Question 1 (20 points) A perfectly competitive industry contains 4 firms in short run equilibrium, each with a cost function given by TC, = 50 + 2q2, 2 - 1, .., 4. The industry demand curve is P(Q) = 120 - Q, where Q is the industry output (the sum of the firms' production). Throughout this question, please show all your derivations. (a) Sketch a representative firm's Average Total Cost (ATC) curve and Marginal Cost curve, making clear the level of output that minimises ATC, and the value of ATC at this point. [15 marks] (b) Calculate the profits made by each of the four firms in short run equilibrium. [25 marks] (c) Find the number of firms in the industry in the long run and the total industry output. Explain the process that brings about this long run equilibrium. [35 marks] (d) Suppose that the industry demand curve is given by P(Q) = A - Q, where A > 0. Find a value of A that would cause the number of firms to fall below 4 in long run equilibrium. [Note that more than one value of A produces this result: you are simply required to find one of these.] [25 marks] Format B I U