X c x x n optimal decision rules n b n x c

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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 B-Benefits of the marginal member=Extra congestion cost it inflicts= -N*MBN- Club a numerical example I Club Benefit for an individual aX-bX2-eN-fN2 Cost cX+dX2 Solve Max N(aX-bX2-eN-fN2)- cX-dX2 Find optimal X for every N and then find the Find optimal N by comparison FOC(X) N(a-2bX)-c-2dX=0 Hence FOC(X) X(N)=(Na-c)/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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