LECTURE 3* Flashcards
<p>How do club goods differ from public goods?</p>
<p>- Partly rivalrous: congestion after a certain point.- Excludable: club membership</p>
<p>Local public good =+ example</p>
<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>
<p>In Buchanan's club model, what assumption do we make about the population</p>
<p>homogenous - identical tastes and preferences</p>
<p>2 choices of club</p>
<p>1. How much of the good to supply2. How many members to admit.</p>
<p>Utility function in club model</p>
<p>U(x, G, n)</p>
<p>U'(x)</p>
<p>> 0</p>
<p>U'(G)</p>
<p>> 0</p>
<p>U'(n)</p>
<p>< 0 congestion =0 no congestion</p>
<p>Individual BC BCM + 2 assumptions on it.</p>
<p>M = x + C(G)/nEach individual pays a fixed share of the cost of providing the public good.Assume Px=1.</p>
<p>What do the club do for optimisation?</p>
<p>Max utility of representative consumer s.t. the individual's BC by choosing x, G and n.</p>
<p>Do we need Lagrange for BCM?</p>
<p>NO - sub BC into U to eliminate x = unconstrained.</p>
<p>BCM FOC wrt G + interpretation</p>
<p>N*MRS(g,x) = C'(G)Sum of MRS across consumers = MC of public goodSAMUELSON RULE.</p>
<p>is the club provision PE? Explain.</p>
<p>YES - FOC wrt G satisfies Samuelson rule</p>
<p>BCM FOC wrt n + interpretation</p>
<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>
<p>What is optimum is U'(n)=0</p>
<p>No congestion = non-rivalrous.Optimal club size infinite.MRSn,x=0 so n--> infinity from foc.</p>
<p>What is optimum is U'(n)<0</p>
<p>Congestion = partly rivalrous.Membership should be restricted.</p>
<p>To determine optimum n* in BCM, what is necessary?</p>
<p>CONGESTION U'(n) < 0 otherwise n-->infinity.</p>
<p>What allows the club to achieve efficiency?</p>
<p>The fact that when consumers join the club they reveal their preferences by how additional members affect existing member's utility.</p>
<p>What's variable utilisation?</p>
<p>Previously, assumed number of visits per member fixed.Now: allow variable in frequency of visits by members.</p>
<p>What is congestion parameter in variable utilisation?</p>
<p>V = nv = total number of visits</p>
<p>Utility function variable util</p>
<p>U(x, G, v, V)</p>
<p>U'(v) =</p>
<p>> 0 - higher utility more u visit the club</p>
<p>U'(V)=</p>
<p>< 0 - lower utility as more congested.</p>
<p>Individual BC variable</p>
<p>M = x + C(G, nv)/n</p>
In variable util, we assume the cost of the public good depends on...
Not only on the level of G, but also the total number of visits.
3 decisions in variable util for club
Efficient level of club good to provide.efficient level of membershipEffective number of visits per member to allow.
Variable FOC wrt G
n MRSx,G = C'(G)Sum MRS = MC of public goodSAMUELSON RULE