
; otherwise, the reservation quality is constant at 
.
Proof of Proposition 1
Let us first consider the special case 
. The equilibrium number of entrepreneurs can be obtained by setting the value of entrepreneurship to zero. When entrepreneurs are searching, eq. [13b] gives us the value of entrepreneurship, and we get
which implies 
for 
, and 
otherwise.
When entrepreneurs take only one draw from the project quality distribution and conduct no further search, the value of entrepreneurship equals:
where 
denotes [13b] evaluated at 
. Note eq. [10] implies the condition for search:
When the condition is violated, 
and 
. Therefore, the equilibrium number of entrepreneurs must be smaller in an equilibrium without search compared to an equilibrium with lower search costs, such that 
and 
.
Search is always optimal in any equilibrium with 
and 
. To see this recall, from the discussion of the reservation quality [10], that there are two effects of 
on the reservation quality: first a negative competition effect that operates through 
and second a positive protection effect through 
. In particular, the reservation quality is a decreasing function of 
for 
and takes a U-shape otherwise. Note that, for 
, the search condition must hold in the limit, as 
. Moreover, search is always optimal at 
, since 
. Whether entrepreneurs stop searching for an intermediate range of 
depends on search costs, parameter values, and redistribution. In such an equilibrium, it must be that 
. Condition [16] follows from the above.
When 
, the equilibrium number of entrepreneurs remains at 
as long as 
, because 
and 
. Note that rent-seeker power does not affect the reservation quality [10]. Therefore, 
is derived by setting the value of entrepreneurship given in eq. [5b] and the value of rent-seeking [5b] equal at 
, which simplifies to
It follows that there is full employment for 
and that all entrepreneurs are searching for projects.
For the second part of Proposition 1, note that either 
or 
whenever entrepreneurs are searching and the value of rent-seeking is zero. There is no closed form solution for 
, when entrepreneurs are not searching or the value of rent-seeking is positive. But, we can easily see that 
is a decreasing function of 
in both cases, and, therefore, 
is decreasing in 
. Moreover, the value of rent-seeking [5b] is increasing in 
, therefore, 
must decline further whenever 
. Finally, since R increases 
, the equilibrium number of entrepreneurs is also decreasing in R.
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- 1
See, for example, Volkov (2002)’s book (appropriately titled) “Violent Entrepreneurs” on the Russian Mafia and Gambetta (1996) on the Italian Mafia.
- 2
The proportions that are redistributed could be interpreted as contest success functions as in this literature. The related model in Schwenkenberg (2005) focuses on alternative property rights institutions, involving private protectors, and entrepreneurship.
- 3
The functions modeling the proportion taken from entrepreneurial production could be interpreted as “contest success functions,” which have been used to model conflict over resources in the relevant economics literature (for example, Hirshleifer (2001), Grossman and Kim (1995), Anderson and Bandiera (2005), Dixit (2004)). Then, a situation with
could be interpreted as “anarchy,” where the unemployed are able to “steal” a share of output that depends on their group size relative to the total size of the two groups (unemployed workers and entrepreneurs) which is equal to one in equilibrium. - 4
Note that the tax rate is applied to revenues, because the government directly determines the fraction of aggregate output that is redistributed to unemployed workers. Therefore, all production, not just profits, is taxed.
- 5
Recall
, and also that 
. - 6
The Appendix shows that the reservation quality is decreasing in the tail index,
, on the relevant support. Recall that 
is increasing as the tail index falls. - 7
When searching is prohibitively expensive, the value of entrepreneurship is still equal to expected profits minus search costs, but this is now lower than profits at
: 
. - 8
A similar effect could be achieved when the worker-skill distribution becomes more skewed to the right, which also increases expected output relative to output at the reservation quality. We focus here on the project quality distribution assuming a fixed distribution of worker ability.
- 9
For details see the proof of Proposition 1 given in the Appendix. Proposition 1, presented in the next subsection, generalizes condition [16].
- 10
Furthermore,
and 
= 
= 10. - 11
For more examples, see Newman (2005).
©2014 by Walter de Gruyter Berlin / Boston
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Articles in the same Issue
- Frontmatter
- Contributions
- Do You Receive a Lighter Prison Sentence Because You Are a Woman or a White? An Economic Analysis of the Federal Criminal Sentencing Guidelines
- Income Distribution and the Occupational Choices of Entrepreneurs
- Determinants of Research Production at Top US Universities
- In Whom We Trust: The Role of Certification Agencies in Online Drug Markets
- The Effect of College Applications on Enrollment
- Topics
- Market-Induced Rationalization and Welfare-Enhancing Cartels
- Food Insecurity and SNAP Participation in Mexican Immigrant Families: The Impact of the Outreach Initiative
- Profit-Seeking Behavior of Medical Providers and Generic Competition in the Pharmaceutical Market: Evidence from Taiwan
- Anticipated Regret or Endowment Effect? A Reconsideration of Exchange Asymmetry in Laboratory Experiments
- New Labour? The Effects of Migration from Central and Eastern Europe on Unemployment and Wages in the UK
