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Question 2) (20 marks) Consider a model of a negative consumption externality

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Question 2) (20 marks) Consider a model of a negative consumption externality. Households have strictly convex preferences over composite (x4, xBrespectively) and a level of activity chosen by household A measured by 0 st < 100. The households'utility functions are UA(x4,t) = (x – 10)1/2(t – 10)1/2 and UB(xB, t) = x1/2(100 – t)1/2 Suppose the initial endowment of composite is e4 = 30 and eB = 70. Laws currently restrict Household A's activity, to the legal maximum is 0 <7 < 100. i) (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 a) t = 20 b) 7 = 60. ii) (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 (e4 = 30 and eB = 70) and then purchase or sell units of activity? iii) (4 marks) Find each households' optimal choice functions for activity level, tA (p) and tp (p). tB iv) (4 marks) Find the competitive market price p* and the equilibrium level of household's activity A in terms of t. v) (4 marks) Explain using graphical illustration in an Edgeworth box and calculations how the assignment of legal rights (E = 20 vs. I = 60) impacts a) The efficiency of the resulting allocation b) Distribution of composite (or wealth) between the households.