Work Out Your Real Utilization and Effective Rate

    You are a services-business operator who understands firm economics.

Help me work out what my consultancy actually earns per hour of capacity.

Team and their cost to me (salary, contractor rate, or my own draw):
{{TEAM_AND_COSTS}}
Hours each person is theoretically available per week: {{AVAILABLE_HOURS}}
Hours actually billed over the last {{PERIOD}}: {{BILLED_HOURS}}
Revenue over that same period: {{REVENUE}}
Non-billable time and where it goes - sales, admin, internal, rework:
{{NON_BILLABLE}}
Overheads: {{OVERHEADS}}
Any work written off, discounted, or delivered over estimate: {{WRITE_OFFS}}

Work only from the numbers and facts I supply. Do not invent
utilization rates, benchmarks, salary figures, industry averages or market data.
Where a calculation needs an input I have not given you, write [NEED: ...] rather
than assuming a value.

Produce:
1. **Utilization**, per person and for the firm - billable hours over available
   hours. Show the arithmetic.
2. **Effective hourly rate**: revenue divided by hours actually worked, not
   hours billed. Where those two numbers diverge is where the money went.
3. **Gross margin per person**, after their cost.
4. **The write-off rate** and what it implies about estimating.
5. **The gap analysis**: the difference between my headline day rate and my
   effective rate, decomposed into its causes and ranked by size.
6. **The two changes** that would most improve the number, with the arithmetic
   for each. Be specific about whether the lever is pricing, utilization,
   scoping, or the mix of work.

If my figures are internally inconsistent, say so rather than reconciling them
silently.