(a)Consider five members of a community, Kwame, Amina, Edmond, Francis and Naana who plan to provide mechanized bore-holes in their community which is suffering from acute water shortage. Their demand functions for the water are given by:
Where , and and are the demand functions of Kwame, Amina, Edmond, Francis and Naana respectively.
Also, the Marginal Cost (MC) for the bore-hole project is given by MC = 80 + 4Q
(a)Assume that it is possible to exclude a member from using the bore-hole upon provision; determine the optimal quantity of bore-holes to be provided.
(b)Assume that it is impossible to exclude members from using the bore-hole being provided, what is the optimal number of bore-holes that will be provided?
(c)If the bore-hole is financed by government, determine how much tax each should pay in order to generate adequate funds to provide the bore-hole project. Assume there is no free riding by any of the members and that there is a true preference revelation by all.
(d)State and briefly explain three (3) potential challenges associated with the provision of such public goods.
