In a duopoly market, Tesla and Toyota are simultaneously choosing the number of cars to produce in 2022. Let q1 be the number of cars produced by Tesla and q2 be the number of cars produced by Toyota. The two firms face a market demand given by P - 1500-5Q where P is the market price and Q is the total market quantity (Q - q1+q2). Tesla's production q1 is given by q1 - 150-0.592 and Toyota's production q2 = 150-0.5q1. 1. Use the two production functions given above, calculate q1 and q2. This is the Nash equilibrium in the market. q1 = .q2 = 2. Calculate the market price P = 3. Firm 1's profit function is given by x1 = Pxq1 and firm 2's profit function is given by n2 = Pxq2. Find the profits for firms 1 and 2. 71 = n2 = Now assume that the two firms enter a collusive agreement in which they act as a monopoly and produce a total quantity Q instead of simultaneously choosing q1 and q2 independently. Their joint profit will be n = PxQ = (1500 - 5Q)Q. Find Q that is maximises the joint profit, the market price P and the maximum joint profit. Q = Each firm will now share the joint profit equally, so each firm will get a profit of Compared to the firms' profits in the Nash equilibrium, firms are (write down either worse off or better off or equally well-off) under a collusive agreement. It=