Modeling of Neccessity Entrepreneuship via General Equilibrium Approach

MACSPro'2019 - Modeling and Analysis of Complex Systems and Processes, Vienna
21 - 23 March 2019

Maria Fomenko, Alexander Shapoval

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1. Modeling Neccessity Entrepreneuship via General Equilibrium Approach w—ri— pomenkoD ƒ—sh— ƒh—pov—l National Research University Higher School of Economics Lab of Modeling and Control of Complex Systems wegƒ€ro PHIWD w—r™h PPD PHIW Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 1 / 22
2. Motivation Aim of the talk gonstru™t — model of o™™up—tion—l ™hoi™e under un™ert—inty ixpl—in the existen™e of the ne™essity entrepreneurs in the fr—mework of this model Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 2 / 22
3. Motivation Aim of the talk gonstru™t — model of o™™up—tion—l ™hoi™e under un™ert—inty ixpl—in the existen™e of the ne™essity entrepreneurs in the fr—mework of this model Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 2 / 22
4. Motivation Aim of the talk gonstru™t — model of o™™up—tion—l ™hoi™e under un™ert—inty ixpl—in the existen™e of the ne™essity entrepreneurs in the fr—mework of this model Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 2 / 22
5. Motivation Entrepreneurship as an engine for growth intrepreneurship is in f—vor of growthX ql—eser PHHUD prits™h IWWUD gh—tterji PHIR qlo˜—l intrepreneurship wonitor reports motiv—tion of entrepreneurshipD ‚eynolds et —l PHHQ sn p—rti™ul—rD — p—rt of entrepreneurs prefers — s—l—ried jo˜ ˜ut f—ils to get —n o'erY these individu—ls ˜e™ome ne™essity entrepreneurs snnov—tive ˜usiness is ™ru™i—l for e™onomi™ developmentY ne™essity entrepreneurs —re ˜—dly represented in innov—tive ˜usiness Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 3 / 22
6. Motivation Entrepreneurship as an engine for growth intrepreneurship is in f—vor of growthX ql—eser PHHUD prits™h IWWUD gh—tterji PHIR qlo˜—l intrepreneurship wonitor reports motiv—tion of entrepreneurshipD ‚eynolds et —l PHHQ sn p—rti™ul—rD — p—rt of entrepreneurs prefers — s—l—ried jo˜ ˜ut f—ils to get —n o'erY these individu—ls ˜e™ome ne™essity entrepreneurs snnov—tive ˜usiness is ™ru™i—l for e™onomi™ developmentY ne™essity entrepreneurs —re ˜—dly represented in innov—tive ˜usiness Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 3 / 22
7. Motivation Entrepreneurship as an engine for growth intrepreneurship is in f—vor of growthX ql—eser PHHUD prits™h IWWUD gh—tterji PHIR qlo˜—l intrepreneurship wonitor reports motiv—tion of entrepreneurshipD ‚eynolds et —l PHHQ sn p—rti™ul—rD — p—rt of entrepreneurs prefers — s—l—ried jo˜ ˜ut f—ils to get —n o'erY these individu—ls ˜e™ome ne™essity entrepreneurs snnov—tive ˜usiness is ™ru™i—l for e™onomi™ developmentY ne™essity entrepreneurs —re ˜—dly represented in innov—tive ˜usiness Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 3 / 22
