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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Transcript

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
   

   View Slide

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
   

   View Slide

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
   

   View Slide

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
   

   View Slide

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
   

   View Slide

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
   

   View Slide

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
   

   View Slide

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
   

   View Slide

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
   

   View Slide

10. Motivation
    Who are entrepreneurs?
    Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 4 / 22
    

    View Slide

11. Motivation
    Who are entrepreneurs?
    Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 4 / 22
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

    View Slide

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
    

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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
    

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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
    

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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
    

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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
    

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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
    

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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
    

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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
    

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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
    

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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
    

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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
    

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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
    

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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
    

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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
    

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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
    

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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
    

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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
    

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53. „ r e x u ‰ y …
    Fomenko & Shapoval (HSE) Necessity Entrepreneurs MACSPro, 2019 22 / 22
    

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