Let’s revisit the maker of spare parts in Problem S1 of Chapter 2 to determine its optimal price. The firm’s demand curve is given by: Q = 400 − .5P, and its cost function by: C = 20,000 + 200Q + .5Q².

a. Treating price as the relevant decision variable, create a spreadsheet (based on the example shown) to model this setting. Compute the price elasticity in cell B12 according to E_P = (dQ / dP) (P / Q).

b. Find the optimal price by hand.

c. Use your spreadsheet’s optimizer to confirm the optimal price.

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THE OPTIMAL PRICE FOR SPARE PARTS Price Quantity Revenue Cost Profit 780 10 7,800 22,050 -14,250 10 Eladicity AC 12 13 -39.0 210 0.7308 006