1. Happy
Degrowth vs
Unhappy
Growth
E. Bilancini
S. D’Alessandro aHappy Degrowth vs Unhappy Growth
Outline
Ennio Bilancini
(Universit` di Modena e Reggio Emilia, Italy)
a
Simone D’Alessandro
(Universit` di Pisa, Italy)
a
still . . . work in progress
Degrowth Conference Barcelona 2010
March 26-29, 2010
Barcelona

2. Happy
Degrowth vs
Unhappy
Growth Outline
E. Bilancini
S. D’Alessandro
Outline
1 Introduction
2 The model
3 Concluding Remarks

3. Happy
Degrowth vs
Unhappy
Growth Outline
E. Bilancini
S. D’Alessandro
Outline
1 Introduction
2 The model
3 Concluding Remarks

4. Happy
Degrowth vs
Unhappy
Growth Outline
E. Bilancini
S. D’Alessandro
Outline
1 Introduction
2 The model
3 Concluding Remarks

5. Happy
Degrowth vs
Unhappy
Growth Outline
E. Bilancini
S. D’Alessandro
Introduction
The model
Concluding
Remarks 1 Introduction
2 The model
3 Concluding Remarks

6. Happy
Degrowth vs
Unhappy
Growth Introduction
E. Bilancini
S. D’Alessandro
The importance of economic growth to fuel well-being in
Introduction rich countries is challenged by different perspectives. In this
The model presentation we will consider the insights from happiness
Concluding economics.
Remarks
Recent developments in endogenous growth theory include
the effect of jealousy and keeping up with Joneses. Clearly,
the outcome of the decentralized equilibrium is sub-optimal
(e.g. Liu and Turnovsky, 2005).
Antoci et al. (2004) present an endogenous growth model
where individual utility depends on consumption of
relational goods.
The present paper seeks to contribute to this debate including
both the aspects: de-growth towards a steady state
characterized by low or zero growth rate is an option, strictly
preferred to others.

7. Happy
Degrowth vs
Unhappy
Growth Introduction
E. Bilancini
S. D’Alessandro
The importance of economic growth to fuel well-being in
Introduction rich countries is challenged by different perspectives. In this
The model presentation we will consider the insights from happiness
Concluding economics.
Remarks
Recent developments in endogenous growth theory include
the effect of jealousy and keeping up with Joneses. Clearly,
the outcome of the decentralized equilibrium is sub-optimal
(e.g. Liu and Turnovsky, 2005).
Antoci et al. (2004) present an endogenous growth model
where individual utility depends on consumption of
relational goods.
The present paper seeks to contribute to this debate including
both the aspects: de-growth towards a steady state
characterized by low or zero growth rate is an option, strictly
preferred to others.

8. Happy
Degrowth vs
Unhappy
Growth Introduction
E. Bilancini
S. D’Alessandro
The importance of economic growth to fuel well-being in
Introduction rich countries is challenged by different perspectives. In this
The model presentation we will consider the insights from happiness
Concluding economics.
Remarks
Recent developments in endogenous growth theory include
the effect of jealousy and keeping up with Joneses. Clearly,
the outcome of the decentralized equilibrium is sub-optimal
(e.g. Liu and Turnovsky, 2005).
Antoci et al. (2004) present an endogenous growth model
where individual utility depends on consumption of
relational goods.
The present paper seeks to contribute to this debate including
both the aspects: de-growth towards a steady state
characterized by low or zero growth rate is an option, strictly
preferred to others.

9. Happy
Degrowth vs
Unhappy
Growth Introduction
E. Bilancini
S. D’Alessandro
The importance of economic growth to fuel well-being in
Introduction rich countries is challenged by different perspectives. In this
The model presentation we will consider the insights from happiness
Concluding economics.
Remarks
Recent developments in endogenous growth theory include
the effect of jealousy and keeping up with Joneses. Clearly,
the outcome of the decentralized equilibrium is sub-optimal
(e.g. Liu and Turnovsky, 2005).
Antoci et al. (2004) present an endogenous growth model
where individual utility depends on consumption of
relational goods.
The present paper seeks to contribute to this debate including
both the aspects: de-growth towards a steady state
characterized by low or zero growth rate is an option, strictly
preferred to others.

10. Happy
Degrowth vs
Unhappy
Growth Ingredients and results
E. Bilancini
S. D’Alessandro
More precisely, we present an endogenous growth model
Introduction where individuals beyond private consumption and leisure,
The model obtain their utility from:
Concluding i. the comparison of their current material situation with their
Remarks
aspiration and status, and
ii. the consumption of relational goods.
We compare three different kinds of equilibria:
i. decentralized economy;
ii. myopically planned economy;
iii. centrally planned economy.
We show that the optimal balanced growth path is
characterized by high levels of leisure and low or zero rate of
growth, and this cannot be obtained with laissez-faire.
The path from the actual state to the optimal trajectory can
easily require a transition with negative rate of growth.

