It is typical to offer what the employer has set in their budget. If you feel that you have additional skills and/or expertise that mean you can exceed their perceived expectations then set a price slightly higher and add a message as to why you’ve set this price.
On the flip side, don’t undervalue yourself! It is not recommended you bid a price below what the employer is offering to pay.
Offering to complete the project for a price far below what the employer is offering (below 20% of the fee or more) will not always give the impression that you will do a good job, and they may think that your skills are limited! If you are bidding under the project value, ensure that you communicate with the employer that you can still get the job done to a high standard!