You have to take into consideration not only the price per pound but the price per serving. If you are buying a cheaper cut and it has a lot of fat and bone, there is going to be less edible meat.
Cheaper cuts are often tougher, but if they are cooked correctly-- long and slow, like in a crock pot, they can be very tasty. Look for recipe advice on this.
Another way to save is to use meat like a condiment. Chinese restaurants usually do this well, small bits of meat with vegetables and noodles or rice.
For instance, you could buy a small piece of filet mignon (on sale, preferably) and slice it into very thin strips to make a fabulous beef and broccoli-- you would be surprised how far you can 'stretch it.