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Answer all parts. Consider a firm that operates in a perfectly competitive market and produces output according to the following cost schedule: Output 0 2 3 4 5 6 7 Total 50 70 110 170 250 350 470 610 Cost The market price is 90. (a) Calculate marginal revenue for each quantity of output from 1 to 7 units, and derive the firm's optimal choice of quantity, and its profit under this optimal choice. (b) What are fixed costs, and why do they exist? (c) Determine the fixed costs in the above table. (d) Due to an unforeseen event, the firm's fixed costs suddenly double. Repeat your analysis from part (a) for this new cost structure. (e) The firm that we have analysed so far is only one of 100 identical firms. Determine the equilibrium quantity in the market and the producer surplus