Could you help me with the following questions please?

Exercise 3: Public Goods Two individuals with identical utility functions on a private good X and a public good G where G = Gi + G2 and G; is the contribution of individual i. The utility function of each individual i is Ui(Xi, G) = 2In(Xi) + In(G). Each individual bugdget constraint is Xit Gi =100. (i) Calculate the private provision of public good G. (ii) Calculate the optimal provision of public good G. Exercise 4: Public Goods 2 Which is the optimal condition for private goods provision? Which is the optimal condition for public goods provision? Explain how to sum individual demand curves horizontally and vertically. (Graphs are helpful). Exercise 5: Public Goods 3 Suppose the (inverse) demand functions for a public good G are P, = a; -b; x G for indi- viduals indexed by i = 1,2 and a; > 0, b; > 0. The marginal cost of public good is e > 0. What is the optimal level for the public good provision? Exercise 6: Natural Monopolies Consider the following two average cost schedules. Table 1 gives the average cost schedule in market 1 and table 2 for market 2. Suppose the maximum amount the consumers are willing to buy at any price in both these markets is 3 units. Which of these markets qualifies as natural monopoly and why? 2 Quantity Average Cost Quantity |Average Cost 2 3 2 5 3 5 4 Table 1: Market 1 Table 2: Market 2 Exercise 7: Natural Monopoly (a) What is the characteristic of natural monopoly that differentiates it from regular monopoly. (b) List three pricing regulations against monopoly. Show monopoly equilibrium and equi- libriums under pricing regulations on a graph and compare these regulations by listing their advantages and disadvantages