The Lindahl Formula:

Erik Lindahl developed a price system that will support the efficient allocation of public goods. For  that  purpose, he viewed  the  sharing  of  costs  by  two customers of the public good as a supply-demand relationship, and worked out a pricing rule. We discuss his results in the following diagram. Assume that  the  vertical axis measures  K  or  the  fraction  of  unit  cost contributed by A. Given the unit cost C and assuming  it to be  constant, kc  is the  price paid by A,  and D_A  is her  demand  schedule for  the public good S.

Since B's price equals (1 -  k)C, and since both  share the same quantity of S, B's demand curve drawn with regard  to k  is given by DB.  Individual A may then look upon D_B  as showing the price at which various quantities of S are available to her  i.e.,  as a supply schedule for the public good which confronts. her. B similarly may regard  D,  as her supply curve. The fraction of the price which  both  are willing  to pay  [k  for A  and (1  -  k)  for B] adds to  I at the intersection of D_A  and D_B,  at output OM.