Cowboy Pete's Ranch and Wily Western Ranch are two dude ranches in the Midwest. The ranches offer horseback riding, sightseeing along winding rivers, a campfire experience, and cabin lodgings. The demand curve for a night at Cowboy Pete's ranch is given by 9c = 400 -7.5pc + 5pw where po is the price charged for a night at Cowboy Pete's ranch and pw is the price charged for a night's stay at the Wily Western Ranch. The demand curve for a night's stay at Wily Western Ranch is 9w=600+ 2.5pc - 5pw The cost of providing a night at Cowboy Pete's is Cc (9c) = ac Wily Western Ranch provides a more authentic (and therefore more costly to maintain?) Western experience for customers. The cost of providing a night at Wily Western Ranch is Cw(9w) = 2qw a. Derive a price reaction function for each ranch. b. Diagram the reaction function for each ranch in price space and indicate the equilibrium on the graph. c. Mathematically, identify the equilibrium price charged by each dude ranch. Also, identify the equilibrium quantity of guest nights provided and profits by each dude ranch. d. In this differentiated-demand Bertrand market structure, are the dude ranches setting the price equal to marginal cost? Demonstrate.