Scitovsky Contour for Public Goods:

Suppose we  have certain amount of the public good. To derive a  Scitovsky contour, we  add vertically  Joe's  and Percy's indifference curves.  The slope of the PPF  (the rate of product  transformation) should be equal to the slope of the Scitovsky contour.  With private goods, the slope of the contour was the common MRS of a single individual. With public goods, its slope  is  the  summation of the MRS  (summed over all  people). So, for public goods:

RPT = ∑MRS

This makes sense because the opportunity cost of producing the public good is the RPT.  Since we all get to consume that unit of the public good, its value to different consumers from consuming that unit  should be equal to the value of the resources that went  into producing that unit.  For a private good, because one uses up the resources that went  into producing it,  it has to be worth  it  to her to pay for all the resources that went into producing it. With a public good, because all get to use it simultaneously, it has to be worth it for all collectively to pay for the resources that went into producing it.