Two gas stations are located side-by-side. As is customary in the industry, they are competing on price (they both have enormous signs advertising their selling price for a litre of gasoline on the roadside). Station 1 has the cost function C(q) = 4q and station 2 has the cost function C(q) = 5q2 where q and q are the number of litres sold by station 1 and station 2, respectively. The market demand for gasoline is Q(p) = 50-p where Q = q +92. a. [4] Write the demand functions of the two firms. b. [4] Are the two firms selling their gas at $5 per liter a Bertrand-Nash equilibrium? Explain why or why not. c. [6] Characterize a Bertrand-Nash equilibrium. How many litres of gas will each firm sell in this equilibrium?