Redistribution of income and providing public goods aren't the same.
8.2 Redistribution of income
(8.1) y (x) = xl (x)
x = productivity
l = hours worked
y(x) = before tax income
u(c,z) c = consumption z = leisure z = 1 - l
(8.2) c = (1 - t) l x+ n
(1 - t) l x = income after tax
n = (state) transfer
(8.3) First order condition
Somebody is indifferent between working and not working iff
(1 - t) xuc(c,z) = uz(c,z)
i.e. if the utilitie after tax is equal to the utility of leisure.
(1 - t) xuc [ (1-t) l x+ n=c , 1-lz] = uz [(1 - t) l x+ n, 1 - l]
(1-t)xuc[(1 - t) l x+ n, 1 - l] - uz [(1 - t)l x+ n, 1 - l] = 0 (8.3)
8.3 ® 8.4
l = 0
(8.3¢) (1 - t) xuc [n, 1 ] - uz [ n, 1] = 0 | + uz[n, 1]
(1 - t) uc [v,1] x = uz[n,1] | : (1-t)uc [n,1]
x0 = [(uz[n,1])/((1 -t)uc[n,1])]
If x £ x0 the individual wouldn't supply labor.
8.5 t ·[`y] = n (goverments budget constraint)
8.19
u(g) - x3(g) - T(g) = u(g) - x(g)
u(g) = utility
x3(g) = for example cost for losing natural resource, a park on which a new highway is build
T(g) = x1(g) + x2(g)
x1(g) = cost which were spent in the own district
x2 (g) = cost's which were spent in the other districts
x(g) = x1(g) + x2(g) + x3(g)
® u¢(g) = x¢(g)
marginal benefit = marginal cost
8.19a
[u(g) + x1(g)] - [x3 (g) + tj T(g)]
u(g) + x1(g) utility plus cost which were spend within the district
x3(g) + tjT(g) costs plus "only" the part they pay of tax cost's
8.19 ® 8.20
[u(g) + x1(g) ] - [x3(g) + tjT(g)] = 0
[u(g) + x1(g) ] = [x3(g) + tjT(g)]
u(g) + x1(g) = x3(g) + tj (x1(g) + x2(g) )
[(¶)/(¶g)]
u¢(g) + x1¢(g) = x3¢(g) + tj (x1¢(g) + x2¢(g)))
8.3 Differential Transfers
core vs. swing voters
opportunistic politicans ® core
8.4 Nonmonetary Redistribution
Benefits on a small group - costs over a large group.
For using free public education, one have the money to spend the time in school instead of working. At public projects it is better to say that the cost's are low and that there were new jobs created.
Vote trading, you vote for my project and i vote for yours.
Inefficiency, nonmonetary is less transparency then monetary transfers.
8.5 Rent Seeking and Predation
Reet seeking, it means seeking for rents especialy for monopoly rents which were created bey a government (trade policy, qoutas etc.). Monopoly rents aren't social loss, they are a redistribution of income from consumers to monopoly producers. Social loss, surplus cost's of consumers and the cost of getting the rents.
Knowing asymmetric valuations of the rent tend to reduce rent-seeking expenditures.
Uncertainty, it's spend more to get rents, even player's which wouldn't play under full information, because they then would know that they loss money, cost for getting rents is higher then the rents, play now.
8.21
W1(x1) = p1u1H + (1 - p1) u1L - x1
= p1u1H + u1L - p1u1L - x1
= u1L + p1( u1H - u1L) - x1
V1 = u1H - u1L
= u1L + p1V1 - x1
8.22
W1(x1) = u1L + G2(x1)V1 - x1
8.22 a
u1L + G2(x1)V1 - x1 = u1L + V1 - V2
u1L + G2(x1)V1 - x1 = u1L + (u1H - u1L) - (u2H - u2L)
u1L + G2(x1)V1 - x1 = u1H - u2H + u2L
= u1H - V2
What's about the generation who's gone to pay but not to decide?
Repudiation of depts ® redistribution from rich to poor.
Sascha Frank
Last modified: Thu Nov 17 14:58:57 MET 2005