There are only two firms that produce and sell hockey equipment, Abel Corporation (A) and Baker Company (B). They each sponsor special events to try to gain customers. As there are only 2 firms, the marketing of one firm clearly affects its own profits and the profits of the other firm too.
Here are the (Gross) Profit Functions of each firm, related to the number of special events in a year, where A represents the number of events that Abel undertakes and В represents the number of events that Baker undertakes.
• Profits, Abel = 1000A -A^2 - 0.5AB
• Profits, Baker = 1000B - B^2 - 0.5ВA
Each special event costs $160, which is NOT included in the Profit functions as shown above.
What is Abel's Reaction Schedule (Best-Response Function)?
Here's how I've done this, I'm not sure if it's right, that's why I'd like your feedback.
Abel's Reaction Function:
1000 - 2A - 0.5B = 160 (differentiated the profits function and equated to 160)
A = 420 - 0.25B (this is the reaction function I derived)
My confusion arises from the thought process that the profits function is essentially the difference between total revenue and total costs so should that be something i need to take into consideration when solving this?