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Unformatted text preview: B( N . X ) ∂ c( X )
−
=0
∂X
∂X
N ∂ B( N . X )
B( N . X ) +
=0
∂N N*MBX=MCX
Marginal benefits of
quantity
To N members
=Marginal cost
BBenefits of the marginal
member=Extra congestion
cost it inflicts= N*MBN Club a numerical example I
Club Benefit for an individual aXbX2eNfN2
Cost cX+dX2
Solve Max N(aXbX2eNfN2) cXdX2
Find optimal X for every N and then find the
Find
optimal N by comparison FOC(X) N(a2bX)c2dX=0 Hence
FOC(X) X(N)=(Nac)/2(Nb+d) This result is a public good result when N is
fixed. But N can be changed
fixed. Special...
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 Spring '11
 ZILBERMAN

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