Suppose that there is a village having 1000 people

 Suppose that there is a village having 1000 people. There is one public good, the irrigation facilities. Villagers have the same utility function u(x,G)=x; -100/G, where x is a numeraire good, measured by the money spent on private consumption and G is the scale of the irrigation facilities. The price of the irrigation facilities is 10 yuan per unit. Every villager has an income of 1,000 yuan per year. (a) Write down an expression for the absolute value of the marginal rate of substitution between private consumption and the public good. (b) What is the marginal cost of producing the irrigation facilities? (c) Write down the condition for a Pareto efficient supply of good G and solve for the Pareto efficient amount. (d) Suppose that everyone in the village pays an equal share of the cost of the public good. When individual decides his demand for the public good and private consumption, what is the budget constraint of each villager? (e) What is the individual optimal demand for the public good G ? Will it be larger than, smaller than, or the same size as the Pareto optimal amount?