Thank you for the response, now we're finally getting to a real answer
So you're saying people won't drop off the waitlist but would refuse the spot eventually and leave you with no clients in the end? Or in other words daycare providers don't have a stable supply of customers and prefer a long waitlist to maintain job security?
However your example is flawed as it represents a bad business practice. Real life businesses do this differently:
1. You start with a price of $100/week and a waitlist of two years
2. You keep the same price for existing customers but raise the price for anyone joining next year to $120
3. As you go through the waitlist it shortens and now your waitlist is 1.5 years long
4. Next year you raise your price for new customers by another 20% to $150
5. After going through the waitlist you've now shortened it to 1 year only and stop raising your fees
That's how my local barbershop which suddenly became very popular did this. I still pay the same fee as I did a few years back, but new customers have to pay 50% more. They are now considering increasing the price even more, as they still have more customers than they can handle.
An alternative option is to have a fee to skip the waiting list. So for say $5000 you'd get to be the first family to get offered a spot. That's how Disneyland works - if you stay at their very expensive hotels you get to skip some of the lines. This is also how airports work - if you buy a business class ticket you can skip the regular line to the security check.