Consider an economy populated by three agents: Tom, Dick, and Harry. Let MRS be exact compensation (measured in some numeraire) for the loss of one unit of a public good (say, football fields). Each person's MRS depends only upon the quantity of football fields, G.
Here, max [0, x] means "the greater of the numbers x and 0." Find the optimal quantity of football fields when the marginal rate of transformation between football fields and the numeraire is 150. Also, find the optimal quantity when the marginal rate of transformation is 50.