Question 1: Assume that firms in the perfectly competitive ice cream industry face a total cost TC = 202 + 20 + 100. Sofia is a producer in this industry and faces this cost structure. (a) What is corresponding marginal cost function? (b) What condition determines guarantees Sofia is maximizing her profits? Explain your answer. (c) What is the profit-maximizing quantity for Sofia when the price in the market is P = $50. What is her profit at this price and quantity? (d) Suppose the government imposes a lump-sum sugar tax on producers of ice cream in the amount of $100 regardless of how much ice cream they produce. What effect does this tax have on the quantity of ice cream that Sofia produces? (e) What do you expect to occur to the number of producers in the long-run following the introduction of this tax? Why? (f) In the long-run profits in a perfectly competitive industry will be zero. Assuming that the cost structure stays the same (and still includes the additional tax) at what price do we expect the long-run cost to ice-cream to fall to