11. Happy
Degrowth vs
Unhappy
Growth Ingredients and results
E. Bilancini
S. D’Alessandro
More precisely, we present an endogenous growth model
Introduction where individuals beyond private consumption and leisure,
The model obtain their utility from:
Concluding i. the comparison of their current material situation with their
Remarks
aspiration and status, and
ii. the consumption of relational goods.
We compare three different kinds of equilibria:
i. decentralized economy;
ii. myopically planned economy;
iii. centrally planned economy.
We show that the optimal balanced growth path is
characterized by high levels of leisure and low or zero rate of
growth, and this cannot be obtained with laissez-faire.
The path from the actual state to the optimal trajectory can
easily require a transition with negative rate of growth.

12. Happy
Degrowth vs
Unhappy
Growth Ingredients and results
E. Bilancini
S. D’Alessandro
More precisely, we present an endogenous growth model
Introduction where individuals beyond private consumption and leisure,
The model obtain their utility from:
Concluding i. the comparison of their current material situation with their
Remarks
aspiration and status, and
ii. the consumption of relational goods.
We compare three different kinds of equilibria:
i. decentralized economy;
ii. myopically planned economy;
iii. centrally planned economy.
We show that the optimal balanced growth path is
characterized by high levels of leisure and low or zero rate of
growth, and this cannot be obtained with laissez-faire.
The path from the actual state to the optimal trajectory can
easily require a transition with negative rate of growth.

13. Happy
Degrowth vs
Unhappy
Growth Ingredients and results
E. Bilancini
S. D’Alessandro
More precisely, we present an endogenous growth model
Introduction where individuals beyond private consumption and leisure,
The model obtain their utility from:
Concluding i. the comparison of their current material situation with their
Remarks
aspiration and status, and
ii. the consumption of relational goods.
We compare three different kinds of equilibria:
i. decentralized economy;
ii. myopically planned economy;
iii. centrally planned economy.
We show that the optimal balanced growth path is
characterized by high levels of leisure and low or zero rate of
growth, and this cannot be obtained with laissez-faire.
The path from the actual state to the optimal trajectory can
easily require a transition with negative rate of growth.

14. Happy
Degrowth vs
Unhappy
Growth Outline
E. Bilancini
S. D’Alessandro
Introduction
The model
Concluding
Remarks 1 Introduction
2 The model
3 Concluding Remarks

15. Happy
Degrowth vs
Unhappy
Growth The utility function
E. Bilancini
S. D’Alessandro We add to the basic leisure consumption trade-off, the fact
Introduction
that individuals can obtain utility from the consumption of
The model
relational goods:
Concluding φ η
Remarks (ci ¯−γ li xi )1−σ
c
ui = f (ci , ¯, li , xi ) =
c , (1)
1−σ
where, c is private consumption, ¯ is average consumption, l
c
is leisure, x is consumption of relational goods, φ, η > 0 and
σ = 1.
Jealousy =⇒ γ > 0,
Keeping up with Joneses (KUJ) =⇒ σ > 1.
Relational goods x are given by:
xi = g(li , V) = li V, (2)
where, V is defined as the stock of social capital.

16. Happy
Degrowth vs
Unhappy
Growth The utility function
E. Bilancini
S. D’Alessandro We add to the basic leisure consumption trade-off, the fact
Introduction
that individuals can obtain utility from the consumption of
The model
relational goods:
Concluding φ η
Remarks (ci ¯−γ li xi )1−σ
c
ui = f (ci , ¯, li , xi ) =
c , (1)
1−σ
where, c is private consumption, ¯ is average consumption, l
c
is leisure, x is consumption of relational goods, φ, η > 0 and
σ = 1.
Jealousy =⇒ γ > 0,
Keeping up with Joneses (KUJ) =⇒ σ > 1.
Relational goods x are given by:
xi = g(li , V) = li V, (2)
where, V is defined as the stock of social capital.

17. Happy
Degrowth vs
Unhappy
Growth The utility function
E. Bilancini
S. D’Alessandro We add to the basic leisure consumption trade-off, the fact
Introduction
that individuals can obtain utility from the consumption of
The model
relational goods:
Concluding φ η
Remarks (ci ¯−γ li xi )1−σ
c
ui = f (ci , ¯, li , xi ) =
c , (1)
1−σ
where, c is private consumption, ¯ is average consumption, l
c
is leisure, x is consumption of relational goods, φ, η > 0 and
σ = 1.
Jealousy =⇒ γ > 0,
Keeping up with Joneses (KUJ) =⇒ σ > 1.
Relational goods x are given by:
xi = g(li , V) = li V, (2)
where, V is defined as the stock of social capital.

