Question 1 (17 marks) Consider a model of a negative consumption externality. Both households have Cobb-Douglas preferences over composite (x4, x respectively) and a hours of activity per day chosen by household A measured by 0 S t s 24. The households' utility functions are U^(x4, t) = x1/21/2 and UB(xB, t) = x1/2(24-t)1/2 Suppose the initial endowment of composite is e = 5 and e" = 5. Laws limit Household A's daily activity to be at most 12 hours, ie. the legal maximum is t = 12