1. Why is there a threshold level of income
Prof. Mingli Zheng
Department of Economics
University of Macau
Mingli Zheng University of Macau

2. Mingli Zheng University of Macau
threshold level of income :
minimum wage
minimum standard of living
Basic income
Boulding (1962, p83): “society lays a modest table at which all can sup and a high table at which the deserving can feast”.
Mingli Zheng University of Macau

3. Mingli Zheng University of Macau
Threshold level of income can’t be explained in standard welfare economics
Lewis and Ulph (1988): assuming non-perfectly divisible commodities.
Sharif (2003): provides a behavior analysis of the minimum standard of living.
In optimal taxation literature, a threshold level of income can also be derived in a second best income distribution under incentive constraint (see Weymark (1984)).
Mingli Zheng University of Macau

4. Mingli Zheng University of Macau
We provide another explanation: the perception of fairness and justice of income distribution
the perception of individual desert and egalitarianism requires a threshold level of income in the first best choice of income distribution.
How to represent the perception of fairness and justice in income distribution?
What is fairness and justice in economics?
Mingli Zheng University of Macau

5. Mingli Zheng University of Macau
We use Savage framework, consider the consistency of the preference in income distribution.
Gilboa (1989), the author pointed out:  
“It is well known that Savage’s formulation of decision-under-uncertainty problem may be interpreted in other ways. If the states are replaced by individuals in a certain group, and the consequence is the income, then an act becomes an income distribution and the problem becomes a preference over different income distributions.”
Mingli Zheng University of Macau

6. Mingli Zheng University of Macau
Savage Framework
Uncertainty
Income distribution
state space Ω: possible states of the world
a consequence space C.
An act: a function from Ω to C.
Preference: binary relation over acts.
state space Ω: individuals in the income distribution
An income space C.
An income distribution (resource allocation): a function from Ω to C.
Preference: binary relation over income distribution.
Mingli Zheng University of Macau

7. Mingli Zheng University of Macau
Savage Axioms
Uncertainty
Income distribution
Mingli Zheng University of Macau

8. If Savage axioms as in Savage are satisfied
Uncertainty
Income distribution
Mingli Zheng University of Macau

9. Savage representation without independent axiom
Mingli Zheng University of Macau

10. Mingli Zheng University of Macau
Mingli Zheng University of Macau

11. Mingli Zheng University of Macau
Proposition: Holding other things fixed, an increase in the weight on egalitarianism will increase the value k and increase the threshold level of income.
More egalitarianism, more individuals will be categorized as poor. The minimum standard of living will increase.
Mingli Zheng University of Macau

12. Mingli Zheng University of Macau
Mingli Zheng University of Macau