18. Happy
Degrowth vs
Unhappy
Growth Social Capital
E. Bilancini
S. D’Alessandro
Social capital changes in time.
Its dynamics depends on the average level of leisure in the
Introduction
society ¯ The simplest way to include this complementarity
l.
The model
Concluding
in leisure is:
Remarks V = B ¯ − δV,
˙ l (3)
where B, δ > 0.
We started with this simple form, but we include
non-linearity in the “productivity” of average leisure which
depends on the current level of social capital (networks):
V = ¯ f (V) − δV,
˙ l (4)
where f (V) takes a logistic form:
θ
f (V) = β + . (5)
1 + eψ−ξV

19. Happy
Degrowth vs
Unhappy
Growth Social Capital
E. Bilancini
S. D’Alessandro
Social capital changes in time.
Its dynamics depends on the average level of leisure in the
Introduction
society ¯ The simplest way to include this complementarity
l.
The model
Concluding
in leisure is:
Remarks V = B ¯ − δV,
˙ l (3)
where B, δ > 0.
We started with this simple form, but we include
non-linearity in the “productivity” of average leisure which
depends on the current level of social capital (networks):
V = ¯ f (V) − δV,
˙ l (4)
where f (V) takes a logistic form:
θ
f (V) = β + . (5)
1 + eψ−ξV

20. Happy
Degrowth vs
Unhappy
Growth Social Capital
E. Bilancini
S. D’Alessandro
Social capital changes in time.
Its dynamics depends on the average level of leisure in the
Introduction
society ¯ The simplest way to include this complementarity
l.
The model
Concluding
in leisure is:
Remarks V = B ¯ − δV,
˙ l (3)
where B, δ > 0.
We started with this simple form, but we include
non-linearity in the “productivity” of average leisure which
depends on the current level of social capital (networks):
V = ¯ f (V) − δV,
˙ l (4)
where f (V) takes a logistic form:
θ
f (V) = β + . (5)
1 + eψ−ξV

21. Happy
Degrowth vs
Unhappy
Growth Social Capital
E. Bilancini
S. D’Alessandro
Social capital changes in time.
Its dynamics depends on the average level of leisure in the
Introduction
society ¯ The simplest way to include this complementarity
l.
The model
Concluding
in leisure is:
Remarks V = B ¯ − δV,
˙ l (3)
where B, δ > 0.
We started with this simple form, but we include
non-linearity in the “productivity” of average leisure which
depends on the current level of social capital (networks):
V = ¯ f (V) − δV,
˙ l (4)
where f (V) takes a logistic form:
θ
f (V) = β + . (5)
1 + eψ−ξV

22. Happy
Degrowth vs
Unhappy
Growth Decentralized economy
E. Bilancini
S. D’Alessandro
The problem
Introduction
∞ φ η
The model
(ci ¯−γ li xi )1−σ −ρt
c
Concluding max e dt (6)
Remarks 0 1−σ
˙
s.t. ki = rki + w(1 − li ) − ci , (7)
ki (0) > 0 and V(0) > 0, (8)
where r and w are the “price” of capital and labour. Production
follow a simple Romer (1986) production function:
yi = A(¯ iα (1 − li )β ,
k)k (9)
with A(¯ = A¯1−α
k) k

23. Happy
Degrowth vs
Unhappy
Growth Decentralized economy
E. Bilancini
S. D’Alessandro
Introduction
The model
Main outcome
Concluding
Remarks
The level of social capital does not affect the equilibrium
allocation of time between labour and leisure.
If we allow for the non-linear dynamics in the accumulation
of social capital, two locally stable levels of V can be
sustained on the balanced growth path.
Jealousy deeply affects the rate of growth and the allocation
of time: γ ↑ =⇒ g ↑ =⇒ li ↓

24. Happy
Degrowth vs
Unhappy
Growth Decentralized economy
E. Bilancini
S. D’Alessandro
Introduction
The model
Main outcome
Concluding
Remarks
The level of social capital does not affect the equilibrium
allocation of time between labour and leisure.
If we allow for the non-linear dynamics in the accumulation
of social capital, two locally stable levels of V can be
sustained on the balanced growth path.
Jealousy deeply affects the rate of growth and the allocation
of time: γ ↑ =⇒ g ↑ =⇒ li ↓

25. Happy
Degrowth vs
Unhappy
Growth Myopically Planned Economy
E. Bilancini
S. D’Alessandro
(MPE)
Introduction
The model
Concluding
Remarks The problem
φ η
∞
(c1−γ li xi )1−σ −ρt
i
max e dt (10)
0 1−σ
˙
s.t. ki = Aki (1 − li )β − ci , (11)
ki (0) > 0 and V(0) > 0, (12)

