There are 2 factors here: the dpi of the image and the dpi used to print.
The dpi of the image does not affect the printing cost at all, a higher dpi just means the print will take longer as the PC (and possibly the printer) has more processing to do.
As far as I know there are no lasers that print 2400 dpi. Some very rare ones can print 1200 dpi, but most are limited to 600 dpi. For example, the Xerox Phaser 7760 ( http://www.office.xerox.com/latest/776BR-01.PDF ) can print 1200 dpi, but its best photo quality is at 600 dpi, where it can use variable spot sizes, i.e. it can vary the amount of toner deposited in each dot. At 1200 dpi it can only produce 1 spot size. The new Phaser 7800 claims "true 1200 x 2400 dpi resolution", but I have not seen any details about it. At higher resolution the toner dots are smaller so the cost difference is negligible.
The same goes for inkjets. I believe some Epsons manage a real 1440 dpi, but that's the highest. All higher dpi specs are for "effective resolution". This compares the printer's optimised haltoning with standard rotated-screen halftoning, and indicates how well the printer prints shades of colours and hence photos; it does not relate to the real resolution. Again, some can vary their spot size, like the Epson Stylus R3000 ( http://www.epson.co.th/epson_thailand/en/printers_and_all_in_ones/inkjet/product.page?product_name=Epson_Stylus_Photo_R3000 ). Higher resolution means smaller dot sizes and no major increase in cost.
Another thing to consider: if, at 1200 dpi, the printer put 4 times as much ink on the paper as at 300 dpi, that would make the paper completely soaked in ink and the result would be unacceptable.
As an aside, there is no real point in printing a photo at more than 300 dpi as the eye will not be able to tell the difference. Note that I'm talking about the resolution as printed, i.e. for a 6" x 4" photo you don't need more than 1800 x 1200 pixels. When buying a camera, 6 Mpixels is adequate for an A4 (US Letter) print. Higher resolutions are only needed when printing larger sizes, or when you're going to crop the photo.