Final answer:
The maximum membership fee that the golf course could charge Colin, based on his demand equation for golf, is $3,200. This is calculated by determining his consumer surplus and subtracting the total cost of playing 40 rounds.
Step-by-step explanation:
The student's question asks how much a golf course could charge Colin in a membership fee before he decides not to play there, given his demand equation for golf is P = 100 - 2Q and the price per round of golf is $20. To solve this, we need to find the quantity demanded (Q) when P is $20 and then calculate the consumer surplus, which is the amount Colin is willing to pay over the total cost of playing. Substituting $20 for P in the demand equation gives us Q = 40. Since the total cost for 40 rounds at $20 each is $800, and Colin's maximum price for 40 rounds is $100 (from P = 100), the membership fee he is willing to pay is his maximum ($4000 for 40 rounds) minus the cost of the rounds ($800), giving us $3200 as the maximum membership fee. Therefore, the golf course could charge up to $3,200 in a membership fee.