Jim and Tammy are partners in Business and in Life. As is all too common in this imperfect world, each has a little habit that annoys the other. Jim’s habit, we will call it activity X, and Tammy’s habit, activity Y. Let x be the amount of activity X that Jim pursues, and y be the amount of activity Y that Tammy pursues. Due to a series of unfortunate reverses, Jim and Tammy have a total of only $1,000,000 a year to spend. Jim’s utility function is given by: Uj = cj + 500 ln(x) – 10y, where cj is the money he spends per year on goods other than his habit, x is the number of units of activity X that he consumes per year, and y is the number of units of activity Y that Tammy consumes per year. Tammy’s utility function is Ut = ct + 500 ln(y) – 10x, where ct is the amount of money she spends on goods other than activity Y, y is the number of units of activity Y that she consumes, and x is the number of units of activity X that Jim consumes. Activity X costs $20 per unit. Activity Y costs $100 per unit. Suppose that Jim has the entitlement to half their joint income and Tammy has the right to the other half. Suppose further that they make no bargains with each other about how much of activities X and Y they will consume. How much of activity X will Jim choose to consume? How much of activity Y will Tammy choose to consume? Is this efficient? Sketch how an efficient solution to this externality problem could be found.