Coke and Pepsi dominate the U. S soft-drink market. Together, they account for about 75% of industry sales. Suppose the quantity of Coke demanded depends upon the price of Coke (PC) and the price of Pepsi (PP)
QC = 15 - 2.5PC + 1.25PP
Where output (Q) is measured in millions of 24-packs per month, and price is the wholesale price of a 24-pack. For simplicity, assume average costs are constant and AC = MC = X dollars per unit. In that case, the total profit and change in profit with respect to own price functions for Coke are
πC = TRC - TCC = PCQC - XQC = (PC - X) QC
∂πC/∂PC = 15 - 5PC + 1.25PP + 2.5X
A. Set∂ πC/∂PC = 0 to derive Coke’s optimal price-response curve. Interpret your answer.
B. Calculate Coke’s optimal price-output combination if Pepsi charges $5 and marginal costs are $2 per 24-pack.