26. Happy
Degrowth vs
Unhappy
Growth MPE vs Decentralized
E. Bilancini
S. D’Alessandro
Introduction
The model
Concluding
Remarks

27. Happy
Degrowth vs
Unhappy
Growth Centrally Planned Economy (CPE)
E. Bilancini
S. D’Alessandro
The problem
Introduction
φ η
(c1−γ li xi )1−σ −ρt
The model ∞
i
Concluding max e dt (13)
Remarks
0 1−σ
˙
s.t. ki = Aki (1 − li )β − ci , (14)
V = ¯ f (V) − δV,
˙ l (15)
ki (0) > 0 and V(0) > 0, (16)
θ
f (V) = β + . (17)
1 + eψ−ξV

28. Happy
Degrowth vs
Unhappy
Growth CPE vs Decentralized
E. Bilancini
S. D’Alessandro
Introduction
The model
Concluding
Remarks

29. Happy
Degrowth vs
Unhappy
Growth Outline
E. Bilancini
S. D’Alessandro
Introduction
The model
Concluding
Remarks 1 Introduction
2 The model
3 Concluding Remarks

30. Happy
Degrowth vs
Unhappy
Growth Comments
E. Bilancini
S. D’Alessandro
Introduction
The model If social planner considers the effect of average leisure on the
Concluding dynamics of social capital accumulation the results change.
Remarks
In order to maximize the individual utility function a higher
share of leisure is needed.
Growth looses importance.
Social planner should shift from a regime based on work for
growth to that based on work for social capital accumulation.
Social planner who implements public policy for growth
does not include aspects of human life which are crucial for
well-being.

31. Happy
Degrowth vs
Unhappy
Growth Transition
E. Bilancini
S. D’Alessandro
Introduction
The model
Concluding
Remarks How to change from a work for growth regime to a work for
social capital one?
preliminary results highlight that:
• High-income countries =⇒ the level of physical capital must
decline, since it cannot be sustained in the other regime.
• Low-income countries =⇒ the level of physical capital still
increases, while the working time should start decreasing.

32. Happy
Degrowth vs
Unhappy
Growth Transition
E. Bilancini
S. D’Alessandro
Introduction
The model
Concluding
Remarks How to change from a work for growth regime to a work for
social capital one?
preliminary results highlight that:
• High-income countries =⇒ the level of physical capital must
decline, since it cannot be sustained in the other regime.
• Low-income countries =⇒ the level of physical capital still
increases, while the working time should start decreasing.

33. Happy
Degrowth vs
Unhappy
Growth Final Remarks
E. Bilancini
S. D’Alessandro
Introduction
The model
We obtain this result without negative externalities of growth
Concluding
Remarks on social capital.
We do not include an effect of social capital on Jealousy and
KUJ.
We do not take into account the natural environment.
All these elements and many others should be included and
would work in our direction: growth cannot be happy.
Only myopically social planners (i.e. economists) can believe
it!

34. Happy
Degrowth vs
Unhappy
Growth Final Remarks
E. Bilancini
S. D’Alessandro
Introduction
The model
We obtain this result without negative externalities of growth
Concluding
Remarks on social capital.
We do not include an effect of social capital on Jealousy and
KUJ.
We do not take into account the natural environment.
All these elements and many others should be included and
would work in our direction: growth cannot be happy.
Only myopically social planners (i.e. economists) can believe
it!

35. Happy
Degrowth vs
Unhappy
Growth Final Remarks
E. Bilancini
S. D’Alessandro
Introduction
The model
We obtain this result without negative externalities of growth
Concluding
Remarks on social capital.
We do not include an effect of social capital on Jealousy and
KUJ.
We do not take into account the natural environment.
All these elements and many others should be included and
would work in our direction: growth cannot be happy.
Only myopically social planners (i.e. economists) can believe
it!

36. Happy
Degrowth vs
Unhappy
Growth Final Remarks
E. Bilancini
S. D’Alessandro
Introduction
The model
We obtain this result without negative externalities of growth
Concluding
Remarks on social capital.
We do not include an effect of social capital on Jealousy and
KUJ.
We do not take into account the natural environment.
All these elements and many others should be included and
would work in our direction: growth cannot be happy.
Only myopically social planners (i.e. economists) can believe
it!

37. Happy
Degrowth vs
Unhappy
Growth Final Remarks
E. Bilancini
S. D’Alessandro
Introduction
The model
We obtain this result without negative externalities of growth
Concluding
Remarks on social capital.
We do not include an effect of social capital on Jealousy and
KUJ.
We do not take into account the natural environment.
All these elements and many others should be included and
would work in our direction: growth cannot be happy.
Only myopically social planners (i.e. economists) can believe
it!