8. Motivation Entrepreneurship as an engine for growth intrepreneurship is in f—vor of growthX ql—eser PHHUD prits™h IWWUD gh—tterji PHIR qlo˜—l intrepreneurship wonitor reports motiv—tion of entrepreneurshipD ‚eynolds et —l PHHQ sn p—rti™ul—rD — p—rt of entrepreneurs prefers — s—l—ried jo˜ ˜ut f—ils to get —n o'erY these individu—ls ˜e™ome ne™essity entrepreneurs snnov—tive ˜usiness is ™ru™i—l for e™onomi™ developmentY ne™essity entrepreneurs —re ˜—dly represented in innov—tive ˜usiness Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 3 / 22
9. Motivation Entrepreneurship as an engine for growth intrepreneurship is in f—vor of growthX ql—eser PHHUD prits™h IWWUD gh—tterji PHIR qlo˜—l intrepreneurship wonitor reports motiv—tion of entrepreneurshipD ‚eynolds et —l PHHQ sn p—rti™ul—rD — p—rt of entrepreneurs prefers — s—l—ried jo˜ ˜ut f—ils to get —n o'erY these individu—ls ˜e™ome ne™essity entrepreneurs snnov—tive ˜usiness is ™ru™i—l for e™onomi™ developmentY ne™essity entrepreneurs —re ˜—dly represented in innov—tive ˜usiness Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 3 / 22
10. Motivation Who are entrepreneurs? Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 4 / 22
11. Motivation Who are entrepreneurs? Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 4 / 22
12. Motivation Who are entrepreneurs? ywners of enterprisesc pounders of sm—ll —nd medium size ™omp—niesc ƒelfEemployed individu—lsc Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 4 / 22
13. Motivation Who are entrepreneurs? ywners of enterprisesc pounders of sm—ll —nd medium size ™omp—niesc ƒelfEemployed individu—lsc Self-employed are likely not ™riti™—l for growth to ˜e ne™essity entrepreneurs Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 4 / 22
14. Motivation Who are entrepreneurs? ywners of enterprisesc pounders of sm—ll —nd medium size ™omp—niesc ƒelfEemployed individu—lsc Self-employed are likely not ™riti™—l for growth to ˜e ne™essity entrepreneurs In the model we ™—nnot split entrepreneurs into groups ˜e™—use of the model simpli™ity Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 4 / 22
15. Motivation Who are entrepreneurs? ywners of enterprisesc pounders of sm—ll —nd medium size ™omp—niesc ƒelfEemployed individu—lsc Self-employed are likely not ™riti™—l for growth to ˜e ne™essity entrepreneurs In the model we ™—nnot split entrepreneurs into groups ˜e™—use of the model simpli™ity Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 4 / 22
16. Motivation Who are entrepreneurs? ywners of enterprisesc pounders of sm—ll —nd medium size ™omp—niesc ƒelfEemployed individu—lsc Self-employed are likely not ™riti™—l for growth to ˜e ne™essity entrepreneurs In the model we ™—nnot split entrepreneurs into groups ˜e™—use of the model simpli™ity Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 4 / 22
17. Motivation Who are entrepreneurs? ywners of enterprisesc pounders of sm—ll —nd medium size ™omp—niesc ƒelfEemployed individu—lsc Self-employed are likely not ™riti™—l for growth to ˜e ne™essity entrepreneurs In the model we ™—nnot split entrepreneurs into groups ˜e™—use of the model simpli™ity Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 4 / 22
