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EC320 PUBLIC POLICY > LECTURE 3* > Flashcards

LECTURE 3* Flashcards

1
Q

<p>How do club goods differ from public goods?</p>

A

<p>- Partly rivalrous: congestion after a certain point.- Excludable: club membership</p>

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2
Q

<p>Local public good =+ example</p>

A

<p>a public good that is only accessible to individuals in a restricted geographical area = excludable to those outside the area. Non-rival/partly rivalrous within the area. Such as local library.</p>

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3
Q

<p>In Buchanan's club model, what assumption do we make about the population</p>

A

<p>homogenous - identical tastes and preferences</p>

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4
Q

<p>2 choices of club</p>

A

<p>1. How much of the good to supply2. How many members to admit.</p>

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5
Q

<p>Utility function in club model</p>

A

<p>U(x, G, n)</p>

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6
Q

<p>U'(x)</p>

A

<p>> 0</p>

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7
Q

<p>U'(G)</p>

A

<p>> 0</p>

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8
Q

<p>U'(n)</p>

A

<p>< 0 congestion =0 no congestion</p>

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9
Q

<p>Individual BC BCM + 2 assumptions on it.</p>

A

<p>M = x + C(G)/nEach individual pays a fixed share of the cost of providing the public good.Assume Px=1.</p>

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10
Q

<p>What do the club do for optimisation?</p>

A

<p>Max utility of representative consumer s.t. the individual's BC by choosing x, G and n.</p>

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11
Q

<p>Do we need Lagrange for BCM?</p>

A

<p>NO - sub BC into U to eliminate x = unconstrained.</p>

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12
Q

<p>BCM FOC wrt G + interpretation</p>

A

<p>N*MRS(g,x) = C'(G)Sum of MRS across consumers = MC of public goodSAMUELSON RULE.</p>

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13
Q

<p>is the club provision PE? Explain.</p>

A

<p>YES - FOC wrt G satisfies Samuelson rule</p>

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14
Q

<p>BCM FOC wrt n + interpretation</p>

A

<p>MRS(n, x) = - C(G)/n^2MU cost of additional member in terms of private good = extent to which additional n reduces cost per person.</p>

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15
Q

<p>What is optimum is U'(n)=0</p>

A

<p>No congestion = non-rivalrous.Optimal club size infinite.MRSn,x=0 so n--> infinity from foc.</p>

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16
Q

<p>What is optimum is U'(n)<0</p>

A

<p>Congestion = partly rivalrous.Membership should be restricted.</p>

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17
Q

<p>To determine optimum n* in BCM, what is necessary?</p>

A

<p>CONGESTION U'(n) < 0 otherwise n-->infinity.</p>

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18
Q

<p>What allows the club to achieve efficiency?</p>

A

<p>The fact that when consumers join the club they reveal their preferences by how additional members affect existing member's utility.</p>

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19
Q

<p>What's variable utilisation?</p>

A

<p>Previously, assumed number of visits per member fixed.Now: allow variable in frequency of visits by members.</p>

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20
Q

<p>What is congestion parameter in variable utilisation?</p>

A

<p>V = nv = total number of visits</p>

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21
Q

<p>Utility function variable util</p>

A

<p>U(x, G, v, V)</p>

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22
Q

<p>U'(v) =</p>

A

<p>> 0 - higher utility more u visit the club</p>

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23
Q

<p>U'(V)=</p>

A

<p>< 0 - lower utility as more congested.</p>

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24
Q

<p>Individual BC variable</p>

A

<p>M = x + C(G, nv)/n</p>

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25
Q

<p>In variable util, we assume the cost of the public good depends on...</p>

A

<p>Not only on the level of G, but also the total number of visits.</p>

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26
Q

<p>3 decisions in variable util for club</p>

A

<p>Efficient level of club good to provide.efficient level of membershipEffective number of visits per member to allow.</p>

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27
Q

<p>Variable FOC wrt G</p>

A

<p>n MRSx,G = C'(G)Sum MRS = MC of public goodSAMUELSON RULE</p>

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28
Q

Variable FOC wrt n + interp

A

vU’(V)/U’(x) = - C(G, nv)/n^2 + vC’(V)/n
MU cost of additional member due to congestion = reduction in cost as n rises + increased cost of servicing additional visits

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29
Q

Variable FOC wrt v + interp

A

U’(v)/U’(x) = C’(V) + nU’(V)/U’(x)

MB of additional visit = marginal maintenance cost + marginal congestion cost

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30
Q

What’s a two part tariff? Why is it beneficial?

