Fixed price works when the requirements are clear, stable and small enough to estimate well: a marketing site, a defined integration, or a feature with finished designs. The client gets a known cost and a known deliverable, which suits procurement processes that need a firm number.
The weakness is change. Because the vendor absorbs overruns, fixed-price quotes usually include a buffer for risk, and every new idea after signing becomes a change request with its own price. For products whose scope will evolve, the result is often slower and more expensive than time and materials.
Known total cost
The price is agreed before work begins.
Vendor carries risk
Overruns on the agreed scope are the vendor's cost.
Rigid scope
Changes go through change requests, each priced separately.
Needs a precise spec
Works only when requirements are detailed and unlikely to change.
Codazz builds this in production — Software Outsourcing.