# American Institute of Mathematical Sciences

April  2022, 9(2): 219-228. doi: 10.3934/jdg.2022005

## Exploring the gender gap in a closed market niche. Explicit solutions of an ODE model

 Facultad de Economía, Universidad Autónoma de San Luis Potosí, San Luis Potosí, SLP 78213, México

* Corresponding author

Received  January 2022 Revised  January 2022 Published  April 2022 Early access  February 2022

We study the effects of bias on the gender gap by building a non-linear system of differential equations that model the evolution of the sex distribution in a closed market as a function of disaggregated bias and solve the equations explicitly. Thus, allowing us to make specific claims about the system's behavior that may shed some light on the development of policy geared towards a more equitable workplace.

Citation: David Sifuentes, Iván Téllez, Jorge Zazueta. Exploring the gender gap in a closed market niche. Explicit solutions of an ODE model. Journal of Dynamics and Games, 2022, 9 (2) : 219-228. doi: 10.3934/jdg.2022005
##### References:
 [1] E. Accinelli and J. Zazueta, Exploring the gender gap in the labor market: A sex-disaggregated view, The Social Science Journal, (2021). [2] M. Baussola and C. Mussida, Regional and gender differentials in the persistence of unemployment in Europe, International Review of Applied Economics, 31 (2017), 173-190.  doi: 10.1080/02692171.2016.1231801. [3] M. Baussola, C. Mussida, J. Jenkings and M. Penfold, Determinants of the gender unemployment gap in Italy and the United Kingdom: A comparative investigation, International Labor Review, 154 (2015), 537-562.  doi: 10.1111/j.1564-913X.2015.00028.x. [4] S. M.Clifton, K. Hill, A. J. Karamchandani, E. A. Auty, P. McMahon and G. Sun, Mathematical model of gender bias and homophily in professional hierarchies, Chaos: An Interdisciplinary Journal of Nonlinear Science, 29 (2019), 023135, 13 pp. doi: 10.1063/1.5066450. [5] L. Hipp, Do hiring practices penalize women and benefit men for having children? Experimental evidence from Germany, European Sociological Review, 36 (2020), 250-264.  doi: 10.1093/esr/jcz056. [6] M. W. Hirsch, S. Smale and R. L. Devaney, Differential Equations, Dynamical Systems & An Introduction to Chaos, 2$^{nd}$ edition, Elsevier, USA, 2004. [7] I. Holman, D. Stuart-Fox and C. E. Houser, The gender gap in science: How long until women are equally represented?, PLOS Biology, 16 (2018). doi: 10.1371/journal.pbio.2004956. [8] B. Petrongolo, The gender gap in employment and wages, Nature Human Behaviour, 3 (2019), 316-318.  doi: 10.1038/s41562-019-0558-x. [9] A. K. Shaw and D. E. Stanton, Leaks in the pipeline: Separating demographic inertia from ongoing gender differences in academia, Proceedings of the Royal Society B: Biological Sciences, 279 (2012), 3736-3741.  doi: 10.1098/rspb.2012.0822. [10] G. F. Simmons, Differential Equations with Applications and Historical Notes, 3rd edition, CRC Press, Taylor & Francis Group, USA, 2017. [11] M. Spivak, Calculus on Manifolds, Addison-Wesley, USA, 1965. doi: 10.1201/9780429501906. [12] I. Zanin, On Okun's lawin OECD countries: An analysis by age cohorts, Economic Letters, 125 (2014), StaringPage–EndingPage. [13] I. Zanin and R. Calabrese, Interaction effects in region-level gdp per capita and age on labour market transition rates in Italy, IZA Journal of Labor Economics, 6 (2017), 243-248.  doi: 10.1016/j.econlet.2014.08.030. [14] Global Gender Gap Report 2020, World Economic Forum, 2020. Available from: https://www.weforum.org/reports/gender-gap-2020-report-100-years-pay-equality. [15] Global Gender Gap Report 2021, World Economic Forum, 2021. Available from: https://www.weforum.org/reports/ab6795a1-960c-42b2-b3d5-587eccda6023.

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##### References:
 [1] E. Accinelli and J. Zazueta, Exploring the gender gap in the labor market: A sex-disaggregated view, The Social Science Journal, (2021). [2] M. Baussola and C. Mussida, Regional and gender differentials in the persistence of unemployment in Europe, International Review of Applied Economics, 31 (2017), 173-190.  doi: 10.1080/02692171.2016.1231801. [3] M. Baussola, C. Mussida, J. Jenkings and M. Penfold, Determinants of the gender unemployment gap in Italy and the United Kingdom: A comparative investigation, International Labor Review, 154 (2015), 537-562.  doi: 10.1111/j.1564-913X.2015.00028.x. [4] S. M.Clifton, K. Hill, A. J. Karamchandani, E. A. Auty, P. McMahon and G. Sun, Mathematical model of gender bias and homophily in professional hierarchies, Chaos: An Interdisciplinary Journal of Nonlinear Science, 29 (2019), 023135, 13 pp. doi: 10.1063/1.5066450. [5] L. Hipp, Do hiring practices penalize women and benefit men for having children? Experimental evidence from Germany, European Sociological Review, 36 (2020), 250-264.  doi: 10.1093/esr/jcz056. [6] M. W. Hirsch, S. Smale and R. L. Devaney, Differential Equations, Dynamical Systems & An Introduction to Chaos, 2$^{nd}$ edition, Elsevier, USA, 2004. [7] I. Holman, D. Stuart-Fox and C. E. Houser, The gender gap in science: How long until women are equally represented?, PLOS Biology, 16 (2018). doi: 10.1371/journal.pbio.2004956. [8] B. Petrongolo, The gender gap in employment and wages, Nature Human Behaviour, 3 (2019), 316-318.  doi: 10.1038/s41562-019-0558-x. [9] A. K. Shaw and D. E. Stanton, Leaks in the pipeline: Separating demographic inertia from ongoing gender differences in academia, Proceedings of the Royal Society B: Biological Sciences, 279 (2012), 3736-3741.  doi: 10.1098/rspb.2012.0822. [10] G. F. Simmons, Differential Equations with Applications and Historical Notes, 3rd edition, CRC Press, Taylor & Francis Group, USA, 2017. [11] M. Spivak, Calculus on Manifolds, Addison-Wesley, USA, 1965. doi: 10.1201/9780429501906. [12] I. Zanin, On Okun's lawin OECD countries: An analysis by age cohorts, Economic Letters, 125 (2014), StaringPage–EndingPage. [13] I. Zanin and R. Calabrese, Interaction effects in region-level gdp per capita and age on labour market transition rates in Italy, IZA Journal of Labor Economics, 6 (2017), 243-248.  doi: 10.1016/j.econlet.2014.08.030. [14] Global Gender Gap Report 2020, World Economic Forum, 2020. Available from: https://www.weforum.org/reports/gender-gap-2020-report-100-years-pay-equality. [15] Global Gender Gap Report 2021, World Economic Forum, 2021. Available from: https://www.weforum.org/reports/ab6795a1-960c-42b2-b3d5-587eccda6023.
Regions $R_1$ and $R_2$. We used $\alpha = 0.6$, $\beta = 0.1$ and $k = 100$. In this case $(f_0^{*},m_0^{*}) = (10.94, 39.06)$. We plotted the solution curve passing through $(f_0^{*},m_0^{*})$ only in the region $R$. All solution curves starting in $R_1$ satisfy $m_{\infty} > f_{\infty}$ and all solution curves starting in $R_2$ satisfy $m_{\infty} < f_{\infty}$
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