18. Canonical models: nancial motivation Lukas (1978): heterogeneous entrepreneurial abilities y™™up—tion—l ™hoi™eX —n individu—l ™omp—res the pro(t of the (rm th—t she ™ould run —nd her s—l—ry if she ™hooses — s—l—ried jo˜Y — l—rger in™ome underlies the de™ision wore t—lented individu—ls ˜e™ome entrepreneurs „he ˜est entrepreneurs run ˜igger (rms Kilhstrom & Laont (1979): heterogeneous risk aversion „woEdimension—l ™hoi™e —s the ˜—l—n™e ˜etween returns —nd risk „he more entrepreneur likes riskD the ˜igger (rm she runs Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 5 / 22
19. Canonical models: nancial motivation Lukas (1978): heterogeneous entrepreneurial abilities y™™up—tion—l ™hoi™eX —n individu—l ™omp—res the pro(t of the (rm th—t she ™ould run —nd her s—l—ry if she ™hooses — s—l—ried jo˜Y — l—rger in™ome underlies the de™ision wore t—lented individu—ls ˜e™ome entrepreneurs „he ˜est entrepreneurs run ˜igger (rms Kilhstrom & Laont (1979): heterogeneous risk aversion „woEdimension—l ™hoi™e —s the ˜—l—n™e ˜etween returns —nd risk „he more entrepreneur likes riskD the ˜igger (rm she runs Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 5 / 22
20. Canonical models: nancial motivation Lukas (1978): heterogeneous entrepreneurial abilities y™™up—tion—l ™hoi™eX —n individu—l ™omp—res the pro(t of the (rm th—t she ™ould run —nd her s—l—ry if she ™hooses — s—l—ried jo˜Y — l—rger in™ome underlies the de™ision wore t—lented individu—ls ˜e™ome entrepreneurs „he ˜est entrepreneurs run ˜igger (rms Kilhstrom & Laont (1979): heterogeneous risk aversion „woEdimension—l ™hoi™e —s the ˜—l—n™e ˜etween returns —nd risk „he more entrepreneur likes riskD the ˜igger (rm she runs Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 5 / 22
21. Canonical models: nancial motivation Lukas (1978): heterogeneous entrepreneurial abilities y™™up—tion—l ™hoi™eX —n individu—l ™omp—res the pro(t of the (rm th—t she ™ould run —nd her s—l—ry if she ™hooses — s—l—ried jo˜Y — l—rger in™ome underlies the de™ision wore t—lented individu—ls ˜e™ome entrepreneurs „he ˜est entrepreneurs run ˜igger (rms Kilhstrom & Laont (1979): heterogeneous risk aversion „woEdimension—l ™hoi™e —s the ˜—l—n™e ˜etween returns —nd risk „he more entrepreneur likes riskD the ˜igger (rm she runs Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 5 / 22
22. Canonical models: nancial motivation Lukas (1978): heterogeneous entrepreneurial abilities y™™up—tion—l ™hoi™eX —n individu—l ™omp—res the pro(t of the (rm th—t she ™ould run —nd her s—l—ry if she ™hooses — s—l—ried jo˜Y — l—rger in™ome underlies the de™ision wore t—lented individu—ls ˜e™ome entrepreneurs „he ˜est entrepreneurs run ˜igger (rms Kilhstrom & Laont (1979): heterogeneous risk aversion „woEdimension—l ™hoi™e —s the ˜—l—n™e ˜etween returns —nd risk „he more entrepreneur likes riskD the ˜igger (rm she runs Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 5 / 22
23. Canonical models: nancial motivation Lukas (1978): heterogeneous entrepreneurial abilities y™™up—tion—l ™hoi™eX —n individu—l ™omp—res the pro(t of the (rm th—t she ™ould run —nd her s—l—ry if she ™hooses — s—l—ried jo˜Y — l—rger in™ome underlies the de™ision wore t—lented individu—ls ˜e™ome entrepreneurs „he ˜est entrepreneurs run ˜igger (rms Kilhstrom & Laont (1979): heterogeneous risk aversion „woEdimension—l ™hoi™e —s the ˜—l—n™e ˜etween returns —nd risk „he more entrepreneur likes riskD the ˜igger (rm she runs Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 5 / 22
