Question 1. Consider a model ofa negative consumption externality. Households have strictly convex preferences over composite (15\

Question 1. Consider a model ofa negative consumption externality. Households have strictly convex preferences over composite (xA,x respectively) and a level of activity chosen by household A measured by 0 t 100. The households' utility functions are 1/2 1/2 and UB(xB, t) Suppose the initial endowment of composite is e 50 and e Household A's activity, to the legal maximum is 0 < t < 100. xl/2 (100 t)l/2 50. Laws currently restrict i) v) (6 marks) Construct a single Edgeworth box measuring composite horizontally and household A's activity level vertically, and represent the initial allocation along with the mutually beneficial set when the legal limit is b) E 60. (2 marks) Suppose a competitive market is introduced for the level of household A's activity to the extent that it deviates from t. The price p per unit of activity is taken as given by each household. What would each households' budget constraint be when they are endowed with composite (e 50 and e 50) and then purchase or sell units of activity? (4 marks) Find each households' optimal choice functions for activity level, tA(p) and te (p). (3 marks) Find the competitive market price p* and the equilibrium level of household's activity A in terms of t. (6 marks) Explain using graphical illustration in an Edgeworth box and calculations how the assignment of legal rights (f 40 vs. t- 60) impacts a) The efficiency of the resulting allocation b) Distribution of composite (or wealth) between the households.