Solve the following problem
Q.1 a) The demand curves for good X of three consumers (A, B and C) are given by the equations: Q = 100-0.2Px Q! = 300 -0.5Px and @ = 500 -0.8Px . The market supply curve for X is: MC =50+8.50 . Determine the market equilibrium if X were a private good. Will the market equilibrium be the same/different if X were instead a public good? Why? In case X is a public good, determine the tax share of each individual using the benefit principle of taxation. Draw graphs to illustrate your answer. b) Using the information on demand and costs given in part (a), explain what might happen if individual B volunteers to provide this good for all. Draw graphs and explain. Q.2 Using the information in Q.1, suppose that: (i) Individual C states that his marginal benefit is 250. (ii) Individual A states that his marginal benefit is 100. Calculate their Clarke tax liability. Also show each case using an appropriate diagram. Q.3 A community of five (05) persons needs to decide whether they should use their (pooled) resources for making a domestic game facility (G) or going out for a picnic trip (P). The table below gives the true benefits that each derives from each option. Determine the Clarke tax of each individual. If (i) Person 2 states that his benefit is 100 (ii) Person 3 states that his benefit is only 60, (iii) Persons 2 and 4 each overstates their benefit by 20, will their Clarke tax liabilities change? Will their total tax liabilities change? Person 1 Person 2 Person 3 Person 4 Person 5 Option G 30 80 Option F 0 70 0 50 0 Q.4 Suppose that the supply and demand for good H is described by the following equations: Q =-150+0.40P Q" = 600-0.2P The production of H also creates marginal external costs of $165 per unit of H. Assuming that H is sold in a competitive market, what is the market price? How many units of good H will be produced per year at that price? What is the socially efficient output of #? Will taxing H @12.5 percent be socially optimal? What alternate tax policy you can suggest to achieve social efficiency? Also calculate the incidence of each of the taxes. Q.5 Suppose that the production of goods X and Y is described using the production functions: X =BLxK x Y = (2/ 1, +2/K, )X' . Determine the competitive equilibrium and the social equilibrium. Also calculate the rate of the Pigouvian subsidy to correct for the misallocation of resources under competitive equilibrium. Q.6 For a particular product y, the average cost of production (AC) is given by the expression: AC = 20+ 2.5y . The demand for good y is: P = 152-0.5y . Assume that the production of y also creates an external effect for its neighbors, the average value of which is given by the expression: E = 12+0.75q. a) Assume that the firm has the property rights. In the absence of an agreement with its neighbors, what level of output would it want to produce? Suppose that the neighbors negotiate with the firm. To what level of output would the negotiations lead? What is the minimum payment that the neighbors must make to the firm to achieve this change in output? What is the maximum payment