24. Canonical models: nancial motivation Lukas (1978): heterogeneous entrepreneurial abilities y™™up—tion—l ™hoi™eX —n individu—l ™omp—res the pro(t of the (rm th—t she ™ould run —nd her s—l—ry if she ™hooses — s—l—ried jo˜Y — l—rger in™ome underlies the de™ision wore t—lented individu—ls ˜e™ome entrepreneurs „he ˜est entrepreneurs run ˜igger (rms Kilhstrom & Laont (1979): heterogeneous risk aversion „woEdimension—l ™hoi™e —s the ˜—l—n™e ˜etween returns —nd risk „he more entrepreneur likes riskD the ˜igger (rm she runs Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 5 / 22
25. Canonical models: Financial gain Open questions ‡ho —re ne™essity entrepreneursc ‡h—t is their role in the e™onomyc Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 6 / 22
26. Canonical models: Financial gain Open questions ‡ho —re ne™essity entrepreneursc ‡h—t is their role in the e™onomyc Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 6 / 22
27. Canonical models: Financial gain Open questions ‡ho —re ne™essity entrepreneursc ‡h—t is their role in the e™onomyc Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 6 / 22
28. Necessity entrepreneurs and unemployment x—rit— @PHIRAD uum—r 8 ƒ™huetze @PHHUAX unemployment in equili˜rium due to imperfe™t se—r™h for employees wil¡ —n @PHIPAX selfEemployment is used —s — route out of unemployment ‡e propose — simpler —ppro—™h th—t le—ds to simil—r ™on™lusions Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 7 / 22
29. Necessity entrepreneurs and unemployment x—rit— @PHIRAD uum—r 8 ƒ™huetze @PHHUAX unemployment in equili˜rium due to imperfe™t se—r™h for employees wil¡ —n @PHIPAX selfEemployment is used —s — route out of unemployment ‡e propose — simpler —ppro—™h th—t le—ds to simil—r ™on™lusions Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 7 / 22
30. Perception about entrepreneurs Ð Ø × Ê × Æ Ó Ò ¹ Ò ØÖ Ô Ö Ò Ù Ö× Ò ØÖ Ô Ö Ò Ù Ö× Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 8 / 22
31. Perception about entrepreneurs Ð Ø × Ê × Æ Ó Ò ¹ Ò ØÖ Ô Ö Ò Ù Ö× Ò ØÖ Ô Ö Ò Ù Ö× Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 8 / 22
32. Perception about entrepreneurs Ð Ø × Ê × Æ Ó Ò ¹ Ò ØÖ Ô Ö Ò Ù Ö× Ò ØÖ Ô Ö Ò Ù Ö× ÖÑ × Þ Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 8 / 22
33. Concept of Equilibrium Income axis, α is a tax rate b (1 − α)w ÙÒ ÑÔÐÓÝ Ò Ø Ø Ö¹Ø Ü Û × ÒØÖ ÔÖ Ò ÙÖ׳ Ø Ö¹Ø Ü ÔÖÓ Ø× ÁÒ ÓÑ Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 9 / 22
34. Concept of Equilibrium Income axis, α is a tax rate b (1 − α)w ÙÒ ÑÔÐÓÝ Ò Ø Ø Ö¹Ø Ü Û × ÒØÖ ÔÖ Ò ÙÖ׳ Ø Ö¹Ø Ü ÔÖÓ Ø× ÁÒ ÓÑ This scheme determines equilibrium if no˜ody is motiv—ted or not —˜le to ™h—nge the o™™up—tion—l ™hoi™eX …nemployed —gents —re not —˜le to run — (rm —nd get —n in™ome th—t is l—rger th—n b xo˜ody ™—n get — jo˜ o'er Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 9 / 22
35. b (1 − α)w ÙÒ ÑÔÐÓÝ Ò Ø Ø Ö¹Ø Ü Û × ÒØÖ ÔÖ Ò ÙÖ׳ Ø Ö¹Ø Ü ÔÖÓ Ø× ÁÒ ÓÑ Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 10 / 22
