A dominant firm in an industry has costs given by C = 70 + 5_qL. The dominant firm sets the market price, and the eight “small” firms coexisting in the market take this price as given. Each small firm has costs given by C = 25 + q² − 4q. Total industry demand is given by Q_d = 400 − 20P.

a. Create a spreadsheet similar to the accompanying example to model price setting by the dominant firm. (If you completed Problem S1 of Chapter 7, you need only make slight modifications in that spreadsheet.)

b. Experiment with prices between P = 7 and P = 16. For each price, determine the output supplied by the typical small firm by setting q such that P = MC. Taking into account the supply response of the eight other firms, what price seems to be most profitable for the dominant firm?

c. Use your spreadsheet’s optimizer to find the dominant firm’s optimal price.

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A|B Dominant Firm Price Leadership Market Supply & Demand Dominant Firm Price | # S. Firms | Qs Cost Profit 8 48 240 192 1030 10 Small Firms Cost AC 12 13 14 15 16 17 18 19 9 MC P -MC Firm Profit 6 8 37 6.167 11.0 Small Firms' supply is determined by P MC Large Firm maximizes profit given net demand.