A

Previously: individuals pay fixed share of C(G) - so individuals only accounted for private cost of additional v, leading to over usage.
Now charge fixed fee F and variable fee p = price per visit.

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31
Q

The best solution for a club w variable utilisation is…

A

2 PART TARIFF

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32
Q

Individual BC for 2 part tariff

A

M = x + F + pv

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33
Q

What’s the break even constraint for 2 part tariff?

A

nF + npv = C(G, nv)

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34
Q

For 2 part tariff, which FOCs are the same as variable?

A

wrt G

wrt v

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35
Q

For 2 part tariff, which FOC is different to variable and how?

A

Same, but then sub in C(G, nv) = nF + npv

FOC: F + pv = C’(V)v - nvU’(V)/U’(x)

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36
Q

Efficient allocation in public good provision is attained by…

A

Consumers separating themselves into a series of efficient clubs.

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37
Q

When is the optimal allocation across clubs simple?

A

When total population = number of clubs * efficient club size i.e. N = D x n*
Allow n* consumers into each club.

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38
Q

In model of 2 clubs, aggregate welfare W(n) =

A

W(n) = nU(n) + (N-n)U(N-n)

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39
Q

If the optimal club size is too small…

A

2n* < N

Efficient allocation is EQUAL division: N/2

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40
Q

If the optimal club size is too large…

A

2n* > N

May be desirable to put more than N/2 in the bigger club where they get higher utility.

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41
Q

How are local public goods excludable?

A

Restricted to a particular geographical area - must be a resident and pay taxes in this area to access.

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42
Q

Localities compete for population by determining… (2)

A
  1. Level of public good to provide.

2. Taxation

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43
Q

Which locality do individuals chose?

A

The one giving them the highest utility based on G and tax.

44
Q

In location choice model, we assume the public good is…(2)

A

a FIXED resource

Only income e.g. welfare benefits

45
Q

How does an increase in local population benefit and cost existing residents?

A 
Benefit = reduced per resident cost of public good.
Cost = reduced public good per person since a fixed resource.
46
Q

Location model charge per person for public good =

A

G/h

47
Q

How does M(h) chage with h?

A

M’(h) < 0 - decreases with local population

48
Q

Location model consumer BC

A

M(h) = x + G/h

49
Q

Is income exogenous in location model?

A

NO - depends on local population.

50
Q

What do we assume about how localities choose G?

A

They choose G optimally, given their populations.

51
Q

FOC wrt G (h as given) for location model

A

h U’(G)/U’(x) = 1
sum MRS = MC
Samuelson rule

52
Q

If not stated otherwise, what do we assume MRT is?

A

1 i.e. 1 unit of private good can be transformed into 1 unit of public.

53
Q

What’s the next step for location model after finding FOC wrt G?

A

Find how utility depends on the location population U’(h) and make G(h).

54
Q

U’(h)=

A

U’(h) = U’(x)M’(h) + U’(x)G/h^2

55
Q

SO: what’s the sign of U’(h)?

A

AMBIGUOUS

56
Q

2 assumptions on U(h) we impose for location model since sign of U’(h) is ambiguous.

A
  1. U(h) N shaped

2. U(H) > U(0) - greater utility from entire population than zero.

57
Q

Why is U(H) > U(0)

A

If small population, too expensive to provide public good.

If large, income not reduced too much to offset lower public good cost per capita = net gains.