36. b (1 − α)w ÙÒ ÑÔÐÓÝ Ò Ø Ø Ö¹Ø Ü Û × ÒØÖ ÔÖ Ò ÙÖ׳ Ø Ö¹Ø Ü ÔÖÓ Ø× ÁÒ ÓÑ ÏÓÖ Ö× ÍÒ ÑÔÐÓÝ ÒØ× ÒØÖ ÔÖ Ò ÙÖ× φb φw A B C D γ(ϕ) Ð Ø × sndividu—ls with entrepreneuri—l —˜ilities φb —nd φw ™—n e—rn —fterEt—x pro(t b —nd (1 − α)w respe™tivelyD when running — (rm Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 10 / 22
37. Baseline Model: Assumptions ‡e ™onsider — single se™tor e™onomy with monopolisti™—lly ™ompeting singleEprodu™t (rms — l¡ — hƒ @IWUUA sndividu—ls —re heterogeneous with respe™t to their entrepreneuri—l —˜ilities ˜ut homogeneous —s workers —nd ™onsumersY —iming —t — l—rger in™omeD they de™ide upon entrepreneurship —nd the entr—n™e to the l—˜or m—rketD whi™h le—ds to — jo˜ o'er or unemploymentY „he distri˜ution of —˜ilities is ™ommon knowledge i—™h spe™i(™ —gent does not —'e™t the m—rket „wo st—ge o™™up—tion—l ™hoi™eX Initial occupational choice can be altered if the alternation increases the income Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 11 / 22
38. Occupational choice as a two stage tree y™™up—tion—l ghoi™e intrepeneurship intrepreneurship to˜ w—rket ƒ—l—ried to˜ …nemployment to˜ w—rket ƒ—l—ried to˜ …nemployment Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 12 / 22
39. Occupational choice as a backward induction foth st—gesX vet Ξe,1 —nd Ξe,2 ˜e the set of entrepreneurs @—nd the set of (rmsD —nd the set of v—rieties of the di'erenti—ted goodA —fter the Ist —nd Pnd st—ges respe™tivelyF sndividu—l ξ ∈ Ξe,∗ ⇐⇒ IncomeEntrepreneur IncomeJob Market. „he se™ond st—ge de™ision is p—r—metrized ˜y the out™ome of the (rst st—ge „he (rst st—geX individu—ls —nti™ip—te the ˜est o™™up—tion—l ™hoi™e of the se™ond st—geF Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 13 / 22
40. Occupational choice: Second stage Risk aversion sndividu—ls who —re —˜le to e—rn —fter t—x pro(t ex™eeding the unemployment ˜ene(t (1 − α)πϕ,2 b ™hoose entrepreneurshipF Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 14 / 22
41. Occupational choice: First stage ξϕ ∈ Ξe,1 ⇐⇒ (1 − α)πϕ,1 E + A(1 − α)πϕ,2 EE τ1(1 − α)w W + Aτ1ρ(1 − α)w WW + Aτ1(1 − ρ)(1 − α)πϕ,2 WU + (1 − τ1)b U + A(1 − τ1)(1 − α)πϕ,1 UE . - A is — dis™ount f—™tor - α indi™—tes t—xes - w —nd π —re the w—ges —nd pro(ts - τ1 —nd ρ —re the pro˜—˜ilities to get — jo˜ o'er —t the (rst st—ge —nd to keep the work —t the se™ond st—ge - ED WD U m—rk individu—ls —fter the (rst o™™up—tion—l ™hoi™eX entrepreneurD workerD unemployed individu—l - „wo sym˜olsD iF eFD WU m—rk the result of the se™ond o™™up—tion—l ™hoi™e Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 15 / 22
42. Supply intrepreneur ξ ∈ Ξe with entrepreneuri—l —˜ilities ϕ = ϕ(ξ) ™h—rges pri™e pϕ in order to m—ximize the pro(t πϕ = pϕqϕ − qϕw ϕ → max, @IA where qϕ —nd w —re the —ggreg—te dem—nd —nd w—ges respe™tivelyF Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 16 / 22
43. Demand under monopolistic competition „he e™onomy produ™es — single di'erenti—ted good represented ˜y — set of v—rieties th—t h—ve mu™h in ™ommonF et st—ge i = 1, 2D — ™onsumer ξ ∈ Ξ with the in™ome Yξ,i ™hooses the dem—nds Qj,ξD j ∈ Ξe,iD to m—ximize her utility U = Ξe,i Qj,ξ σ − 1 σ j,ξ dj σ σ−1 → max, @PA su˜je™t to the ˜udget ™onstr—in Ξe,i pjQj,ξ dj Yξ,i, @QA where pj is the pri™e for the v—riety j —t the st—ge i = 1Y σ ∈ (0, 1) is the el—sti™ity of su˜stitution ˜etween v—rieties of the di'erenti—ted goodF Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 17 / 22
