9.5 Suppose a firm faces the following demand curves: q = 60 – 2P Calculate the total revenue curve for the firm (that is, TR in the terms of q). Using a tabular proof, show that the firm’s MR curve is given by MR = 30 - q . Assume also that the firm has an MC curve given by MC = 0.2q. What output level should the firm produce to maximize profits? Graph the demand, MC, and MR curves and the point of profit maximization.

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9.6 A local pizza shop has hired a consultant to help it compete with national chains in the area. Because most business is handled by these national chains, the local shop operates as a price taker. Using historical data on costs, the consultant finds that short-run total costs each day are given by STC = 10 + q + 0.1q2 , where q is daily pizza production. The consultant also reports that short-run marginal costs are given by SMC = 1 + 0.2q. a. What is this price-taking firm’s short-run supply curve? b. Does this firm have a shutdown price? That is, what is the lowest price at which the firm will produce any pizza? The pizza consultant calculates this shop’s short-run average costs as SAC = 10/q + 1 + 0.1q and claims that SAC reaches a minimum at q = 10. How would you verify this claim without using calculus? d. The consultant also claims that any price for pizza of less than $3 will cause this shop to lose money. Is the consultant correct? Explain. e. Currently the price of pizza is low ($2) because one major chain is having a sale. Because this price does not cover average costs, the consultant recommends that this shop cease operations until the sale is over. Would you agree with this recommendation? Explain.