Before you contract the framers to make the frame for you it is a good idea to have a rough idea of what you want. Picture frames can vary dramatically in cost and there is no way you will get a frame made cheaply if you have a large or ornate molding in mind. The cheapest frames are usually narrow, non-elaborate frames. Picture framers cost their frames according to the raw material costs. Frames are generally graded from A frames to E frames with A frames being the cheapest.
The framer will usually have many off-cuts of the cheapest range of frames in stock, as they will be the most popular and therefore the most ordered-in by the framer. The only way you can reduce the cost further would be to not include a mount around the picture. Any mount will increase the overall size of the frame and therefore the amount of molding needed to make it. Not including a mount can reduce the picture in size and aesthetic appeal. It is not something I would recommend if you have taken the effort to have the picture framed in the first place.
If keeping the price down is really important, ask the framer if they had any off cuts that could reduce the price. This is like music to the framers ears. They are longing to get rid of old stock and will run out the back to find a suitable off-cut, with an excited step you probably had not witnessed before!
The framer is always managing the amount of old stock and new stock coming in. Storage space is a premium and the framer needs to get rid of old stock and at the same time make money out of it.
Many times the customer might choose a frame molding that is not in stock. For a small picture this actually results in a loss of money for the framer on that job. If the cost for the frame job on a small picture is 35 Pounds and a three metre length of molding costs the framer 30 Pounds you can see that there would be a loss on that job. Moldings come in lengths of Three metres and the framer has to manage where to store left over and how to recover the loss on that length.
In the past moldings were only delivered in packs of molding lengths. To overcome this up front expense the framer would only display a few molding options. Today there are new companies that deliver moldings in single lengths and this has allowed for a greater variety in molding choices.