Hey there

Here is one approach:

# Hair Salons = (# hours required for men's haircuts per year + # hours required for women's haircuts per year) / average service capacity of 1 hair salon (which would be: opening hours x average # hair dressers x utilization rate).

Reasoning

I usually like to estimate these from the demand side - the logic being that a sizing of demand is actually an estimate of the maximum efficient supply of hair salons that can be supported in the market. Estimating it from the supply side is also a great approach, but you leave yourself open to the risk that there is undersupply in the market.

High level illustration (you can add more segments to this)

Total service hours required for haircuts p.a.:

• Assume 8m people in NY; 4m men and 4m women
• Service hours for men:
  • Assume men go to hair salon average once every month, 30min each time
  • Service hours p.a. = 4m x 12 x 0.5 = 24m hours
• Service hours for women:
  • Assume women go to hair salon average once every 3 months, 1 hours each time
  • Service hours p.a. = 4m x 4 x 1 = 16m hours
• Total time spent in hair salons is 40m hours p.a. in NY

Total service capacity per hair salon

• Assume 8 hours operating time, average 3 hair dressers, 50% utilization rate, open 6 days per week for 50 weeks.
• Note: the key assumption here is that a hair dresser cannot work
• Hence service hours per hair salon p.a. = 8 x 3 x 0.5 x 6 x 50 = 3600 hours p.a.

Therefore, total number of hair salons = 40m hours / 3600 hours = 11,000 hair salons

Sense check: 11,000 salons implies 1 salon every ~700 people in NYC (350 men, 350 women). Given men cut their hair 12 times p.a. and women cut their hair 4 times p.a., that implies 5600 visits per year, or around 15-20 clients per day, which feels reasonable.

Note again that demand side estimation assumes there is a maximum efficient supply in the market, which may not be case.

Hope that is helpful!