Suppose you and a competitor have just introduced similar new golf balls. Your new golf ball flies 30% longer than standard golf balls while your competitors flies 15% longer than existing golf balls. Your marketing research department runs some surveys and informs you that your demand curve looks as follows:.
Q = 88 - 10p1 + 8p2 + 2(a1)^1/2 - (a2)^1/2
where Q is the quantity (in units of 10,000) of golf balls you sell. p1 is your price per golfball, p2 is your competitors price per golf ball, a1 is the dollars (in units of S10,000) you spend on advertising, and a2 is the dollars (in units of $10,000) your competitor spends on advertising. Your marginal cost of production is $1 per golf ball
(a) Suppose that you believe that your competitor will set p2 = 2 and a2 = 16 regardless of your decisions of p1 and a1. What advertising and price levels should you set? What are your profits (note: to get the profits correct, you need to pay close attention to the units Q, a1, and a2 are measured in)?
(b) Instead suppose you anticipate your competitor will respond to your decisions of p1 and a1. Describe in words how you might proceed (i. e. you do not need to do any calculations). Would you need additional data? If so, what data would you want, and what would you do with it?