Let's say that BLUE and MAGENTA have utility functions xJ + J ln (g) where J = B for BLUE

and J = M for MAGENTA. xJ is a private good and g is a public good. B = 2 and M = 4. Each of

them has 10 units of the private good that can be transformed into units of the public good on a one

to one basis. Here are four allocations of those goods: