6.3 Assume that the cola market is a Bertrand oligopoly and that Coke’s estimated demand function (based on Gasmi et al., 1992) is qc = 58 - 4pc + 2pp, where qc is the number of cases of Coke, pc is Coke’s price per case , and pp is Pepsi’s price per case. The average and marginal cost of producing a case of Coke or Pepsi is 5.

a. Create a spreadsheet with Column A denoted Pepsi Price, and with Coke’s price, quantity, revenue, cost, and profit in the following columns.

Enter the values 10 to 15 in increments of 1 in the Pepsi price column. Leave the Coke Price column blank. Enter the formulas for Coke’s quantity, revenue, cost, and profit functions. Because the Coke Price column is blank, the revenue and profit columns initially show what happens if the Coke price is zero – zero revenue and large losses. Use Excel’s Solver tool to determine Coke’s best price response (the one that maximizes its profit) for each Pepsi price in Column A. Solver generates a dialog box in which you should select Keep Solver Solution then click on OK. Solver enters the profit-maximizing Coke price in the Coke Price column. You must apply Solver in each row of the spreadsheet. (Hint: See the instructions for using Solver in Question 6.2 of Chapter 8 or use Excel’s Help feature.)

b. Use the Excel Scatterplot feature to illustrate Coke’s best responses to each Pepsi price. Use the Trendline option to determine the equation of Coke’s best-response function. (Hint: The Trendline option will report the equation if you select Display Equation on chart in the Trendline dialog.)

c. Pepsi’s demand function is qp = 63.2 -

4pp + 1.6pc. Create a new spreadsheet to determine Pepsi’s best price response to Coke prices that range from 10 to 15 in increments of 1.

Verify that each firm charging a price of 13 is a Nash-Bertrand equilibrium.