58
Q

If each U(h) peaks BEFORE H/2 i.e. h* < H/2, what are the stable equilibria?

A

h1 = 0, h2 = H
h1 = h2 = H/2
h1=H, h2=0

59
Q

If each U(h) peaks AFTER H/2 i.e. h* > H/2, what are the stable equilibria?

A

h1 = 0, h2 = H
h1=H, h2=0
- equal populations is now UNSTABLE.

60
Q

Optimal fiscal federalism is the question of…

A

which activities should take place at which level of government

61
Q

Fiscal decentralisation =

A

delegation of spending and tax to lower levels of government = opposite of fiscal centralisation.

62
Q

Tiebout insight of 2 factors missing in public goods market compared to private

A
  1. shopping - consumers need options so they can threaten to leave.
  2. competition - providers of public goods must compete.
63
Q

When do shopping and competition arise in public good provision? Why?

A

when they’re provided at the LOCAL level because consumers can vote with their feet and threaten to move to another town –> induces efficiency.

64
Q

Does samuelson think there’s a market based solution to provide public goods efficiently?

A

NO

65
Q

In Tiebout model, how many families are there, how many homes, how much income?

A

2N families
2 towns with N homes each
Families have identical income Y

66
Q

In Tiebout, are the public goods pure?

A

YES

67
Q

2 types of families in Tiebout ]. How do their U differ?

A

N families with kids: U(C, G)

N elderly: U(C) - only value private consumption.

68
Q

2 CONDITIONS FOR ALLOCATION OF FAMILIES ACROSS TOWNS TO TIEBOUT EQUILIBRIUM.

A
  1. G decided by median voter in each town & financed equally be residents.
  2. NO 2 families want to exchange locations.
69
Q

Individual BC in Tiebout

A

Y = C + G/N

70
Q

If G decided by median voter in Tiebout, what does this mean for the 2 towns?

A

If majority elderly, G=0

If majority families, G=G* which maximises U(Y-G/N, G)

71
Q

TIEBOUT THEOREM PART 1

A

In equilibrium, families sort themselves into towns according to their tastes for the public goods –> 1 town with elderly only, 1 with families with kids only.

72
Q

Proof of why timeout theorem part 1 holds

A
  • If elderly dominate town 1 initially, G1=0
  • This means family dominate town 2, G=G*
  • Any families in town 1 and elderly left in town 2 want to switch = not an equilibrium.
73
Q

TIEBOUT THEOREM PART 2

A

in each town, the level of public good provision is EFFICIENT. In elderly town, G=0 is efficient since G not valued; In family, G* satisfies Samuelson rule.

74
Q

3 main messages from Tiebout

A
  1. people can vote with their feet based on tax and level of G.
  2. This puts competitive pressure on towns to reflect taste of median voter = Samuelson rule.
  3. Individuals sort themselves into communities.
75
Q

Tiebout sorting outcome:

A

Heterogeneity across communities

Homogeneity within communities

76
Q

4 institutional limitations to Tiebout

A
  1. Local gov political so profit max may not be achieved.
  2. Barriers to entry - new towns cannot freely form (unlike clubs)
  3. > 2 types of individuals = need > 2 towns to allow sorting so it’s an equilibrium.
  4. Perfect instruments to adjust size of community such as advertising and zoning do not exist.
77
Q

4 unrealistic assumptions of Tiebout

A
  1. Assumes income exogenous - migration actually affects income.
  2. Assumes no externalities of public goods across communities
  3. Assumes 0 mobility cost and only care about G and C.
  4. Assumes perfect information about G and taxes in different towns.
78
Q

What’s a well established empirical result on Tiebout sorting?

A

More choice –> more sorting.

So within each community, homogenous, across = heterogenous.

79
Q

Do we see Tiebout sorting leading to greater efficiency empirically e.g. more productive schools?

A

Not proven - controversial result.

80
Q

Do we see Tiebout sorting becoming more efficient over time due to declining mobility costs in the data?

