1. (36 marks) The Kings and the Warriors, two of the original NBA franchises, did not begin in Sacramento and San Francisco, respectively. The Kings began as the Rochester Royals the Warriors as the Philadelphia Warriors. After leaving Rochester in 1957, the Royals moved to Cincinnati, then to Kansas City in 1972, where they were renamed the Kings, and then to Sacramento in 1985. The Warriors lasted in Philadelphia until 1962 before moving to San Francisco/Oakland in 1962. Consider, then, the Kings and the Warriors, who are choosing where to locate. Both offer the same good (which, until recently, was poor performance) at a constant cost per unit, c. The Kings charge px and the Warriors charge P,- Consumers are distributed uniformly along the interval [0, 10] and incur a transportation cost per unit of squared distance, t. Gross consumer surplus, s, is sufficiently large to cover the market. Utility is given by U = s- p-td'. The teams first choose where to locate and then determine the price to charge their fans. Let k E 0, 10 denote the location of the Kings and 10-we 0, 10 denote the location of the Warriors.e. (2 marks) Setup the Kings' profit function, Ix (k, w, t, PK, PW) f. (2 marks) With or without calculus, derive the profit-maximising condition for AT K AP K g. (2 marks) Rearrange the first-order condition to derive the Kings' reaction function. h. (2 marks) Use symmetry to derive the Warriors' reaction function