1. Political Economics Riccardo Puglisi Lecture 5
Content:
Welfare State: Redistributive Transfers
Economic Model
Winners and Losers
Political Decision

2. Welfare State: General Transfer
IDEA: Agents differ in their income.
The redistributive system consists of
a Proportional Income Tax (t)
a Lump-sum Transfer (T)
Redistribution from the Rich to the Poor
LIT: Romer (1975), Roberts (1977), Meltzer and Richard (1981), Krussel and Rios-Rull (1999)

3. Effective disposable time
Economic Model
Static economy: one period
Economic Agents work and consume
Agents are Heterogeneous in their working ability (e)
Time constraint:
1 + e = l n
Effective disposable time
Leisure
Work

4. Features of Working Abilities
e [el, eu] el < 0, eu > 0
e ˜ G (e) E (e) = Average Ability
G (eM) = 1/ Median Ability
eM < Median < Average
Distribution of Ability
Poor
Rich el eu e eM
E (e) = 0

5. Individual Economic Decision
Selfish Preferences Ue = c + V (l)
V is increasing and concave
Budget Constraint c = (1 - t) n (e) w + T
with w = 1
Time Constraint 1+e = l + n

6. General redistribution:
The Welfare State
General redistribution:
tax rate t
transfer T
Government Budget Constraint
T = t E (n(e))
Average
Income

7. How does this Redistributive Policy work?
Assume that everybody works “full time”: ne=1+e, l=0
Tax Burden: t(1+e)
Transfer: T =t E(1+e) =t since E(e)=0
Utility: Ue= c = (1-t)(1+e)+T =
= (1-t)(1+e)+t
 Ue=1+e-te

8. Winners and Losers Type-e Agent’s utility: Ue =1+e-te
Winners: Poor (e < 0)  -t e > 0
Losers: Rich (e > 0)  -t e < 0
transfer
t (1 + e)
contributions
Losers t
Winners
t (1 + e) el eM eu

9. Economic Decisions and Distortions
Economic Agents choose how much to work: ne
Distortion: facing a tax they may decide to work less: lower production
Economic decision:
Max c + V (l)
s.t. c = (1 - t) (1 + e - l) + T
F.O.C.: t =  V (l) /  l l
1 - t
 V (l) /  l
Distortion:
t  l* n*  E (n* (e)) l l*

10. Welfare State and distortion
Government budget constraint: T = t E(n*(e))
An increase in the tax rate, t, has two effects:
increase the government revenue
reduces the tax base and thus the revenue
LAFFER CURVE t T 0%
100% tL

11. Max Ue (t) = (1 - t) n (e) + t E (n (e)) + V (e)
Political decision
Voting behavior: every agent indicates the tax rate that maximizes her utility, given her economic decision:
Max Ue (t) = (1 - t) n (e) + t E (n (e)) + V (e)
How agents vote depend on three elements:
Direct cost (tax burden): n (e)
Direct benefit (transfer): E (n (e))
Distortion: [t  E(n(e)) /  t]:  t   E (n (e))

12. Political Equilibrium
Individual voting:
Agent’s votes can be ordered according to their type: poorer individuals vote for more redistribution
Preferences are single-peaked  Median voter’s theorem applies
The equilibrium tax rate is the one voted by the agent with Median working ability
Poor (e < 0)  t > 0
Rich (e > 0)  t = 0 [no redistribution]

13. Results In the political-equilibrium there is redistribution,
since em <  t* > 0
The amount of redistribution depends on the degree of income inequality
Income inequality is measured by the difference between Median and Average Ability
More inequality leads to more redistribution
If Rich agents become Richer  More redistribution
If Poor agents become Poorer  Less redistribution

14. Discussion How does this theory compare with the data ?
Can theory explain the cross-country differences and the dynamics of Welfare State expenditure ?
Early growth of welfare State may be also due to
extension of voting rights to poor voters
reduction in the cost of collecting taxes
Recent growth and cross-country differences not well explained

15. Extensions Dynamic model: Voting does not occur only once
Taxation affect Capital Accumulation and Economic Growth
Krusell and Rios-Rull (1999) show that “Dynamic Distortions” lead to lower Welfare State
Fairness: what if some voters are altruistic ?
Intergenerational transfer: Income is not the only source of difference among agents