A

Should see more homogenous within communities, greater heterogeneity across in terms of preferences for and levels of public goods and taxes. BUT: we see less variation across communities in terms of policies AND preferences.

81
Q

Tibeout suggests there is no need for central governments. But what argument (2) is there for central governments?

A

Local governments cannot redistribute from rich to poor as then would see rich leaving and it would break down. Also, hard to vote with your feet in reality.

82
Q

How can migration of the rich be avoided at a local level when increasing taxes?

A

Tax-benefit linkages.

83
Q

Intergovernmental grants are what kind of form of redistribution?

A

INDIRECT

direct = taxes and spending.

84
Q

When we analyse intergovernmental grants, whose ICs and BC do we look at and why?

A

Assume local communities choose G and tax according to median voter, so G* and X* is where the IC of the median voter is tangent to their BC.

85
Q

State 3 types of grants

A
  1. Matching
  2. Block
  3. Conditional block
86
Q

Define matching grant

A

The amount of the grant is tied to the local communities spending on the public good only. Usually 1 to 1.

87
Q

How does a matching grant affect IC/BC diagram?

A

1 to 1 matching = halves the cost of the public good = BC pivots outwards (not shift). This BC is tangent to a higher IC.

88
Q

Impact of matching grant ob public and private spending.

A

Both increase.

But public good cost for local community decreases (don’t double spending) which they use on the private good.

89
Q

Define block grant

A

Fixed amount with no mandate on how to spend it.

90
Q

How does a block grant affect IC/BC diagram?

A

Transfer of income = BC SHIFTS OUT PARALLEL.

No change in price.

91
Q

Matching vs block grant IE and SE.

A

Matching: IE increases both, SE increase public good.
Block: IE increases both - NO SE since no change in price.

92
Q

On diagram to compare matching and block, how do we shift out the BC for block to make them comparable?

A

Shift out BC so that it cuts through the matching new equilibrium so that this is affordable (yet is isn’t chosen).

93
Q

Matching vs block which gives higher utility? Which increases G more?

A

BLOCK HIGHER UTILITY.

Matching increases G more.

94
Q

Define conditional block grant

A

Fixed amount WITH a mandate on how to spend it.

95
Q

How does a conditional block grant affect IC/BC diagram?

A

KINKED IC: flat portion at low G so that a certain amount must be spent on G and it makes a certain part of BC unfeasible. After this, normal trade off between x and G as in block grant.

96
Q

A conditional grant has no effect over a block grant if…

A

If under a block, optimise where G > x* and x* is the point of the kink under conditional block.

97
Q

does a conditional block have IE and SE?

A

NO SE - only IE.

98
Q

Based on standard economic grant models, money is said to be …. what does this mean in practice?

A

FUNGIBLE: an X increase in private income has the same effect as an X increase in block grant (both shift BC the same). An X increase in grant for schools has same effect on schools and private good as X increase in grant for police. Only total resources matter, doesn’t matter where the money comes from or what it’s intended for with block grant.

99
Q

The flyer paper effect is an anomaly to money fungibility. What is it?

A

When a $1 of exogenous grants leads to a significantly greater effect on public spending than $1 in citizen income (tax): money sticks where it hits i.e. money stays in gov sector.

100
Q

What’s the opposite effect to flypaper i.e. that standard economics shows.

A

Crowd out: state spending crowded out by federal block grants so public spending doesn’t increase by full amount - what we saw in the graphs.

101
Q

school finance equalisation =

A

laws that mandate redistribution of funds across communities in a state to ensure more equal financing os schools.

102
Q

In America, local Govs fund schools how?

A

With property taxes.

103
Q

Tax price =

A

the amount of revenue a local district has to raise to gain $1 of spending.

104
Q

When is tax price = 1

A

No equalisation so get to keep while $1 raises.

105
Q

When is tax price infinity.

A

Perfect equalisation so have to pool all of revenue.

EC320 PUBLIC POLICY (7 decks)

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