The world first phone was made by Motorola on April 3, 1973, Martin Cooper was a Motorola researcher and executive, made the first mobile telephone call from handheld subscriber equipment, placing a call to Dr. Joel S. Engel of Bell Labs, his rival.
The name of that mobile phone is Dynatac. It was released to public market in 1983 at a price of $3,995. Yes it's more expensive than today's flagship. It has around 20 minutes of talk time for a full charge and takes roughly 10 hours to become full charge. It has an LED display for dialing or recall. It can store 30 phone numbers only.