44. Unemployment benet e p—rt α of w—ges —nd pro(ts is redistri˜uted equ—lly —mong unemployed —gents Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 18 / 22
45. Initial choice b (1 − α)w ¯ Y ÙÒ ÑÔÐÓÝ Ò Ø Ø Ö¹Ø Ü Û × ÒØÖ ÔÖ Ò ÙÖ׳ Ø Ö¹Ø Ü ÔÖÓ Ø× ÁÒ ÓÑ where ¯ Y is the expe™ted in™ome of jo˜ m—rket ™—ndid—tes Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 19 / 22
46. Initial choice b (1 − α)w ¯ Y ÙÒ ÑÔÐÓÝ Ò Ø Ø Ö¹Ø Ü Û × ÒØÖ ÔÖ Ò ÙÖ׳ Ø Ö¹Ø Ü ÔÖÓ Ø× ÁÒ ÓÑ b (1 − α)w ÙÒ ÑÔÐÓÝ Ò Ø Ø Ö¹Ø Ü Û × ÒØÖ ÔÖ Ò ÙÖ׳ Ø Ö¹Ø Ü ÔÖÓ Ø× ÁÒ ÓÑ Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 19 / 22
47. Initial choice and adjustment b (1 − α)w ¯ Y ÙÒ ÑÔÐÓÝ Ò Ø Ø Ö¹Ø Ü Û × Ð ×× Ø Ð ÒØ ÒØÖ ÔÖ Ò ÙÖ× ÒØÖ ÔÖ Ò ÙÖ׳ Ø Ö¹Ø Ü ÔÖÓ Ø× ÁÒ ÓÑ b (1 − α)w ÙÒ ÑÔÐÓÝ Ò Ø Ø Ö¹Ø Ü Û × ÒØÖ ÔÖ Ò ÙÖ׳ Ø Ö¹Ø Ü ÔÖÓ Ø× ÁÒ ÓÑ Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 19 / 22
48. Equilibrium Proposition 1 Equilibrium exists and it is unique. In equilibrium, rms do not hire any additional worker. Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 20 / 22
49. Concluding remarks ‡e introdu™e the me™h—nism of the o™™up—tion—l ™hoi™e th—t le—d to gener—l equili˜rium with ne™essity entrepreneurs —nd unemployed —gentsF xe™essity entrepreneurship redu™es the unemployment r—te v—˜or—tory experiment th—t models the o™™up—tion—l ™hoi™eF €rogr—mming the rules G g—me @—n open pro˜lemA wultiEst—ge modelX numeri™—l solutionF ixisten™e —nd uniqueness of the equili˜riumc Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 21 / 22
50. Concluding remarks ‡e introdu™e the me™h—nism of the o™™up—tion—l ™hoi™e th—t le—d to gener—l equili˜rium with ne™essity entrepreneurs —nd unemployed —gentsF xe™essity entrepreneurship redu™es the unemployment r—te v—˜or—tory experiment th—t models the o™™up—tion—l ™hoi™eF €rogr—mming the rules G g—me @—n open pro˜lemA wultiEst—ge modelX numeri™—l solutionF ixisten™e —nd uniqueness of the equili˜riumc Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 21 / 22
51. Concluding remarks ‡e introdu™e the me™h—nism of the o™™up—tion—l ™hoi™e th—t le—d to gener—l equili˜rium with ne™essity entrepreneurs —nd unemployed —gentsF xe™essity entrepreneurship redu™es the unemployment r—te v—˜or—tory experiment th—t models the o™™up—tion—l ™hoi™eF €rogr—mming the rules G g—me @—n open pro˜lemA wultiEst—ge modelX numeri™—l solutionF ixisten™e —nd uniqueness of the equili˜riumc Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 21 / 22
52. Concluding remarks ‡e introdu™e the me™h—nism of the o™™up—tion—l ™hoi™e th—t le—d to gener—l equili˜rium with ne™essity entrepreneurs —nd unemployed —gentsF xe™essity entrepreneurship redu™es the unemployment r—te v—˜or—tory experiment th—t models the o™™up—tion—l ™hoi™eF €rogr—mming the rules G g—me @—n open pro˜lemA wultiEst—ge modelX numeri™—l solutionF ixisten™e —nd uniqueness of the equili˜riumc Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 21 / 22
53. „ r e x u ‰ y … Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 22 / 22